6.2.1 Token Frequency

Token frequency captures how often an element or structural pattern appears in language use. It is measured through counts of elements in linguistic corpora. For example, in the British National Corpus, the word time has a token frequency of more than 150,000, whereas the word chronology appears a mere 300 times. Token frequencies are commonly normalized, for example to instances per million words, in order to make them comparable across corpora. High token frequency is known to impact language processing in several ways (Ellis Reference Ellis2002). Five effects of high token frequency that have direct implications for constructionist theories of language are known as chunking, entrenchment, reduction, conservation, and conservatism.

The first of these, chunking, refers to the phenomenon that speakers cognitively process a string of linguistic elements as a holistic unit (Bybee & Scheibman Reference Bybee and Scheibman1999). This is the case for strings such as by the way or you know, which serve as discourse markers and thus convey meanings that go beyond the meaning of their component parts. By the way signals that the speaker temporarily deviates from the discourse topic (Fraser Reference Fraser2009). With you know the speaker can invite the hearer to draw an inference (Jucker & Smith Reference Jucker, Smith, Jucker and Ziv1998). Such non-compositional meanings, which constitute an important definitional criterion of constructionhood, are directly related to holistic processing, which in turn is driven by high token frequency. Chunking is further relevant for the processing of complex syntactic constructions. For example, speakers of English holistically represent constructions such as the Xer the Yer (Kay & Fillmore Reference Kay and Fillmore1999; Hoffmann Reference Hoffmann2019), so that when they hear an utterance that begins with The more I think about it, the first part of the construction will trigger expectations about how the utterance will be continued, thereby facilitating language processing. Another effect of chunking relates to syntactic constituency (Bybee Reference Bybee2010: 136). If a string of elements is frequently processed, speakers will treat it as a syntactic unit. Hilpert (Reference Hilpert, Dąbrowska and Divjak2015: 348) offers the example of the string sitting and waiting, arguing that its syntactic behavior in questions such as What are you sitting and waiting for? is that of a single verbal unit. Questioning the prepositional object of the verb waiting is only possible because sitting and waiting is processed as a chunk. By comparison, a question such as What are you walking and waiting for? sounds unidiomatic, since the string walking and waiting is not processed as a chunk and does not function as a single verbal constituent.

A second important effect of high token frequency is entrenchment. Repeated exposure to a linguistic unit increases the strength with which that unit is mentally represented. Elements and patterns that are highly entrenched can be retrieved from memory more quickly and more accurately (Ellis Reference Ellis2002: 152). A finding that is particularly relevant for Construction Grammar has been reported by Arnon and Snider (Reference Arnon and Snider2010), who conducted an experiment in which the participants had to indicate whether English n-grams like don’t have to worry and don’t have to wait are possible parts of grammatically formed sentences. Both fragments are indeed grammatically well-formed, but there is a difference in that the first one is more frequent than the other. The participants were quicker to confirm the grammaticality of the more frequent n-gram. Crucially, this is not due to the token frequency of the component words and word pairs, which were controlled for in such a way that they are actually identical in frequency. Entrenchment can thus be shown to facilitate language processing even at the level of multi-word units.

Another common effect of high token frequency concerns language production. Linguistic units that are used frequently tend to become phonologically reduced. Bybee and Thompson (Reference Bybee and Thompson1997: 576) give the example of BE supposed to, which can be reduced to [spostə] in utterances such as That’s not supposed to happen. Phonological reduction of this kind is common in cases of grammaticalization (Hopper & Traugott Reference Hopper and Traugott2003: 69), as for instance in the case of be going to and its reduction to gonna, or want to and wanna. The phonologically reduced forms can be shown to establish themselves as independent constructions that differ in terms of meaning and structure from their respective sources (Lorenz Reference Lorenz2013).

What the effects of chunking, entrenchment, and reduction show is that high token frequency is a powerful driver of language change. At the same time, high token frequency also has a conserving effect (Bybee & Thompson Reference Bybee and Thompson1997: 577). Linguistic elements that are frequently used are relatively more resistant to analogical change, which is apparent for example in irregular past tense formations such as keep – kept. Whereas keep has retained its irregular past by virtue of its high token frequency, less frequent verbs such as weep or leap have succumbed to analogical pressure and have adopted regularized past tense forms. The conserving effect of high token frequency is also evident in syntax, for example in English expressions that maintain older forms of sentential negation (Tottie Reference Tottie and Kastovsky1991; Bybee Reference Bybee2006). Whereas the canonical pattern for an English negated sentence involves do-support, as in I don’t believe that, post-verbal negation is preserved with modal auxiliaries (You should not believe that) and in fixed expressions that involve lexical verbs (make no mistake, it gives me no joy). In these cases, high frequency of use motivates the maintenance of the older syntactic patterns.

A speaker who experiences a linguistic unit with high token frequency forms increasingly clear expectations about its distributional behavior. This is even true for children who are still acquiring their first language. Children are known to produce overgeneralization errors such as *bringed for brought or *breaked for broke (Clark Reference Clark and MacWhinney1987: 19). Brooks et al. (Reference Brooks, Tomasello, Dodson and Lewis1999) showed that this phenomenon is sensitive to token frequency. Specifically, it was shown that children are less open towards new combinations of words and constructions if the words in question are highly frequent. In the study, children were encouraged to use intransitive verbs in a transitive way. Existing intransitive verbs were extended more readily if they were infrequent. That is, while children were reluctant to transitivize frequent verbs such as come (e.g., He came the car), they showed a greater tendency to transitivize infrequent intransitive verbs with the same meaning, as for example arrive (e.g., He arrived the car).

With regard to Goldberg’s (Reference Goldberg2006: 5) second definition of constructions, the effects discussed in this section motivate why token frequency is important to consider in constructional analyses. The effects also suggest that high token frequency tends to bring about non-predictable characteristics in constructions. An entrenched multi-word unit such as I don’t know is syntactically canonical and semantically transparent, but in actual usage that string will often be used in its phonologically reduced form dunno and with a non-compositional meaning. As a response to the question Would you like to watch Netflix?, the string I dunno would indicate that the speaker actually has a different preference. The inclusion of high token frequency as a definitional criterion of constructionhood is therefore fully compatible with a view of constructions as idiosyncratic linguistic units that need to be learned.

Token frequency is further relevant with regard to the influence of linguistic context on speakers’ choices between alternative options. Rivas and Brown (Reference Rivas and Brown2012) show this in a study of Spanish presentational constructions with haber ‘have’, as in Hubo problemas ‘There are problems’ (lit. have_SG problems). Prescriptively, the presentational construction calls for a singular form of the verb, regardless of whether the noun phrase that is presented is in the singular or the plural. That said, in many varieties of Spanish plural noun phrases may actually trigger plural agreement in the verb. Rivas and Brown (Reference Rivas and Brown2012) demonstrate that this phenomenon is sensitive to token frequency, more specifically the frequency with which a plural noun appears as a grammatical subject in other clause-level constructions. A plural noun such as estudiantes ‘students’, which frequently appears as a grammatical subject, exhibits a stronger tendency to trigger plural agreement than a plural noun such as fraternidades ‘fraternities’, which is used less often with the function of a grammatical subject.

6.2.2 Type Frequency

Type frequency represents the number of different variants of a construction in language use. More specifically, type frequency can be determined through the use of corpora by exhaustively extracting the instances of a given construction, so that the different elements that can fill a slot of that construction can be counted. The concept can be illustrated with the English regular past tense construction, which is a pattern with very high type frequency (Bybee Reference Bybee1995). The suffix -ed appears with a large number of verbs, yielding forms such as walked, painted, or opened. By comparison, the type frequency of forming the past tense through a vowel contrast, such as drink – drank, sing – sang, or swim – swam, is much lower. Type frequencies can not only be determined for morphological constructions but also for syntactic ones. For example, Israel (Reference Israel and Goldberg1996) investigated the diachronic growth in type frequency of the English way-construction by examining the main verbs that appeared in that construction during different historical periods.

Goldberg (Reference Goldberg2006: 99) points out that high type frequency is connected to productivity, that is, the ease with which speakers produce and process new instances of a construction. A construction that accommodates a broad range of elements as slot-fillers is more likely to be extended further to new elements, as opposed to a construction that occurs only with a select few. Corpus-based operationalizations of productivity often combine type counts with other measures, including token frequency and the relative prevalence of hapax legomena, that is, types that appear only once. For example, the measure of ‘potential productivity’ is calculated by taking the hapax legomena of a construction and dividing that number by the overall token frequency of the construction (Baayen Reference Baayen, Lüdeling and Kytö2009: 902). If a construction is used with high token frequency and a large ratio of its types occurs just once, this constitutes strong evidence that speakers regularly use that construction in creative ways.

Barðdal (Reference Barðdal2008: 34) argues that assessments of the productivity of a construction need to take into account the coherence between its types. Coherence can be defined both in terms of meaning and phonological similarity. Type frequency and coherence are seen as inversely correlated, so that if a construction occurs with many types, their coherence is likely to be low. Suttle and Goldberg (Reference Suttle and Goldberg2011: 1239) make a similar point when they relate the productivity of constructions to type frequency, variability, and similarity. If a speaker observes a pattern with a large number of types that are variable in terms of meaning, a new instance that is similar to any one of those types will have a good chance of being acceptable.

An effect of type frequency can be seen in a study by Brooks and Tomasello (Reference Brooks and Tomasello1999), who presented children between 2 and 4 years of age with nonce verbs such as meeking and tamming. The respective verbs were presented exclusively in either the active voice or the passive voice. After the training phase, the children were encouraged to use the verbs themselves, and they were provided with contexts that would favor either the use of the active or the passive. Brooks and Tomasello (Reference Brooks and Tomasello1999: 34) observe that the children are generally reluctant to generalize the verbs from one construction to the other, but they further note an asymmetry between the two constructions, namely that generalizations towards the passive, which is characterized by a relatively lower type frequency, are especially scarce.

Dąbrowska (Reference 168Dąbrowska2008) tests the respective effects of type frequency and phonological similarity in an experiment that prompts speakers of Polish to add dative endings to nonce nouns. In the Polish case system, the masculine dative ending -owi has a higher type frequency than the feminine dative endings -’e and -i, which in turn have higher type frequencies than the neuter dative ending -u. Dąbrowska (Reference 168Dąbrowska2008: 937) designed stimuli in such a way that the nonce words differed systematically in their phonological neighborhood density. Items with high neighborhood density were similar to a large number of existing words, whereas items with low neighborhood density were dissimilar to other elements in the Polish lexicon. The results indicate that performance is better if the type frequency of the case inflection is higher and if the phonological neighborhood is densely populated (Dąbrowska Reference 168Dąbrowska2008: 947).

Like high token frequency, high type frequency drives phonological reduction effects. Bybee (Reference Bybee2002) examined final t/d-deletion in a corpus of spoken English, comparing pre-vocalic deletion rates across auxiliaries with contracted negation (don’t), lexical items ending in an unstressed syllable with final nt (government, different), and regular past tense forms (kissed, burned). Bybee (Reference Bybee2002: 276) finds that the highest rates of pre-vocalic t/d-deletion are observed with regular past tenses, which can be motivated in terms of the high type frequency of that construction. This result is corroborated by Díaz-Campos and Gradoville (Reference Díaz-Campos, Gradoville and Ortiz-López2011), who study intervocalic d-deletion in Spanish participles with -ado and -ido. Deletion rates are higher with -ado, which is characterized by a relatively higher type frequency.

To summarize this section, type frequency is central for measures of constructional productivity, in which it interacts with both semantic coherence between types and phonological neighborhood density. High type frequency is furthermore correlated with rates of phonological reduction in forms that instantiate a pattern.

6.2.3 Relative Frequency

Relative frequency measurements compare the token frequency of one linguistic unit to that of one or several related linguistic units and express the result in terms of a ratio. This is often done with constructions that serve as alternative expressions of similar or near-identical concepts. For example, the English dative alternation comprises two constructions, the ditransitive construction (Mary gave John the book) and the prepositional dative construction (Mary gave the book to John), which both serve to express the transfer of an object between an agent and a recipient. The constructions differ in terms of the sequence with which the arguments of the verb are presented, which means that speakers’ choices between the two are commonly rooted in principles of information structure, such as the principle of end-focus (Hilpert Reference Hilpert, Aarts, MacMahon and Hinrichs2021). In naturally occurring language use, the ditransitive construction has higher token frequency than the prepositional dative construction (Bresnan et al. Reference Bresnan, Cueni, Nikitina, Baayen, Bouma, Krämer and Zwarts2007). Another pair of constructions with similar functions and a marked frequency asymmetry comprises the English active and passive. Sentences such as The dog bit the mailman or The mailman was bitten by the dog serve to express the same state of affairs with a difference in focus on either the agent or the patient. Passive sentences are much less frequent than active transitive sentences. As a third example, the English comparative can be formed morphologically and periphrastically, as in prouder or more proud (Hilpert Reference Hilpert2008). In general English usage, morphological comparatives vastly outnumber periphrastic comparatives.

Asymmetries in relative frequency influence language use and language processing in several ways. One such effect can be observed in structural priming (see also Chapters 8 and 23). When speakers process a syntactic construction, this increases the likelihood that they will produce that construction in subsequent language use (Bock Reference Bock1986). This tendency is frequency-sensitive. The so-called inverse-preference effect (Ferreira & Bock Reference Ferreira and Bock2006) is the phenomenon that in a pair of related constructions, structural priming is stronger for the construction with the lower relative frequency. Jaeger and Snider (Reference Jaeger and Snider2007) demonstrate this for the English dative alternation, in which prepositional datives yield a stronger priming effect, and for the English voice alternation, in which passives have a more pronounced impact. The inverse-preference effect has been widely replicated. For example, Rosemeyer and Schwenter (Reference Rosemeyer and Schwenter2019) document it for the Spanish past subjunctive forms -se vs. -ra in historical corpus data. Torres Cacoullos (Reference Torres Cacoullos, Adli, García García and Kaufmann2015) further documents a relation between priming and the analyzability of constructions. In a study that addresses the Spanish progressive with the copula estar ‘be’ and a gerund on the basis of historical corpus data, Torres Cacoullos tests whether speakers are more likely to use the progressive construction if they have been primed with other constructions that contain the verb estar, such as locative, resultative, and predicate adjective constructions. The data reveal that such priming effects exist and that they become increasingly weaker over time (Torres Cacoullos Reference Torres Cacoullos, Adli, García García and Kaufmann2015: 278). This suggests that the holistic unit status of the progressive construction has become strengthened over time.

Relative frequencies are also relevant for an effect that is known as statistical preemption (Goldberg Reference Goldberg2019). The basic premise of statistical preemption is that speakers form generalizations over pairs of constructions that serve comparable functions, such as the dative alternation or the morphological comparative and the periphrastic comparative. It is further assumed that speakers’ mental representations of these construction pairs comprise knowledge of the lexical items that they encounter in each construction. For example, speakers’ knowledge of the dative alternation would include the fact that verbs such as give, send, or promise occur both in the ditransitive construction and in the prepositional dative construction. Importantly, the relative frequency distribution of some verbs is highly asymmetric, so that for example the verb explain regularly occurs in the prepositional dative construction (She explained the problem to me), but not at all in the ditransitive construction (*She explained me the problem). Speakers subconsciously take note of such statistical asymmetries and interpret them as grammatical constraints. In more concrete terms, this reasoning process can be spelled out as follows. Speakers know that the ditransitive construction and the prepositional dative construction convey similar meanings and occur with similar sets of verbs. They register that the ditransitive construction is overall more frequent. Yet, they encounter the verb explain frequently in the prepositional dative construction, but not at all in the ditransitive construction. Since this imbalance could not be due to chance, it has to be the case that explain cannot be used in the ditransitive construction. In a study that approaches this issue experimentally, Boyd and Goldberg (Reference Boyd and Goldberg2011) expose participants to novel adjectives such as adax and ablim. Those forms phonologically resemble English adjectives such as awake or afraid, which can be used predicatively (The child is awake, The passenger is afraid) but not attributively (*the awake child, *the afraid passenger). In other words, their relative frequency distribution across predicative and attributive contexts is maximally asymmetrical. Boyd and Goldberg (Reference Boyd and Goldberg2011: 69) observe that the participants of their study avoided using forms like adax and ablim in attributive contexts. Statistical preemption can thus account for the fact that speakers do not produce certain expressions and find them ungrammatical, when they are asked about them. Entrenchment as such can only explain why certain expressions sound familiar to speakers, but it cannot explain the difference between previously unseen structures that are fully acceptable and unseen structures that are completely unacceptable.

Another effect of relative frequencies has been documented by Hilpert (Reference Hilpert2008) in a study of English comparative constructions. Adjectives such as proud or healthy can form the comparative either morphologically (prouder, happier) or periphrastically (more proud, more healthy). The variation between the two variants is influenced by a broad range of factors including the length of the adjective, its stress pattern, its final phonological segment, and its syntactic context (Hilpert Reference Hilpert2008: 407). Frequency of use impacts speakers’ choices in two ways. First, there is an effect of high token frequency. A highly frequent adjective such as easy has a stronger tendency to form the morphological comparative than a less frequent adjective with similar phonological characteristics, such as queasy. A second frequency effect concerns the relative frequency of adjectives in the positive form and its comparative formations. An adjective such as tall is frequently used comparatively, whereas this is not the case for adjectives such as red or square, which are less gradable. Highly gradable adjectives show a greater tendency to be used with the morphological comparative.

The main point to take away from this section is the following. Effects such as statistical preemption and the inverse-preference effect in structural priming reveal that speakers are sensitive to relative frequencies in language use, and that this sensitivity impacts their choices between constructions that function as mutual alternatives.

6.2.4 Frequency of Co-occurrence

Measuring frequencies of co-occurrence is one of the fundamental analytical techniques of corpus linguistics, which has a long tradition of studying collocations (Gries Reference Gries2013). Collocations can be broadly defined as multi-word units that exhibit varying degrees of fixedness. They are exemplified by word pairs with non-compositional, conventionalized meanings such as fast food, word combinations with elements that co-occur much more frequently than would be expected by chance, such as unmitigated disaster, and multi-word idiomatic expressions such as make hay while the sun shines. The term collocation has further been used to describe the regular co-occurrence of lexical items in close proximity, which is observed for example for the words refugee and crisis.

Whereas token frequency, type frequency, and relative frequency are measured through basic counts of instances in a corpus, frequencies of co-occurrence are studied in terms of various association measures, which include for example mutual information, log likelihood, or Delta P (Brezina Reference Brezina2018: 72). These measures take into account how often two linguistic elements appear together and how often the same elements appear on their own in other contexts. A comparison of the co-occurrence frequencies with the individual token frequencies shows how strongly the elements of a collocation are mutually associated. A collocation such as sustainable development can serve as an example. Table 6.1, which uses data from the British National Corpus, shows the token frequency of the collocation, the token frequencies of the individual elements that make up the collocation, and the total number of words in the corpus.

Table 6.1 shows that the collocation sustainable development appears 147 times in the corpus, which contains a total of almost 97 million words. Given the token frequencies of the individual words sustainable (665) and development (31,711), it can be computed how often the two words would be expected to appear together by pure chance. The expected frequency of the collocation is the product of the individual token frequencies divided by the total number of words in the corpus, which in this case yields a value of 0.22. So whereas less than one instance of sustainable development would be expected, almost 150 are observed, which indicates a high degree of mutual association between sustainable and development. Association measures express collocation strength through scores that allow comparisons between different word pairs, so that for example the mutual attraction of sustainable development can be compared to that of sustainable tourism or sustainable seafood.

Whereas the study of collocations has a long tradition that focuses on associations between specific words, the family of methods known as collostructional analysis (Stefanowitsch & Gries Reference Stefanowitsch and Gries2003; Gries & Stefanowitsch Reference Gries and Stefanowitsch2004a, Reference Gries, Stefanowitsch, Achard and Kemmer2004b) applies the concept of collocations to the analysis of mutual associations between a construction and the lexical items that appear within it. Collostructional analysis thus takes into account the grammatical context in which lexical words appear. Stefanowitsch and Gries (Reference Stefanowitsch and Gries2003: 219) illustrate this idea with the English [NOUN waiting to happen] construction. The construction has an initial slot for nouns that is typically filled by semantically negative words such as disaster or accident, as for example It’s a disaster waiting to happen or That was an accident waiting to happen. In order to analyze the mutual association between the construction and the nouns that occur in it, collostructional analysis determines the token frequency of the nouns in the construction, their overall token frequency in the corpus, and the overall token frequency of the construction as such. Table 6.2, taken from Stefanowitsch & Gries (Reference Stefanowitsch and Gries2003: 219), illustrates this for the noun accident. The lower right corner of the table represents the total of clause-level constructions in the British National Corpus. The co-occurrence frequency of accident and waiting to happen is much higher than would be expected.

The output of a collostructional analysis is a list of lexical elements that are ranked in terms of their strength of association with the construction that is being studied. Association measures that are used to obtain these rankings include the Fisher–Yates exact test and log likelihood (Flach Reference Flach2021). A collostructional analysis can not only determine the lexical elements that are most strongly associated with a construction, but it also serves to identify the elements that occur significantly less often than would be expected by chance. Inspecting the words that are repelled by a construction often yields useful insights into the semantic constraints that characterize its usage.

There is no single collocation measure that could be said to reflect mutual association in the best or most objective way. Rather, measures such as mutual information or log likelihood differ in the relative importance they assign to aspects such as the token frequency of a collocation or the mutual faithfulness of the component words. For example, the collocation unmitigated disaster is much less frequent than sustainable development, but when the adjective unmitigated is observed, it acts as a very strong cue for the upcoming noun disaster. Measures such as Delta P further allow researchers to take the directionality of association into account. For example, the word instead is a strong cue that the following word would be of. This association is not symmetric, since of is frequently preceded by other elements than instead. Conversely, the word vitro is typically preceded by in, but in is not a reliable indicator that the next word will be vitro.

Frequencies of co-occurrence lie at the heart of distributional semantic approaches (Turney & Pantel Reference Turney and Pantel2010), which model the meanings of linguistic units in terms of their collocational profiles. To give a simple example, the meaning of a word such as violin is reflected in its distributional behavior, which is to say that words such as piano, orchestra, play, or sonata are strongly represented in contexts in which the word violin appears. On the basis of a corpus, it is possible to generate a frequency list of all words that appear in the neighborhood of the word violin. With an association measure, that frequency list can be transformed into a vector of values that shows which words are overrepresented or underrepresented, so that a semantic profile of violin emerges. Distributional semantic techniques typically compare many such vectors to establish patterns of semantic similarity or dissimilarity in larger sets of linguistic units. Analyses of that kind are able to determine that, for example, words such as piano, flute, and cello have collocational profiles that are very similar to that of violin, whereas words such as rose, tulip, and daffodil conform to a profile that is altogether different. Perek (Reference Perek2018) uses a distributional semantic approach in a diachronic study of the English way-construction. He uses data from the Corpus of Historical American English (Davies Reference Davies2010) in order to compute semantic vectors for the lexical verbs that appear in the way-construction. By comparing the semantic vectors of verbs that enter the construction across historical periods of time, Perek finds that the verbs of the way-construction occupy an increasingly broader semantic range, specifically in the manner sense of the construction (e.g., John joked his way into the meeting). For the path-creation sense of the construction, there is a development towards increasingly more varied and also more abstract verbs, including groups such as verbs of ingestion (eat, drink, etc.), verbs of commercial transactions (buy, purchase, acquire, etc.), speech act verbs (mumble, whisper, etc.), and others (announce, explain, write, etc.). In general terms, Perek’s study illustrates how co-occurrence frequencies, put into the service of distributional semantic analyses, can reveal how constructions behave with regard to schematicity and abstractness. The elements that co-occur with a construction reflect its meaning, and historical shifts in the co-occurrence patterns between a construction and its lexical collocates can yield insights into the diachronic semantic trajectory of a construction.

Frequency of co-occurrence can be also shown to affect language processing and language use. Relevant evidence is presented by Gries et al. (Reference Gries, Hampe and Schönefeld2005), who devised a sentence completion task in which speakers had to find continuations for sentence fragments. Gries and colleagues used the English as-predicative construction (The idea was considered as a major innovation) as a case study. The participants were exposed to sentence fragments that contained a subject, a passive auxiliary, and a past participle, as in The idea was considered. Their task was to complete the fragment in any way they saw fit. Gries et al. measured how often the participants’ continuations resulted in a complete as-predicative construction. With regard to the verbs that appeared in the fragments, Gries et al. controlled for their token frequency as well as their frequency of co-occurrence with the as-predicative construction. For the latter, the Fisher–Yates exact test was used as an association measure (Gries et al. Reference Gries, Hampe and Schönefeld2005: 647). Verbs such as regard, describe, or see are strongly associated with the construction. The results of the experiment show that participants were more likely to complete a fragment with the as-predicative if the verb in the fragment was strongly attracted to the construction. By contrast, Gries et al. (Reference Gries, Hampe and Schönefeld2005: 659) did not observe an independent main effect of token frequency.

Another effect of co-occurrence frequency is observed by Hilpert and Flach (Reference Hilpert, Flach, Krawczak, Lewandowska-Tomaszczyk and Grygiel2022) in a study of a phenomenon that is called constructional contamination (Pijpops & Van de Velde Reference Pijpops and Van de Velde2016; Pijpops et al. Reference Pijpops, de Smet and Van de Velde2018). The term describes a relation between two constructions of a language, such that usage frequencies of one construction influence patterns of variation in another construction. Hilpert and Flach (Reference Hilpert, Flach, Krawczak, Lewandowska-Tomaszczyk and Grygiel2022) study constructional contamination in the English passive, which exhibits variation with regard to the adverbial modification of participles. In a passive sentence, the past participle can be either preceded by an adverb, as in The government was democratically elected, or it can be followed by an adverb, as in The government was elected democratically. Pijpops and Van de Velde (Reference Pijpops and Van de Velde2016) argue that variation of this kind can potentially be influenced by a construction that features word strings that can also appear in one of the variants. With regard to the English passive, sequences of an adverb and a participle occur in noun phrases such as a democratically elected government. If uses of this kind appear with high token frequency in language use, the prediction is that speakers will favor the adverb-initial variant of the passive. Hilpert and Flach (Reference Hilpert, Flach, Krawczak, Lewandowska-Tomaszczyk and Grygiel2022) test this prediction on the basis of data from the Corpus of Contemporary American English (Davies Reference Davies2008) and they find that the token frequency of adverb–participle combinations in English noun phrase constructions significantly biases speakers towards the use of adverb-initial passives. Beyond this effect of high token frequency, they further observe an effect of co-occurrence frequency. Combinations such as dimly lit or randomly selected are not highly frequent in English noun phrases. Yet, the fact that these collocations have a strong degree of mutual association may bias speakers towards adverb-initial order in the passive construction. Hilpert and Flach controlled for a possible effect of mutual association strength with covarying collexeme analysis (Gries & Stefanowitsch Reference Gries, Stefanowitsch, Achard and Kemmer2004b), which was used to determine degrees of mutual association between adverbs and participles in the English noun phrase construction. The results indicate that frequency of co-occurrence is a significant predictor of speakers’ bias towards adverb-initial order in the English passive construction.

The studies described in this section suggest that language processing and production are shaped by co-occurrence frequencies of linguistic units. The respective effects go beyond effects of high token frequency as such. Degrees of mutual association can impact language use even when the linguistic units in question are relatively low in token frequency.

6.2.5 Dispersion (Burstiness)

The dispersion, or burstiness, of a linguistic unit concerns the regularity with which it appears and reappears in language use. Two linguistic units with the same token frequency may behave very differently with regard to their dispersion, so that their respective tokens are either spaced out evenly and regularly or tightly clustered together. To take an example, consider the words without and system, which appear with roughly the same token frequency in the British National Corpus. Whereas without appears in just about every text that is featured in the corpus, this is not the case for system. Tokens of the word system have a greater chance of following each other in close proximity, but there are also longer stretches in the corpus that do not contain the word system at all. What this means is that without is more evenly dispersed than system.

Various techniques have been proposed to measure dispersion (Gries Reference Gries2008, Reference Gries, Gries, Wulff and Davies2010, Reference Gries2022a). The conceptual basis for most of these techniques is that a corpus is divided into parts. The corpus parts may be defined in terms of a fixed number of running words or by dividing the data into the different text documents that constitute the corpus. Based on such a division, it can be determined how frequently a given linguistic unit appears in each of the parts. The dispersion measure known as ‘range’ simply assesses the percentage of corpus parts in which a linguistic unit is represented (Gries Reference Gries2008: 407). The higher the range, the more even the dispersion. The dispersion measure deviation of proportions (Gries Reference Gries2008: 415) is based on more sophisticated calculations and is computed as follows. In a first step, a corpus is divided into parts and it is determined for each part how much of the corpus it represents. A text of 10,000 words would thus represent 1 percent of a corpus with one million words. To assess the dispersion of a linguistic unit in that corpus, its frequency in the entire corpus and in each corpus part is determined. For example, the word without might appear 400 times in the corpus as a whole, and six times in a first text of 10,000 words. This means that without is overrepresented in that corpus part. Whereas only 1 percent of tokens would be expected, the text in fact contains six tokens which add up to 1.5 percent. Deviation of proportions is calculated in such a way that for all corpus parts the differences between expected percentage and observed percentage are added up, and the sum of differences is divided by two. If the resulting value is close to 0, the analyzed word is very evenly distributed. Values close to 1 indicate a highly uneven dispersion.

An alternative to measuring dispersion on the basis of corpus parts is to observe distances between the tokens of a linguistic unit (Gries Reference Gries2008: 409). For the word without, the maximal distance will be lower than for the word London. If the distances are distributed in such a way that some of them are very large and most are very small, this indicates an uneven dispersion.

It has been argued that certain effects of token frequency are more adequately explained as effects of dispersion. For example, Adelman et al. (Reference Adelman, Brown and Quesada2006: 817) analyzed latencies in six separate data sets from experiments that included word-naming and lexical decision tasks, finding that dispersion (operationalized as range) is a better predictor of word-processing times than token frequency, and that token frequency has no measurable effect that would be independent of dispersion. Baayen (Reference Baayen, Jarema, Libben and Westbury2011: 454) draws a similar conclusion on the basis of data from lexical decision tasks, arguing that any effect of token frequency is minimal once variables such as dispersion, morphological family size, or syntactic entropy are controlled for. It is important to note in this context that most of the established measures of dispersion, including range, are known to correlate strongly with token frequency (Adelman et al. Reference Adelman, Brown and Quesada2006: 815; Baayen Reference Baayen, Jarema, Libben and Westbury2011: 445). Infrequent lexical items will necessarily appear in only a few corpus parts, whereas frequent items stand a better chance of being represented in a large percentage of the parts. In order to address this problem, Gries (Reference Gries2022a) has recently proposed a measure that avoids this correlation and thus allows for a more reliable assessment of the respective effects of token frequency and dispersion. Gries uses deviation of proportions as the basis for a new measure that is labeled DP_nofreq. The measure calculates theoretical lower and upper bounds for the dispersion of a linguistic item, given its token frequency. In other words, the measure assesses whether a word could be potentially more even or more uneven in its dispersion. Unlike other dispersion measures, DP_nofreq can yield high dispersion values for infrequent linguistic items. Gries (Reference Gries2022a: 29) uses data from lexical decision tasks to show that DP_nofreq, in combination with the variables of token frequency and word length, outperforms other dispersion measures in predicting reaction times.

Besides facilitating greater ease of processing, evenness of dispersion also correlates with aspects of linguistic meaning. Using a distance-based measure of dispersion, Pierrehumbert (Reference Pierrehumbert, Santos, Linden and Ng’ang’a2012: 104) shows that linguistic units with more specialized meanings are dispersed less evenly. Specifically, in a comparison of deverbal nouns (evolution, failure, growth) and their verbal bases (evolve, fail, grow), the nouns show a stronger tendency to appear in bursts, whereas the verbs are dispersed more evenly. In a study with a similar outlook, Hilpert and Correia Saavedra (Reference Hilpert and Correia Saavedra2017) analyze a matched set of lexical words and grammatical items that are balanced in terms of their respective token frequencies. They use regression modeling to determine whether even dispersion, measured in terms of deviation of proportions (Gries Reference Gries2008), is predicted more accurately by high token frequency or by semantic generality. The results indicate that both token frequency and semantic generality have significant effects. The semantic effect is, however, considerably weaker than the frequency effect.

In comparison to other measures of frequency, dispersion has received relatively less attention in research that is concerned with constructions and Cognitive Linguistics more generally. The importance of considering dispersion and its effects has been argued forcefully by Gries in a series of papers (Reference Gries2008, Reference Gries, Gries, Wulff and Davies2010, Reference Gries2022a, Reference Gries and Boas2022b). Aside from the issues that have been presented in this section, Gries (Reference Gries and Boas2022b: 62) further suggests that the effects of dispersion on language learning merit further attention.

7.2.1 Largely Qualitative Corpus Approaches

As mentioned above, the initial uses of corpus or corpus-like data in CxG papers were largely only presentative in nature and served to make some theoretical point(s) by means of authentic examples, but often without the kind of systematic feature annotation that is characteristic of much contemporary work. This pointing out a lack of multivariate annotation is not meant as a criticism, given the different goals of papers at the time, but what is perhaps a bit more critical is that some such literature often did not clarify whether examples provided were made up or attested (and, if they were attested, what the source was). For example, Fillmore et al. (Reference Fillmore, Kay and O’Connor1988: 519) discuss hundreds of example sentences but usually provide no information on them, let alone on their source. One time they state “we have come across incontrovertible cases of attested utterances of non-negative let alone sentences that seem perfectly natural and which there is no apparent justification to ignore as performance errors” and proceed to discuss their examples (71) and (72) by stipulating (admittedly likely) contexts in which they may have been uttered. Kay and Fillmore (Reference Kay and Fillmore1999) proceed in a similar way: We don’t learn much about where examples are from etc., and the same is true of many other studies such as Smith (Reference Smith1994), Kemmer and Verhagen (Reference Kemmer and Verhagen1994), Dancygier and Sweetser (Reference Dancygier and Sweetser1997), Morgan (Reference Morgan1997), Gutzmann and Henderson (Reference Gutzmann and Henderson2019), and many others, which were all introspection-based and, if they used the word data, typically used it to refer to introspective judgments and/or example sentences.

Crucially, this is not just some complaint from a quantitative corpus linguist who wants corpus examples for the sake of corpus examples; the point is that what seem like clear-cut judgments from native speakers on made-up or even attested examples can look very different once one looks at (larger) quantities of data – as Sinclair (Reference Sinclair1991: 100) said, “Language looks very different when you look at a lot of it at once.” For example, it is likely that traditional linguists would consider a sentence such as He [_VP donated [_REC her] [_PAT transplant money]] ungrammatical, since it is widely held that the verb donate cannot be used ditransitively (even though its meaning is so similar to that of the prototypical ditransitive verb give). However, Stefanowitsch (Reference Stefanowitsch2006: 69) shows that even the British National Corpus – a great but by today’s standards not particularly large corpus – already contains at least one example exactly like this (in a maybe atypical newspaper headline, admittedly), and Stefanowitsch (Reference Stefanowitsch2007: 65) lists ten examples of donate used ditransitively from a variety of internet pages from .uk domains, all of which “do not conform to what we might think of as the default donate frame”; instead, they appear to instantiate a frame that Stefanowitsch describes as follows:

Thus, while linguistics in general and CxG in particular have benefited a lot even from papers that did not feature corpus data or analyses, linguists clearly have no unbiased and axiomatically correct view of what is possible (i.e., what can or cannot be said; see Labov Reference Labov and Austerlitz1975), let alone what is likely. Even theoretical works without any kind of quantification might have turned out a bit different if corpora or corpus-like data had been consulted systematically, and I think it is fair to say that usage-based linguistics and CxG have evolved precisely in this direction. For instance, Hamunen (Reference Hamunen2017) is not the least bit quantitative but still not only bases its diachronic exploration of the Finnish Colorative Construction mostly on 1,741 examples from three different corpora/corpus-like databases (viz. the Finnish Syntax archive, the Digital Morphology Archive, and the Digital Dictionary of Finnish Dialects), but also highlights all made-up examples as such. Beliën (Reference Beliën, Yoon and Gries2016) explicitly points out this methodological turn –

– before discussing the failure of traditional syntactic constituency tests regarding the analysis of Dutch particle constructions. However, it seems to me that most more recent and contemporary studies based on corpus data do involve at least some kind of quantification and I think that there are very few questions, if any, that cannot or should not be studied quantitatively as a matter of principle (but of course, there may be situations where, for example, data sparsity may rule out the use of certain statistical methods); see Jenset and McGillivray (Reference Jenset and McGillivray2017: section 3.7); Gries (Reference Gries2019b: 25–29), or Gries (Reference Gries2021 [2009]: section 1.2) for more on this question. We now turn to the simplest kind of quantification: frequencies of (co-)occurrence and (conditional) probabilities.

7.2.2 Frequencies of (Co-)occurrence and Conditional Probabilities

In spite of the statistical simplicity of frequencies and probabilities, if they are applied in the right kind of research context, they can be instructive, as is evidenced by a variety of studies having to do with issues of frequency as a mechanism driving, affecting, or at least correlating with entrenchment, learning/acquisition, language change, and productivity. For instance, in the area of language acquisition/learning, by now classic studies such as Goldberg’s (Reference Goldberg and MacWhinney1999) analysis of L1 acquisition data from CHILDES (to determine how highly frequent semantically light verbs facilitate the acquisition of semantically similar argument structure constructions) or Ellis and Ferreira-Junior’s (Reference Ellis and Ferreira-Junior2009a, Reference Ellis and Ferreira-Junior2009b) longitudinal study of L2 acquisition of verb-argument constructions in the European Science Foundation corpus were among the first to empirically highlight the importance of frequency of occurrence (of constructions) and frequency of co-occurrence (words in constructional slots) for language acquisition/learning, or for the ubiquity of Zipfian distributions of constructions, or for material within slots of constructions. Another hugely influential application of conditional probabilities – as cue validity – is Goldberg et al. (Reference Goldberg, Casenhiser and Sethuraman2004), which shows that certain patterns (e.g., V-Obj-Loc) have very high cue validities for certain meanings (e.g., caused motion), which reinforces the notion of constructions as pairings of form and meaning reliable enough to facilitate acquisition based on recognizing association patterns and chunking.

Quantitatively similar applications can also be found in other areas. An example of how corpus frequencies can inform theoretical argumentation is Boas (Reference Boas, Achard and Kemmer2004), who challenges a Minimalist Program account of wanna contraction in English. He shows that less than 1 percent of the examples of wanna contraction in the Switchboard corpus are instances within WH-clauses, which is interesting because most analyses put a lot of emphasis on wanna contraction in WH-clauses even though wanna contraction is actually more frequent than want to in relative clauses. As Boas (Reference Boas, Achard and Kemmer2004: 482) argues, if a theory of language claims not only to be descriptively but also explanatorily adequate, the question for Ausín’s (Reference Ausín2001) minimalist program analysis is how it may account for these differences in distribution.

Another study that is based on statistically very down-to-earth percentage data but uses them to make valuable theoretical contributions is Gaeta and Zeldes (Reference Gaeta and Zeldes2017). They use DeWaC, a 1.6 billion-word corpus of web-based German to study -er compounds (with agent noun heads) from a Construction Morphology perspective. On the basis of type, token, and hapax counts, they explore with which frequencies different combinations and orders of compounds are attested and the direction in which prototypical instances are generalized, and argue that Construction Morphology’s flexibility (in terms of permitting different derivational pathways of compounds) makes it an approach that supersedes purely syntactic or purely morphological approaches.

Quantitatively similar work – using type and token frequencies – is also found in Quochi (Reference Quochi, Yoon and Gries2016), a paper on a radial-category family of Italian light-verb constructions and their acquisition in L1 data from the CHILDES database. Approximately 2,100 instances of fare (‘do’) + noun constructions from children and adults are investigated in terms of the nouns/noun categories they occur with and the type–token ratios of verb-related nouns. Tracking new types over time she finds, among other things, that fare + nouns derived from verbs by suffixation appear to be rote-learned rather than instances of creative production. The general time course of acquisition, Quochi observes, is one where children first pick up on the most frequent uses, then develop a more abstract schema, which becomes generalized to intransitive actions, a development that is compatible with usage-based approaches to language acquisition of the kind outlined by Tomasello (Reference Tomasello2003), among others.

Let us finally look at a couple of statistically simple yet interesting applications that also bridge the gap to studies that involve higher degrees of statistical complexity. One of these is Vázquez Rozas and Miglio’s (Reference Vázquez Rozas, Miglio, Yoon and Gries2016) study of which linguistic features are associated with Spanish and Italian speakers’ choices of experiencer-as-subject (ES) and experiencer-as-object (EO) constructions. They look at clauses with an experiencer and a stimulus, where some such clauses construe the experiencer as Subject and the stimulus as Object while others have experiencers coded as dative/accusative Objects and stimuli as Subjects. For Spanish, they rely on the ARTHUS corpus of American and Peninsular Spanish; for Italian, they combine several databases to approximate a similar (and similarly sized) corpus (La Repubblica, C-ORAL, and the BAdIP database). Both corpora were searched for two-argument clauses with active-voice feeling verbs (excluding volition verbs). The main body of their paper reports a variety of frequency/percentage results for many different features of the clauses, including experiencer animacy, person, number, syntactic category, as well as stimulus animacy and syntactic class, and register/genre. Specifically, they point out correlations between ES vs. EO choice and experiencer and stimulus characteristics. However, they go beyond these monofactorial explorations by also subjecting the data to a multi-factorial analysis using a conditional inference tree, which is much more able to identify complex relations and interactions in the data, in particular how discourse-related factors can interact with the syntactic form and semantic structure of the clause. Their paper therefore bridges the gap from frequency/percentages-only studies to the kind of multi-factorial work that seems to be the state of the art today and will be discussed more below.

Another interesting application is Chen (Reference Chen2017), a diachronic CxG study based on (i) contemporary Mandarin Chinese data from the Academia Sinica Balanced Corpus of Modern Chinese and (ii) diachronic data for Old Chinese, Middle Chinese, and Early Mandarin from the Academia Sinica Ancient Chinese Corpus. She tracks the frequency of senses and what they co-occur with to explore how diachronic realignment processes gave rise to a synchronic polysemy network of ‘one’-phrases in Mandarin involving counting/quantifying senses, but also meanings involving a negative-polarity sense and an attenuating positive polarity sense. As Chen concludes, “The associations [between ‘one’-phrases and already established constructions] have been shaped by the environments where the ‘one’-phrases frequently occur. The combination inherits syntactic, semantic, and pragmatic properties from the higher-level constructions, leading to new constructs” (Reference Chen2017: 97). This makes for a perfect transition to one of the, if not the, most widely used statistical methods in corpus-based CxG, the measurement of association strength and its implications for acquisition/learning, use, and change, which is the topic of the next section.

7.2.3 Association Strengths

Another frequent statistical method in corpus-based CxG involves a class of measures called association measures, that is, measures that are ultimately based on frequencies but then quantify the degree to which (typically two) elements from any level of the constructicon like or dislike to co-occur with each other; or, put differently, the degree to which the presence of one element makes the presence of another element more likely. This is a central issue for many questions, from as seemingly minute as the preference of words to occur with particular inflectional morphemes via the preference of words to occur in syntactic/argument structure constructions to, most fundamentally, actually any association of form and meaning (e.g., as when children determine from co-occurrence patterns that certain verbs have certain meaning and like to occur in certain constructions). The maybe most widely used statistical application in this context involves quantifying the degree of association between words and (slots of) constructions. The four papers by Stefanowitsch and Gries (Reference Gries2003, Reference Stefanowitsch and Gries2005) and Gries and Stefanowitsch (Reference Gries and Stefanowitsch2004a, Reference Gries, Stefanowitsch, Achard and Kemmer2004b) develop a family of methods referred to as ‘collostructional’ analysis (see also Chapter 6), a blend of collocation and construction:

• collexeme analysis: the quantification of how much words are attracted to, or repelled by, a syntactically defined slot in a construction (e.g., the verb slot in the ditransitive construction or the noun slot in the N-waiting-to-happen construction);

• (multiple) distinctive collexeme analysis: how much a word (dis)prefers to occur in a certain slot of two or more functionally similar constructions (e.g., the verb slot in the two constructions making up the dative alternation); and

• two variants of covarying collexeme analysis: how much elements in two slots of one construction (dis)like to co-occur (e.g., the two verb slots in the into-causative, i.e., in V DO_NP into V-ing).

Most applications of either of these methods have been based on 2×2 co-occurrence tables such as Table 7.1, in which the elements’ and cell frequencies’ meanings depend on which analysis one conducts:

• for a collexeme analysis of the ditransitive,

  • – element 1 might be one verb in the ditransitive (e.g., give) and element 2 would be the ditransitive construction;

  • – a+b would be give’s frequency in the corpus, a+c would be the ditransitive’s frequency in the corpus, and a would be the frequency of give in the ditransitive;

• for a distinctive collexeme analysis of the dative alternation,

  • – element 1 might be one verb in the ditransitive or the prepositional dative (e.g., give), element 2 might be the ditransitive construction, and ‘not element 2’ would be the prepositional dative;

  • – a+b would be give’s frequency in the corpus, a+c would be the ditransitive’s frequency in the corpus, and b+d would be the frequency of the prepositional dative;

• for a covarying collexeme analysis of the into-causative,

  • – element 1 might be one verb₁ in the into-causative (e.g., trick) and element 2 would then be a verb₂ in the into-causative (e.g., believe);

  • – a+b would be trick’s frequency in the verb₁ slot of the into-causative, a+c would be believe’s frequency in the verb₂ slot of the into-causative, and a would be the frequency of trick DO_NP into believing in the into-causative.

Each of these applications follows a very similar four-step template, which is identical to the same decades-old approach in collocation studies in non-CxG corpus linguistics:

1. (1) one retrieves (ideally) all instances of a construction of interest C;

2. (2) for the element(s) of interest (e.g., a verb in a slot of C) one computes (a) measure(s) of association that is/are (usually) based on the relevant 2×2 tables of the above kind;

3. (3) one sorts the elements of interest according to that association measure; and

4. (4) one analyzes the top x elements of interest (often called collexemes) in terms of their structural, semantic, or other functional characteristics.

This family of methods was already relatively widespread ten years ago, when it was already used in studies on near-synonymous constructions (alternations), where, for instance, the method was precise enough to discover the iconicity difference (Thompson & Koide Reference Thompson and Koide1987) between the ditransitive (small distances between recipient and patient) and the prepositional dative (larger distances between recipient and patient) and many other domains: for example, in the study of priming effects (Gries Reference Gries2005; Szmrecsanyi Reference Szmrecsanyi2006), L1/L2 acquisition and learning of constructions (Gries & Wulff Reference Gries and Wulff2005, Reference Gries and Wulff2009; Ellis & Ferreira-Junior Reference Ellis and Ferreira-Junior2009a, Reference Ellis and Ferreira-Junior2009b; Wulff & Gries Reference Wulff, Gries and Robinson2011, and especially the extremely comprehensive Ellis et al. Reference Ellis, Römer and O’Donnell2016), constructional change over time (Hilpert Reference Hilpert2006, Reference Hilpert2008), etc. In addition, the approach has received some experimental support (Gries et al. Reference Gries, Hampe and Schönefeld2005, Reference Gries, Hampe, Schönefeld, Rice and Newman2010) and has stimulated research that combined it with other methods. Backus and Mos (Reference Backus, Mos and Schönefeld2011), for instance, explore the productivity and similarity of two Dutch potentiality constructions – a derivational morpheme (-baar) and a copula construction (SUBJ COP_finite te INF) – and combine association measures with acceptability judgments. They report the results of a distinctive collexeme analysis to determine which verbs prefer which of the two constructions in the Corpus of Spoken Dutch, and follow this result up with a judgment experiment to probe more deeply into seemingly productive uses of the constructions. The authors find converging evidence such that acceptability is often correlated with corpus frequencies and lexical preferences (see also the chapters in Schönefeld Reference Schönefeld2011 for more examples of converging evidence and more on frequency vs. acceptability below).

More recent applications have broadened the scope even more, have used suggested improvements, and/or even extended the method and, thereby, have added to the theory of CxG. For example, Hoffmann et al. (Reference Hoffmann, Horsch and Brunner2019) extend collostructional analysis by exploring the elements in slots on a more schematic level and the correlations between what happens in a construction’s slots on that more abstract level. They study 1409 tokens of the comparative correlative constructions (e.g., the more, the merrier) from the 2015 part of the Corpus of Contemporary American English (COCA) in terms of several of the construction’s characteristics: the grammatical/phrasal filler type (of either comparative), the lexical filler, and the presence/absence of different kinds of deletion. They first apply a covarying collexeme analysis using the unidirectional association measure Delta P (Ellis & Ferreira-Junior Reference Ellis and Ferreira-Junior2009b; Gries Reference Gries2013b) rather than the usual bidirectional measures, and not only explore the words in the slots per se, but also in relation to the more schematic characteristics. Among other things, they find that the only filler types significantly attracted to each other are pairs of the same filler type, indicating that one’s account of the construction should not attempt to treat the construction’s slots as independent, an observation that can only be made when corpus data meet statistical methods in the analysis. Another example of the use of the unidirectional Delta P approach to collostructions is Rastelli’s (Reference Rastelli2020) analysis of lexical aspect in L2 Italian, which is not a study of argument structure (the ‘usual suspect’ in this type of analysis) but of lexeme–morpheme associations. A generally similar analytical approach, which also explores co-occurrences at multiple levels of generality, is pursued in Abdulrahim (Reference Abdulrahim2019), who studies ‘go’-constructions with three types of verbs in Modern Standard Arabic and their association to a variety of lexico-syntactic features. Abdulrahim uses a multi-dimensional extension of collostructions, so to speak, Hierarchical Configural Frequency Analysis (HCFA, Gries Reference Gries2021 [2009]; Stefanowitsch & Gries Reference Gries2005), a method that tries to identify over- and under-represented cells in multi-dimensional frequency tables.

None of the above should imply that collostructional analysis has not also been criticized, but much of the critique was based on a variety of misunderstandings with regard to both the method’s goals and their implementation. For instance, with regard to the former, Bybee (Reference Bybee2010: chapter 5) criticized collostructional analysis for its lack of considering semantics (especially on the input side of the analysis) when in fact the whole point of collostructional methods is to be able to infer semantic (or other functional patterns) from its output. Similarly, Bybee criticized the collostructional approach for a lack of discriminability in her results, but did not actually perform a full-fledged analysis herself: Rather than applying the method to all words in a certain construction and as described in the four steps above, she restricted her input to extremely low-frequency items that collostructional methods were not developed for and then performed only step 2 of the above four. Schmid and Küchenhoff (Reference Schmid and Küchenhoff2013) suffers from similar problems. For instance, they misunderstood how software handles extremely small values (e.g., <10^–320) and falsely claim that one needs more powerful computers for collostructional computations (when all that is needed is a specific software package, which would allow any normal computer to handle such numbers); also, they object to how most collostructional applications compute association strength (using the p-value of a Fisher–Yates exact test), but at least some of their argumentation is self-contradictory: For instance, they criticize p_FYE for, among other things, being bidirectional, but devote quite some space to discussing an alternative they prefer, the odds ratio, which is also bidirectional (for the specifics of this debate, see Bybee Reference Bybee2010: chapter 5 and Gries Reference Gries2012 for a rebuttal, as well as Schmid & Küchenhoff Reference Schmid and Küchenhoff2013 and Gries Reference Gries2015a for another rebuttal). Gries (Reference Gries2019a) is an attempt to place collostructional analysis on a new statistical foundation, by encouraging the use of many more and independent dimensions of information that an analyst should consider, namely frequency, association (independently of frequency and potentially bidirectionally), dispersion, entropy, and possibly others.

In some recent research, collostructional methods are now more often combined with other kinds of data and methods (see the discussion in Ellis et al. Reference Ellis, Römer and O’Donnell2016; Sommerer & Baumann Reference Sommerer and Baumann2021; Chen Reference Chen2022), and collostructional results are sometimes included as predictors or control variables, given how they can help bring item-specific (e.g., verb-specific) variability under statistical control. This may also help validate/critique the approach, but of course much remains to be done and by now many such attempts are underway. For example, Bernolet and Colleman (Reference Bernolet, Colleman, Yoon and Gries2016) raise the bar for just about all collostructional studies in that they take polysemy more seriously than nearly all others and incorporate sense information into the analysis. Gries (Reference Gries, Daems, Zenner, Heylen, Speelman and Cuyckens2015b) is a first step to try to disentangle the correlations between directions of attraction and experimental data in the as-predicative. Flach (Reference Flach, Sanchez-Stockhammer, Günther and Schmid2020b) revisits the frequency vs. association issue with data on gonna/wanna/gotta contraction and shows that contingency/association measures consistently outperform string frequency. Finally, Herbst (Reference Herbst2020) is an interesting new proposal to change one’s perspective on co-occurrence away from a view of items-attracted-to-constructions (as in all collostructional studies, e.g., verbs in the verb slot of an argument construction) to a view of items-in-constructions.

The above should not also imply that collostructional studies are the only examples of association measures in corpus-based CxG. As an example of a different kind of application, Cappelle et al. (Reference Cappelle, Depraetere and Lesuisse2019) retrieve n-grams involving necessity modal verb lemmas from the BNC that meet a frequency and an association strength threshold (50 and MI≥3 respectively). Adopting a perspective of “contexts as constructions,” they then cluster the modal verb lemmas on the basis of the contexts they share; they find a hierarchical cluster structure that can be represented as (([have to, need to], must), should) (with parentheses and square brackets indicating less and more robust clusters respectively). While not much is done with that specific quantitative result, Cappelle et al. proceed with some qualitative discussion of how the modals’ functions are reflected in terms of the preferred n-grams.

The second most widespread quantitative treatment of corpus data in CxG involves various kinds of modeling, to which we turn now.

7.2.4 Monofactorial, Multi-factorial, and Multivariate Approaches

Corpus-based CxG studies using both mono- and multi-factorial tests have increased substantially, especially over the last ten or so years. Petré and Anthonissen (Reference Petré and Anthonissen2020), for example, report results from monofactorial regressions on individual variation in diachronic data, finding, among other things, excellent fits of (i) first attestations of motionless be-going-to INF in the sixteenth to seventeenth centuries with time (the expected logistic s-curves) and (ii) within-individual uses of Nominativus-cum-Infinitivo and prepositional passive constructions. However, the ‘standard’ by now are multi-factorial/multivariate approaches. While I am splitting this section up into ‘inferential’ and ‘exploratory’ approaches, it needs to be pointed out that the dividing line is often more tenuous than one might think. Many studies use inferential tools, such as regression modeling, but incorporate a certain degree of exploration because their modeling involves model selection; similarly, a method like HCFA as in Abdulrahim (Reference Abdulrahim2019) also combines inferential and exploratory aspects. In addition, the notion of “exploratory” I am using is rather broad and intended to cover all methods covered in traditional statistics textbooks such as different kinds of cluster analyses, principal component/factor analysis, correspondence analysis, and multi-dimensional scaling, but also unsupervised machine-learning methods such as vector spaces and deep learning.

8.3.1 Priming of Syntax

Bock (Reference Bock1986) was the first study to report evidence for structural priming, that is, the fact that hearing a sentence with a certain syntactic structure makes it more likely for the same structure to be subsequently used. Participants were presented with prime sentences instantiating one of a pair of functionally similar syntactic structures: active vs. passive structure for transitive primes (e.g., One of the fans punched the referee vs. The referee was punched by one of the fans), and prepositional dative vs. double-object structure for ditransitive primes (e.g., The lifeguard tossed a rope to the struggling child vs. The lifeguard tossed the struggling child a rope). After each prime, a target picture was shown that could be described using either the structure exemplified by the prime sentence structure or the functionally similar structure (i.e., active vs. passive or double-object vs. prepositional dative). This design is diagrammed in Figure 8.1. Bock (Reference Bock1986) found that it was more likely for participants to describe each picture using the same structure as the one in the preceding prime sentence, even if the prime and target did not share the same verb.

Figure 8.1 Experimental design of Bock’s study on structural priming

(pictures from Bock Reference Bock1986: 361)

In subsequent studies, Bock (Reference Bock1989) and Bock and Loebell (Reference Bock and Loebell1990) argue for a purely syntactic account of structural priming, driven by the constituent structure of sentences alone, independently of the words occurring in it and the meaning that they convey. Bock (Reference Bock1989) finds that prepositional datives with to (e.g., A cheerleader offered a seat to her friend) and benefactives with for (e.g., A cheerleader saved a seat for her friend), which are matched in syntactic structure but differ in their preposition (to vs. for), equally prime to-datives (see also Pappert & Pechmann Reference Pappert and Pechmann2013 for a similar finding with the German equivalent of these alternations). Similarly, Bock and Loebell (Reference Bock and Loebell1990) find priming effects between pairs of sentences with the same structure but different meanings, notably in terms of event structure and thematic roles. They find that prepositional datives (e.g., The wealthy widow gave an old Mercedes to the church) and transitive locative sentences with to (e.g., The wealthy widow drove an old Mercedes to the church) equally prime prepositional datives, and that full passives (e.g., The construction worker was hit by the bulldozer) and intransitive locative sentences with by (e.g., The construction worker was digging by the bulldozer) equally prime full passive sentences. Because primes share the same structure as the target but not their meaning, Bock and Loebell (Reference Bock and Loebell1990) argue that syntactic structure alone causes priming, independently of semantics.

While Bock and Loebell’s (Reference Bock and Loebell1990) interpretation of these findings might seem at first blush to provide evidence for the autonomy of syntax, and thus indirectly against the constructional approach, a vast body of research since their seminal study has investigated the nature of structural priming more closely, and many scholars have argued against a purely syntax-driven account. While genuine cases of priming of syntactic structure alone have certainly been found, many studies report that various other aspects of the form and meaning of sentences can also drive priming. In fact, Bock’s (Reference Bock1989) and Bock and Loebell’s (Reference Bock and Loebell1990) original conclusions have since been criticized on the basis of possible confounds that may explain the priming effects for the pairs of constructions under study, and subsequent research suggests that these effects may be best attributed to semantic and lexical overlap. First, to-datives and for-benefactives on the one hand, and to-dative and to-locative sentences on the other hand, may not be as semantically distinct as assumed by Bock (Reference Bock1989) and Bock and Loebell (Reference Bock and Loebell1990) respectively. In many for-benefactives, the referent of the for-PP is the intended recipient of some item, similar to that of the to-PP in to-datives. As pointed out by Hare and Goldberg (Reference Hare, Goldberg, Hahn and Stoness1999), the use of to in to-datives can be seen as metaphorically related to the literal goal meaning of the preposition found in to-locatives, with transfer of possession construed as a metaphorical change of location (e.g., Jackendoff Reference Jackendoff1983). Moreover, some of the to-locative primes used in Bock and Loebell’s (Reference Bock and Loebell1990) experiment may not be purely locative and could actually be considered prepositional datives as well, for example, The hospital returned the bill to the patient by mistake (cf. Hare & Goldberg Reference Hare, Goldberg, Hahn and Stoness1999). To-datives and to-locatives also share one function word (the preposition to), and similarly, by-locative and passive sentences share even more of their lexical make-up, namely the auxiliary be and the preposition by. Hence, in addition to semantic similarity, lexical overlap may also explain these priming effects. These confounds suggest that structural priming might not be purely driven by shared syntactic structure, prompting Ziegler, Bencini, et al. (Reference Ziegler, Bencini, Goldberg and Snedeker2019) to conduct a follow-up study adding a condition to Bock and Loebell’s (Reference Bock and Loebell1990) original experiment. While Ziegler, Bencini, et al. (Reference Ziegler, Bencini, Goldberg and Snedeker2019) do replicate the critical by-locative to passive priming effect from Bock and Loebell (Reference Bock and Loebell1990), they also find that this effect disappears in the absence of lexical overlap: locative sentences with a different auxiliary from be and a different preposition from by (e.g., The 747 has landed near the airport control tower) do not prime passive sentences.

Importantly, the structural priming effects discussed above can occur independently of the lexical items involved. Ivanova et al. (Reference Ivanova, Pickering, Branigan, McLean and Costa2012) even report priming effects in the dative alternation when the prime sentence contains a nonce verb (e.g., The waitress brunks the book to the monk) or a verb that does not normally occur in these constructions (e.g., The waitress exists the ball to the monk), which confirms that structural priming does not rely on lexical information. Hence, it is hard to explain these priming effects without assuming at least some level of syntactic representation that is separate from lexis, which lines up with the constructional approach whereby aspects of sentence structure are stored and retrieved independently of particular lexical items (cf. Konopka & Bock Reference 218Konopka and Bock2009; Bencini Reference Bencini, Hoffmann and Trousdale2013). Moreover, since Construction Grammar posits that phrasal patterns are directly paired with meaning, it also predicts that constructions with similar forms as well as constructions with similar meanings should prime each other. Many priming studies do show that the semantic properties of constructions can also be a source of priming effects, in particular the abstract event structure conveyed by a construction and the thematic roles assigned to constructional slots.Footnote ¹ These two kinds of priming effects are discussed in the next two sections.

8.3.2 Priming of Thematic Roles

Several studies show that overlap in thematic roles can create priming effects, either independently from syntactic structure or in addition to purely syntactic priming. In a picture-description task with transfer events similar to Bock’s (Reference Bock1986) experiment, Hare and Goldberg (Reference Hare, Goldberg, Hahn and Stoness1999) used three kinds of prime sentences: double-object (His editor offered Bob the hot story), to-dative (His editor promised the hot story to Bob), and ‘provide-with’ structures (His editor credited Bob with the hot story). The latter two have the same syntactic structure, but the provide-with sentences also have the same order of thematic roles as the double-object construction (Agent-Recipient-Theme), thus providing a semantic foil to syntactic priming. Hare and Goldberg (Reference Hare, Goldberg, Hahn and Stoness1999) find that provide-with sentences prime double-objects as much as double-objects themselves (as compared to a baseline with intransitive primes), thus providing evidence for priming of thematic roles independently of syntactic structure (see also Ziegler & Snedeker Reference Ziegler and Snedeker2018 for a replication of this finding).

Chang et al. (Reference Chang, Bock and Goldberg2003) report similar results using Rapid Serial Visual Presentation (RSVP, Potter & Lombardi Reference Potter and Lombardi1998), a protocol in which participants are asked to read a sentence word by word silently and then repeat the sentence out loud after a distractor task interfering with their memory. In such a design, priming effects are found when participants change the structure of the repeated sentence by using the structure of a prior prime sentence. Two related constructions involved in the so-called spray/load alternation were used to construct pairs of prime and target sentences: theme-location sentences (The chef sprayed oil onto the pan) and location-theme sentences (The chef sprayed the pan with oil). Chang et al. (Reference Chang, Bock and Goldberg2003) did find priming effects for both constructions, that is, location-theme sentences changed to theme-location after a theme-location prime, and vice versa. Because both constructions have the same syntactic structure, these effects can only be attributed to the repetition of thematic role assignment (see also Ziegler & Snedeker Reference Ziegler and Snedeker2018 for a replication using a similar picture-description design to Bock’s original studies). The same priming effect was also found between the variants of the corresponding spray/load alternation in Brazilian Portuguese (Ziegler, Morato, & Snedeker Reference Ziegler, Morato and Snedeker2019).

Pappert and Pechmann (Reference Pappert and Pechmann2014) report similar findings with the dative alternation in German, which has more flexible word order than English due to case marking. Specifically, the theme and recipient arguments in the double-object construction are marked, respectively, in the accusative and dative case, and while the Dative-Accusative order is more common (e.g., Der Händler verkauft [dem Bauern]_DAT [einen Traktor]_ACC ‘The merchant sells the farmer a tractor’), the opposite order is also possible (Der Händler verkauft [einen Traktor]_ACC [dem Bauern]_DAT). Pappert and Pechmann (Reference Pappert and Pechmann2014) find priming effects between the double-object and prepositional dative constructions in ways that are consistent with the order of thematic roles: NP-PP prepositional datives (e.g., Der Sohn schreibt einen Brief an die Mutter ‘The son writes a letter to his mother’) prime the Accusative-Dative double-object order, and shifted prepositional datives (PP-NP) prime the Dative-Accusative order, and vice versa. Finally, Cai et al. (Reference Cai, Pickering and Branigan2012) report similar effects in the dative alternation in Mandarin Chinese; they find that double-object primes with the ba-construction or the Topic construction, which both shift the order of the Theme argument before the Recipient, prime prepositional datives, which have the same order of thematic roles.

8.3.3 Priming of Semantics

The studies cited in the previous section show that a construction with a certain set of thematic roles may prime another construction with the same set of thematic roles presented in the same linear order, regardless of the formal realization of each role (cf. Ziegler & Snedeker Reference Ziegler and Snedeker2018). Other studies show priming effects to be sensitive to other aspects of constructional semantics besides thematic roles. Griffin and Weinstein-Tull (Reference Griffin and Weinstein-Tull2003) compare the effect of object-raising (e.g., A teaching assistant reported the exam to be too difficult) vs. object-control primes (e.g., Rover begged his owner to be more generous with food) on the production of object-raising targets in an RSVP task similar to Chang et al. (Reference Chang, Bock and Goldberg2003). Both object-raising and object-control sentences have the same constituent structure, that is, an NP followed by a to-infinitive VP. However, while the object-raising construction encodes a two-participant relation between the subject and a proposition (i.e., ‘The exam is difficult’ in the example above), similarly to a that-clause construction (e.g., A teaching assistant reported that the exam was too difficult), the object-control construction involves an additional participant of the verb realized as a direct object (his owner in the example above). In other words, the two constructions differ in event structure, that is, in constructional meaning, regardless of the verb instantiating them. Griffin and Weinstein-Tull (Reference Griffin and Weinstein-Tull2003) find more object-raising productions (as opposed to that-clause productions) after object-raising primes compared to a control condition, but this effect was weaker with object-control primes despite the same constituent structure. These results show that shared event structure meaning also causes priming, in addition to syntactic structure.

Similarly, Ziegler et al. (Reference Ziegler, Snedeker and Wittenberg2018) show that the priming of ditransitive sentences with give varies according to their event-structure properties, despite their shared syntax. Specifically, they compare so-called compositional ditransitives, that is, typical uses of the construction with a recipient and theme arguments (e.g., Big Bird gives Julia a feather), light-verb ditransitives (e.g., Bert gives Ernie a hug), and idiomatic ditransitives (e.g., Miss Piggy gives Kermit the cold shoulder) which are non-compositional. Importantly, both light-verb and idiomatic ditransitives are essentially two-place predicates with a patient realized as the first object, while compositional ditransitives are paired with a three-argument event structure. Ziegler, Bencini, et al. (Reference Ziegler, Bencini, Goldberg and Snedeker2019) find this difference in event structure to correspond to a difference in priming: While all three types of ditransitives prime compositional ditransitives, the priming effect is significantly stronger with other compositional ditransitive primes.

There is thus ample evidence that various aspects of the meaning conveyed by a construction are activated when instances of the construction are used, and such aspects make it more likely for constructions featuring the same aspects of meaning to be subsequently used. The same can also be seen in comprehension, in that items with a similar meaning to the meaning of a construction are processed faster following instances of that construction. In a reaction time study, Eddington and Ruiz de Mendoza Ibáñez (Reference Eddington, Ruiz de Mendoza Ibáñez, De Knop, Boers and De Rycker2010) presented participants with sentences, and they had to judge whether each sentence was grammatical as quickly as possible. In the list of sentences, targets for priming were constructed from six different argument structure constructions, such as the Resultative construction (e.g., Ron kicked the door open); prime sentences preceding each target were either instances of the same construction or sentences with the same formal pattern but without the same event-structure meaning (e.g., Josh thought the treatment unfair for the Resultative construction). They found that judgments were significantly faster following a prime that matched both the form and the meaning of the sentence than following one that matched only its form. This shows that witnessing an instance of a form–meaning pair speeds up subsequent processing of instances of the same form–meaning pair.

Johnson and Goldberg (Reference Johnson and Goldberg2013) similarly investigate the priming of constructional meaning using Jabberwocky sentences (see Section 8.2), for example, He daxed her the norp. Because none of these words convey meaning, the only source of semantic information associated with the sentence comes from the meaning of the construction, for example, the transfer meaning of the ditransitive construction in He daxed her the norp. They find that Jabberwocky sentences can prime a word matching the meaning of the construction (give for the ditransitive) or a word with a similar meaning (transfer), as measured by decreased reaction times in a lexical decision task. Busso et al. (Reference Busso, Perek and Lenci2021) use a similar methodology to study the processing of sentences with valency coercion in Italian, using prime sentences that combine an argument structure construction with an unusual yet compatible verb (e.g., La donna sbriciola pane agli uccelli ‘The woman crumbles bread for the birds’). Similarly to Johnson and Goldberg (Reference Johnson and Goldberg2013), they find that the four Italian argument structure constructions used in the experiment prime verbs that match the central meaning of the construction, for example, mettere ‘put’ for the Caused-Motion construction. In addition, this priming effect is found to vary according to the degree of compatibility between the verb and the construction, as measured by a grammaticality rating study (Busso et al. Reference Busso, Lenci and Perek2020); namely, the strength of priming increases with the acceptability of the prime sentence. This finding too can be explained through the notion of constructions as units of meaning: When a construction is successfully combined with a verb in a sentence involving valency coercion (high acceptability), the meaning of the construction is fully integrated with that of the verb and thus primes the related verb. However, if there are difficulties in combining the meaning of the verb with that of the construction (low acceptability), semantic integration of the constructional meaning may be unsuccessful or incomplete, which predicts that semantically related verbs are primed to a lesser degree.

In sum, there is evidence that constructions prime aspects of their form and/or meaning, in that not only can instances of the same construction prime each other, but they can also prime constructions with a similar form and/or meaning. While the exact mechanisms behind structural priming have been debated from the start (e.g., Chang et al. Reference Chang, Dell, Bock and Griffin2000; Ferreira & Bock Reference Ferreira and Bock2006), priming effects for both form and meaning suggest that form and meaning are stored in the cognitive representation of grammar, which gives further credence to the central constructional tenet that grammar consists of form–meaning pairs. Because these effects occur across different lexical items, they line up with the idea that abstract grammatical patterns are stored independently of lexical items.

8.4.1 Inheritance Relations: Constructions and Their Instantiations

Inheritance is one of the most common and widely accepted relations between constructions across the many variants of Construction Grammar (see Pijpops et al. Reference Pijpops, Dirk Speelman, Van de Velde and Grondelaers2021 and Sommerer & Baumann Reference Sommerer and Baumann2021 for two recent studies on this topic). It essentially captures the commonalities in form and meaning between a range of ‘sister’ constructions into a more general ‘mother’ construction that they all inherit from. One of the most typical kinds of inheritance link is between an abstract construction and a lexically specific construction in which one of the slots of the abstract construction is filled by a specific lexical item, for instance between the ditransitive construction (NP V NP NP) and the ditransitive use of the verb bring (NP bring NP NP). This is illustrated in Figure 8.2. Inheritance relations are symbolized by arrows in Figure 8.2: They represent the fact that the form and meaning of the abstract ditransitive construction (top) is generalized from the double-object use of a range of verbs, including the four represented here (bottom); conversely, the form and meaning of the general construction is inherited by sub-constructions, including many more than these four, some of which may or may not be stored as verb-specific constructions.

Figure 8.2 Illustration of a constructional network with the ditransitive construction and four of its verb-specific constructions

Much of the evidence cited earlier in support of abstract constructional meaning is also, ipso facto, evidence for such inheritance links. For instance, Bencini and Goldberg’s (Reference Bencini and Goldberg2000) sorting task experiment illustrates speakers’ ability to extract the similarity in form and meaning between sentences with different verbs and consider them members of the same category. Many priming studies also provide evidence for abstract constructions and therefore for inheritance relations: The fact that instances of the same construction with different lexical items can prime each other precisely points to a higher, lexically independent level of representation linked to all of the lexically specific instantiations.

Importantly, just because a certain use of a lexical item is subsumed by a construction and can be arrived at by merging the item with this construction (cf. Goldberg Reference Goldberg1995) does not necessarily mean that this use is not stored as a construction itself, in line with Langacker’s (Reference Langacker1987) rejection of the ‘rule/list fallacy’. In other words, in a constructional approach, a construction and its lexically specific instantiations can coexist in the network of constructions with inheritance links between them, even if the latter exemplify fully predictable uses of the former. There is actually a large body of psycholinguistic research reporting differences in the processing of sentences with different verbs used in the same constructions in language comprehension, indicating differences in status in the mental grammar. In particular, many studies focus on temporarily ambiguous sentences like the ones below from Garnsey et al. (Reference Garnsey, Pearlmutter, Myers and Lotocky1997):

1. (1) The talented photographer accepted the money could not be spent yet.

1. (2) The novice plumber realized the mistake would cost someone some money.

Upon reading both sentences, the noun phrase following the first verb (accepted and realized) can be tentatively analyzed either as a direct object or as the subject of an embedded clause; only when the next word is read (i.e., an auxiliary verb, could or would) can it be decided that the latter analysis is correct. When such sentences are presented word by word or segment by segment in a self-paced reading task, which forces participants into an incremental way of reading, many studies find that participants will tend to make early assumptions about the syntactic frame the verb is used in, and thus predictions about the upcoming constituents, resulting in processing difficulties if these predictions are contradicted (Trueswell et al. Reference Trueswell, Tanenhaus and Kello1993; Garnsey et al. Reference Garnsey, Pearlmutter, Myers and Lotocky1997; Hare et al. Reference Hare, McRae and Elman2003; Traxler Reference Traxler2005; Wilson & Garnsey Reference Wilson and Garnsey2009). More precisely, such studies typically report so-called ‘garden-path effects’ at the disambiguating region, that is, a sharp increase in processing time that indicates reanalysis caused by the mismatch between the expected structure and the actual one.

Importantly for our present purposes, the presence of garden-path effects (and to some extent their strength, cf. Traxler Reference Traxler2005) is also found to depend on the specific verb used in the sentence. Verbs vary in their preference towards various syntactic frames, which can be measured by norming studies or corpus data (cf. Lapata et al. Reference Lapata, Keller and Schulte im Walde2001; Wiechmann Reference Wiechmann2008). Garden-path effects arise when a verb’s syntactic preference does not match the structure in temporarily ambiguous sentences. For example, while both accept and realize in (1) and (2) can be used either with a direct object NP or with a finite complement clause, accept is more commonly found with the former and realize with the latter, predicting processing difficulties at the disambiguating region for (1) but not (2) (and vice versa when a verb biased towards a complement clause is used with a direct object NP, cf. Wilson & Garnsey Reference Wilson and Garnsey2009). Note that while processing differences between verbs are most dramatic when measured by garden-path effects in temporarily ambiguous sentences, they can also be found with simpler and unambiguous structures. For example, Gries et al. (Reference Gries, Hampe and Schönefeld2005, Reference Gries, Hampe, Schönefeld, Rice and Newman2010) show that the most common verbs in the as-predicative construction (e.g., They regard this as a challenge), as measured by collostructional analysis (see also Chapters 6 and 7), are the most frequently chosen in a sentence completion task and are associated with shorter processing time of the construction in a self-paced reading experiment.

These processing effects which relate to the use of specific verbs in a given construction point to differences in storage of verb-construction combinations. Such differences are difficult to explain in a model which separates lexical and syntactic information, but they are readily compatible with the inheritance network approach of Construction Grammar, in which verb-specific sub-constructions can be posited along with the verb-general argument structure construction that they inherit from. Not all of the possible sub-constructions are necessarily stored, and those that are stored may have different levels of accessibility, explaining the reported differences in processing between different verbs.Footnote ² Processing differences between uses of different verbs in the same structure are widely documented, but Perek (Reference Perek2015) also reports differences between uses of the same verb in different syntactic frames. In a variant of a self-paced reading task, participants were presented with sentences containing the commercial transaction verbs buy, pay, and sell, which can all be followed by a direct object and optionally by another prepositional phrase argument referring to another participant in the commercial transaction scene: the money (e.g., for €50), the buyer/recipient (e.g., to his cousin), the goods (e.g., for a bike), or the seller/source (e.g., from her neighbor). Perek (Reference Perek2015) finds differences in processing time between the two different types of argument available for each verb following the direct object (e.g., Sam sold his bike for £50 vs. Sam sold his bike to his cousin), which also correlate with differences in the frequency with which each verb occurs in these constructions in corpus data.

Finally, further evidence for differences in the cognitive status of different verb-construction combinations can also be found in the priming literature. First, there is a well-known ‘lexical boost’ in structural priming (Pickering & Branigan Reference Pickering and Branigan1998), whereby priming effects are stronger when prime and target share the same verb than when the verb changes. Such an effect is readily explained by the constructional approach: If a given verb-specific construction is stored in the network, it is activated by a prime sentence containing that verb and construction. The more general construction is also activated, but if the same sub-construction is used again in the target, it should be accessed with more ease than the combination of the general construction with a different verb (whether it is retrieved from another sub-construction or computed on the fly). Second, Bernolet and Hartsuiker (Reference Bernolet and Hartsuiker2010) find that the strength of priming effects in the Dutch dative alternation is inversely correlated with the syntactic preference of the verb used in the prime (see also Jaeger & Snider Reference Jaeger and Snider2007, Reference Jaeger and Snider2013). For instance, subjects were more likely to describe a picture using the prepositional dative construction following a prepositional dative prime, and this tendency was stronger if the prime sentence contained a verb that is more typically found in the double-object construction than the prepositional dative, such as aanbieden ‘offer’; hence the example De kok biedt een pistool aan aan de dokter ‘The cook offers a gun to the doctor’ was a stronger prime for prepositional datives than another prepositional dative sentence with a verb that does not show a preference for the double-object construction, such as verkopen ‘sell’. In other words, the stronger the preference of a verb for a particular construction, the less strongly this verb primes this construction, and vice versa. This finding too can be explained in the constructional network approach, if we consider that the syntactic preference of a verb for an argument structure construction correlates with the degree of entrenchment of the corresponding verb-specific construction. Entrenchment is usually taken to lead to a higher degree of autonomy (Bybee Reference Bybee2010); hence, if a prime sentence activates a more entrenched sub-construction, the more general construction should be less strongly activated than if the prime uses a less entrenched or even non-stored sub-construction, leading to a reduced priming effect.

8.4.2 Other Kinds of Links between Constructions

Besides inheritance, various other kinds of links between constructions have been proposed in the literature. These ‘horizontal’ relations, thus called in contrast to the ‘vertical’ relations of inheritance (Perek Reference Perek2012; Van de Velde Reference Van de Velde, Boogaart, Colleman and Rutten2014), have also started to gain attention in experimental studies.

Construction Grammar has characteristically emphasized ‘surface generalizations’ (Goldberg Reference Goldberg2002), capturing grammar in terms of generalizations of the same form and meaning across utterances, as opposed to deriving sentences from others when they are perceived to be semantically related (such as active/passive pairs and the variants of the dative alternation mentioned earlier). While this was a theoretically and empirically grounded move away from earlier generative and in particular derivational approaches, it has led constructional approaches to sideline relations of alternation between constructions with similar functions, for example, the ditransitive and to-dative constructions involved in the dative alternation (e.g., He threw Mary the ball vs. He threw the ball to Mary). More recently, some scholars have argued that such relations should also be part of the constructional network in some form, either as a special kind of link between constructions (Goldberg Reference Goldberg1995; Van de Velde Reference Van de Velde, Boogaart, Colleman and Rutten2014) or as ‘allostructions’ in the inheritance network, that is, sub-constructions of a more abstract ‘constructeme’, which captures their shared meaning paired with an underspecified form (Cappelle Reference Cappelle and Schönefeld2006; Perek Reference Perek2012, Reference Perek2015). While such highly abstract constructions might seem to clash with the constructional commitment to only describe constructions that are directly attested in language data (‘what you see is what you get’), constructemes and their allostructions arguably capture important aspects of language users’ knowledge and behavior, specifically the idea that more than one construction might be available to encode a certain type of message, and correspondingly that a given instance of a construction can be reformulated using another construction in the family, if the right conditions are met.Footnote ³

Several studies report evidence suggesting that such relations between constructions should be represented in the constructional network. Using a sorting task experiment design similar to Bencini and Goldberg’s (Reference Bencini and Goldberg2000) study, Perek (Reference Perek2012) finds that participants are more likely to group instances of the to-dative construction with the ditransitive construction than with instances of the Caused-Motion construction, although the latter are presumably members of the same constructional generalization of both form and meaning. This is interpreted as evidence that speakers notice the functional overlap between formally different constructions and may use this knowledge to establish relations between such constructions; they may then use those relations to infer that a word used in one construction can also be used in the other.

Support for alternations can also be found in priming studies. If the variants of an alternation are related in some way in the mental grammar, a prediction for the priming paradigm is that one variant of an alternation should prime the other variant at least to some extent (though of course not as strongly as itself). Classical priming studies (e.g., Bock Reference Bock1986, Reference Bock1989; Bock & Loebell Reference Bock and Loebell1990) have typically not tested this possibility, because they usually involve only two kinds of primes related by an alternation. Those studies measured priming effects by comparing productions after one kind of prime vs. the other kind, but they cannot measure whether production of one variant also increases production of the other variant, because they lack a baseline condition to compare this to; for instance, a prime sentence that is unrelated to either construction (e.g., an intransitive sentence) and should therefore not increase their production. More recent studies, however, do include such a baseline, and even though they do not address the question of alternations directly, they do report that variants of an alternation can prime each other. In a picture-description task with 4- to 5-year-old children, Goldwater et al. (Reference Goldwater, Tomlinson, Echols and Love2011) find that both variants of the dative alternation prime the other variant: Compared to a baseline condition in which participants were not exposed to any prime sentence, a to-dative prime increases the production of picture descriptions using the ditransitive construction, and vice versa. Similarly, in a priming study of active vs. passive constructions in Russian, Vasilyeva and Waterfall (Reference Vasilyeva and Waterfall2011) find that exposure to ‘canonical’ passives not only increases the production of the same construction both by children and adult speakers, but also the production of a number of other formally different constructions that fulfill the same discourse function (namely, emphasizing the patient argument), such as, for instance, the so-called Impersonal Active consisting of an active clause with a fronted accusative complement and no overt subject. These findings can be explained under the allostructions model: If one assumes that speakers generalize over these constructions on the basis of their shared function and distribution, activating one construction should activate their constructeme and contribute to activating the other constructions that inherit from it.

Perek (Reference Perek2015) further shows that alternation relations between constructions can be asymmetrical. In a sentence production task with novel verbs, speakers readily used a verb in the to-dative construction when they first witnessed that verb in the ditransitive construction, but not the other way around. Such an asymmetry is not found in the spray/load alternation, for example, He sprayed paint on the wall vs. He sprayed the wall with paint, in which verbs tend to be used in the same variant they were witnessed in. Perek finds that this pattern of results correlates with ratios of type frequencies between classes of verbs occurring in only one variant of the alternation (vs. both variants) in a corpus: There are many more verbs attested only in the to-dative construction than alternating verbs or ditransitive-only verbs, while in the locative alternation most verbs are restricted to one or the other variant and only a minority of verbs alternate. In a usage-based constructional approach, this correlation suggests that speakers internalize these statistical relations between constructions (see also Chapters 6 and 7).

Finally, there are other types of links recognized by various scholars. For example, Goldberg (Reference Goldberg1995) distinguishes between four types of inheritance: instance, subpart, polysemy, and metaphorical extension. These other links have typically received less attention in the literature and have not extensively been studied empirically (including experimentally). However, a notable exception to this is a recent study by Ungerer (Reference Ungerer2021) on metaphorical extension links. Specifically, Ungerer investigates the relation between the Caused-Motion construction (e.g., James rolled the ball down the hill) and the Resultative construction (e.g., Susan hammered the metal flat) by means of a priming experiment. Interestingly, he finds an effect of negative priming between the two constructions in a self-paced reading task: Sentences with the Caused-Motion construction are read more slowly after a Resultative construction prime, and vice versa. Even if it is not facilitatory, the very existence of the priming effect can be taken as evidence for some kind of relation between the two metaphorically related constructions.

9.2.1 Generalized (Domain-General) Network Theory

From a usage-based perspective, language is a Complex Adaptive System (CAS): Grammar is an emerging phenomenon, linguistic change happens through use, and the developing linguistic knowledge of a language learner lends itself well to being modeled as a network (Gell-Mann Reference Gell-Mann, Hawkins and Gell-Mann1992; Tomasello Reference Tomasello2003; Beckner et al. Reference Beckner, Blythe, Bybee, Christiansen, Croft, Ellis, Holland, Ke, Larsen-Freeman and Schoenemann2009; Bybee Reference Bybee2010; Steels Reference Steels2011; Diessel Reference Diessel2019, Reference Diessel2023). In general, the network view is motivated by two angles: On the one hand, empirical observations confirm that constructions influence each other in intricate ways which are best explained if one takes a network perspective of relations (Traugott & Trousdale Reference Trousdale2013; Schmid Reference Schmid2016; Hilpert & Diessel Reference Hilpert, Diessel and Schmid2017). On the other hand, an analogy is drawn to neural network structures in the brain. Construction Grammar is highly interested in general human cognition and adheres to the principle of cognitive plausibility (Boas Reference Boas, Hoffmann and Trousdale2013), as well as to the idea that language emerges from domain-general capacities (Hudson Reference Hudson2007: 5; Bybee Reference Bybee2010; Divjak Reference Divjak2019). If language is not unlike other mental capacities, it makes sense to assume that its organization is not sui generis.

Networks can be approached from a domain-general point of view. When doing so, one issue is of crucial importance, namely, that networks can take various shapes depending on how ‘dense’ they are, that is, how many and what kind of connections exist between the different components. Some networks are sparse, other networks consist of many interconnecting links. Components of networks are called ‘nodes’ (or ‘vertices’), connections between these nodes are called ‘links’ (or ‘edges’). These edges can be labeled or not, can be bidirectional, unidirectional, or non-directional, and can be weighted or unweighted (see Figure 9.1).

Figure 9.1 General network graph

Additional concepts from network analysis, a subdiscipline of mathematics known as ‘graph theory’, are walks, paths, (a)cyclicity, degrees, etc. This terminology is necessary to neatly approach a network’s mathematical characteristics (e.g., Ke et al. Reference Ke, Gong and Wang2008; Ogura & Wang Reference Ogura, Wang, Dossena, Dury and Gotti2008; Perc Reference Perc2014).Footnote ²

Remarkably, Construction Grammar has been slow in integrating the aforementioned concepts and the corresponding methodology. Getting a numerical grasp on the size and nature of a particular network can provide a quantitative operationalization on diachronic change (see Van de Velde & Fonteyn Reference Van de Velde and Fonteyn2017 for some pioneering work). For instance, comparing density changes over time can tell us something about the ‘entrenchment’ of a construction.

However, constructional networks may not readily compare to connectionist networks or neurological lattices. For example, in the vast majority of constructional network sketches, connections between nodes are not being ‘weighted’ (like in computational connectionist networks: Rumelhart & McClelland Reference Rumelhart and McClelland1986; Elman et al. Reference Elman, Bates, Johnson, Karmiloff-Smith, Parisi and Plunkett1996). The desire to work with an overarching network theory approach may ultimately be in conflict with doing justice to the linguistic facts. It remains to be seen how well language networks can be analyzed in a domain-general way.

The recent rapprochement between usage-based Construction Grammar and sociolinguistic approaches, and variationist perspectives in particular (see Colleman & Van de Velde Reference Colleman and Van de Velde2015 for references), adds to the network idea by highlighting the correspondence with social networks (Schmid Reference Schmid2016). In this chapter we will not discuss aspects of social diffusion (see Labov Reference Labov2007; Ke et al. Reference Ke, Gong and Wang2008), which is treated in detail in Chapter 19. But we feel the need to clarify the fact that linguists face two different types of networks. Language is both a symbolic network with interconnected signs, as well as a social tool, with speakers who form a network among themselves. Propagation of innovations thus plays out on two tiers: social diffusion (i.e., conventionalization) external to the linguistic system and system-internal diffusion within the lexicon or the grammar. Say, a new formal mutant of a given signifié arises, for example, analytic perfect replacing the old preterite (e.g., French je suis été vs. je fus ‘I was’). The new variant has to spread over the lexicon, encroaching on an ever-expanding range of verbs (see Coussé Reference Coussé2014 for a case study on Dutch) but it also has to propagate through the community, with new speakers adopting the variant (Petré & Van de Velde Reference Van de Velde and Booij2018). The two kinds of propagation are not always well separated in the literature, and studies that integrate both are relatively rare (Schmid Reference Schmid2020).

9.2.2 Assuming Networks at All Linguistic Levels

In Construction Grammar, the network view pervades the whole language: Networks can be found in phonology, syntax, morphology, the lexicon, and pragmatics.

In essence, Figure 9.2 brings out the very basic idea of ‘co-activation’, that is, the simultaneous activation of phonetically, morphologically, and semantically similar words when expressing a target word. When a speaker utters cat, phonetically similar words like rat, hat (but also: categorize, catharsis, etc.) resonate in the background and may surface in mispronunciation of contaminations. With regard to morphological families, language users may extend or generalize suffixes to new hosts, reorganizing the constructicon (Coussé Reference Coussé, Van Goethem, Norde, Coussé and Vanderbauwhede2018). The underlying mechanism behind these links is analogy (Fischer Reference Fischer, Hancil, Breban and Lozano2018) and in Construction Grammar, this analogical process is known as ‘activation spreading’ or ‘spreading activation’, where the use of a construction primes semantically and phonologically similar constructions (Traugott & Trousdale Reference Trousdale2013: 54–58; Diessel Reference Diessel2019: 201). The mechanism works at the lexical level as well as at the syntactic level, both syntagmatically (Szmrecsanyi Reference Szmrecsanyi2005) and paradigmatically (Pijpops & Van de Velde Reference Pijpops and Van de Velde2016).

Figure 9.2 Networks at different levels of linguistic analysis

(Diessel Reference Diessel2019: 202)

9.2.3 Classification Schemes

Over time, several classification schemes for different types of links have been put forward. Early on, Goldberg (Reference Goldberg1995: 74–81) proposed the following four types of constructional links:

1. (1) instance links, existing between constructions of different degrees of specificity;

2. (2) polysemy links, which are posited between the prototypical sense of a construction and its extensions;

3. (3) metaphorical extension links, connecting a basic sense of a construction to a metaphorically extended sense; and

4. (4) subpart links, which hold between constructions of different degrees of complexity.

In recent years, other scholars have proposed more elaborate classification schemes to account for the different nature of connections between linguistic elements (e.g., Schmid Reference Schmid2020; Hilpert Reference Hilpert2021). For example, Diessel (Reference Diessel2019: 12f., 22) lists the following six relations:

1. (1) symbolic relations: associations between form and meaning;

2. (2) sequential relations: associations between linguistic elements in sequence;

3. (3) taxonomic relations: associations between representations at different levels of specificity;

4. (4) lexical relations: associations between lexemes;

5. (5) constructional relations: associations between constructions; and

6. (6) filler–slot relations: associations between particular items and slots of constructions.

A comparison between such classifications is outside the scope of this chapter. It is not always clear whether they aim at parsimony or exhaustiveness, and network classifications differ tremendously. Acknowledging this fact, we will present a two-dimensional network representation in which two main types of connections are being distinguished: vertical and horizontal – a basic distinction that can be found in most network sketches.

9.3.1 Different Types of Inheritance (Default Inheritance vs. Total Entry)

In current modeling, three different interpretations of inheritance exist for capturing vertical relations: the complete inheritance model, the default (normal) inheritance model, and the full entry (redundant storage) model. The debate revolves around the question whether constructional information is stored only once or redundantly. The complete inheritance model postulates that any information is represented non-redundantly at the highest possible level and then inherited by all lower-level constructions. This way of modeling is economical in the sense that the cognitive load is reduced by not storing information more than once (Kay & Fillmore Reference Kay and Fillmore1999). It is particularly scholars who subscribe to this model who are also open to postulating abstract, purely syntactic nodes high up in the network without semantic specifications (see Section 9.3.2). At the same time, this model of inheritance frequently employs the notion of ‘multiple inheritance’ (Section 9.3.3).

In the default (normal) inheritance model (Lakoff Reference Lakoff1987; Goldberg Reference Goldberg1995), only information from above which does not conflict is inherited: Lower constructions may block inheritance from above and contain more specific information. In contrast, the full entry model redundantly specifies all information in every node in the network. Similar to the default inheritance model, a lower node does not necessarily change when the higher nodes change (Croft & Cruse Reference Croft and Cruse2004: 262–279; Boas Reference Boas, Hoffmann and Trousdale2013: 245; Hilpert Reference Hilpert2014: chapter 3, Reference Hilpert2021; Barðdal & Gildea Reference Barðdal, Gildea, Barðdal, Smirnova, Sommerer and Gildea2015: 4; Dąbrowska Reference Dąbrowska2017).

Some constructional approaches (e.g., Berkeley Construction Grammar and Sign-Based Construction Grammar) favor the complete inheritance model due to its elegance and for reasons of parsimony (e.g., Fillmore Reference Fillmore1988; Michaelis Reference Michaelis1994; Boas & Sag Reference Boas and Sag2012). However, most scholars in CxG adopt a default inheritance model or a full entry model (Ginzburg & Sag Reference Ginzburg and Sag2000: 5–8). Especially Cognitive Construction Grammar or Radical Construction Grammar allow for redundancy in mental storage (Croft Reference Croft2001; Goldberg Reference Goldberg2006; Bybee Reference Bybee2010). This means that the same semantic or formal information can be stored in more than one construction. Even if speakers form a linguistic generalization, it is possible that they still store the same information more than once. This is seen as unproblematic because “memory is cheap and computation is costly” (Diessel Reference Diessel2011: 834). Whereas a complete inheritance model maximizes storage parsimony, a full entry model maximizes computing parsimony. With complete inheritance, the redundant storage of information is minimized. In the full entry model, as much information as possible is stored in multiple places, so that online computation is minimized (Barsalou Reference Barsalou, Lehrer and Kittay1992). Inheritance is a crucial network feature; still, it has to be investigated in much more detail (especially multiple inheritance, see below).

9.3.2 Emergence of Vertical Relations

Constructional networks – from a usage-based, cognitive point of view – are ‘constructed’ in a bottom-up fashion during language acquisition. The repeated usage of a particular construct leads to its successful memorization and entrenchment. At the same time, the speaker’s ability to detect similarities between constructs (i.e., realizations of constructions in language production) and his/her ability to abstract and to analogize lead to the generalization of more schematic constructions (Tomasello Reference Tomasello2003; Rowland Reference Rowland2014; Diessel Reference Diessel2019: 30–32).

The repetition of varied items which share formal or functional similarities can lead to the formation of a variable schema. For example, structures with a high type frequency, that is, patterns which occur with many different lexicalizations (e.g., John kicks the ball, Peter kisses Mary), still share a common, albeit abstract meaning, namely, {A affects B}. The repeated exposure to such constructs can lead to the generalization of the abstract, transitive argument structure construction [Subj V_tr Obj] (Goldberg Reference Goldberg2006: 39, 98–101; Schmid Reference Schmid2016: 10–12).

To provide another example for vertical relations, Figure 9.4 shows a partial sketch of a taxonomic hierarchy of deictic NPs with a common noun head in English.

Figure 9.4 Partial network sketch of deictic NPs in Modern English

(adapted from Smirnova & Sommerer Reference Smirnova, Sommerer, Sommerer and Smirnova2020: 21)

It is assumed that a child during his/her acquisition process, influenced by listening to many constructs including count nouns (CN) such as this doggie, this picture, this house, at one point recognizes and successfully stores the following semi-specific [[this]+[CN_sg]]_NPdef template, which corresponds to the meaning of {proximal singular entity}.Footnote ⁶ In a similar vein, the speaker will store the following form–meaning pairing: [[these]+[CN_pl]]_NPdef ↔ {proximal plural entity}.

The learner at one point will also conclude that this and these are both demonstrative markers of proximity, which presumably leads to the formation of an even more abstract schema [[DEM_prox]+[CN]]_NPdef. Once this node is in place and connected to the nodes below, information is inherited in a downwards manner. The learner establishes a similar relationship for distal demonstratives (that/those). This results in further abstractions/schematizations and linking and, ultimately, in the postulated network in Figure 9.4 (also see Hilpert’s Reference Hilpert2015 notion of ‘upward strengthening’).

9.3.3 Multiple Inheritance and Unification

Another design feature of the network is ‘multiple inheritance’ (henceforth also MI). This concept refers to constructions being instantiations of several higher constructions (Goldberg Reference Goldberg2003; Hudson Reference Hudson2007: 27–30; Van de Velde et al. Reference Van de Velde, De Smet and Ghesquière2013; Hilpert Reference Hilpert2014: 62–65). A particular construct (i.e., an actual expression) is usually the result of the parallel activation of several constructions. Note that this process has also been termed ‘fusion’, ‘unification’, or in some special cases ‘blending’ by other scholars (Herbst & Hoffmann Reference Herbst and Hoffmann2018; Hoffmann Reference Hoffmann2022). MI is a crucial feature for a slot-and-filler model of language which can ‘generate’ complex embedded linguistic structures. The term describes the fact that “any specific utterance’s structure is specified by a number of distinct schematic constructions” (Croft Reference Croft2001: 26). One construction can instantiate “several, successively more abstract constructions at the same time” (Hilpert Reference Hilpert2014: 63–65). Goldberg elaborated on MI already in 1995. Inheritance systems “may resemble tree diagrams if each child only has one parent, but in the general case they are ‘tangled’ and … this allows a given construction in the hierarchy to inherit from more than one dominant construction” (Goldberg Reference Goldberg1995: 73). On top of that, MI “allows us to capture the fact that instances of some construction type seem to resist being uniquely categorized in a natural way” (Reference Goldberg1995: 97).Footnote ⁷

For example, the sentence I didn’t sleep is an instantiation of both the ‘Intransitive Verb construction’ (a) [Sbj V_intranstive]_Cx and the ‘Negative construction’ (b) [Sbj Aux-n’t V]_Cx. As construction (a) does not provide any information about tense-aspect-mood or negation marking, this information is inherited from construction (b) and the sentence has multiple parents in the taxonomy of constructions which it belongs to (Croft Reference Croft2001: 26). Similarly, the ditransitive construction [Sbj V_ditr Obj₁ Obj₂], as in He gave her a book, only specifies the predicate with its arguments. It does not specify the presence or position of other elements in the utterance, such as modal auxiliaries or negation as in an utterance like He won’t give her the book. For such an utterance, the ditransitive schematic template sketched above only provides a partial specification of the structure and the utterance will need to inherit information from other schemas as well (Croft Reference Croft2001: 26).Footnote ⁸

Multiple inheritance also plays a role in ‘syntactic amalgams’ (for a detailed presentation of this phenomenon, see Chapter 11). Lakoff’s (Reference Lakoff1974: 321) example John invited you’ll never guess how many people to his party is the unification of a ‘complement clause construction’ and a ‘transitive construction’. Also, the syntactic amalgam The Smiths felt it was an important enough song to put on their last single is another elucidating example of MI. The ‘attributive adjective’-construction which is instantiated by an important song and the ‘enough to-infinitive’-construction intertwine (Hilpert Reference Hilpert2014: 63). MI can also be observed in the semantic, lexical, and conceptual domain in the sense that, for example, the concept [cat] inherits properties from both [mammal] and [pet] (Hudson Reference Hudson2007, Reference Hudson2010; Trousdale Reference Trousdale2013). This makes MI an important cognitive, psychological concept as well.

MI features prominently in constructional textbooks and handbooks (Hoffmann & Trousdale Reference Trousdale2013; Hilpert Reference Hilpert2014; Hoffmann Reference Hoffmann2022: 272–275), as well as in some detailed case studies (Michaelis & Lambrecht Reference Michaelis and Lambrecht1996; Fried & Östman Reference Fried, Östman, Fried and Östman2004; De Smet & Van de Velde Reference De Smet and Van de Velde2013; Trousdale Reference Trousdale2013). In general, however, constructional accounts “often remain silent when it comes to detailing the specifics of how different constructions interact” (Boas Reference Boas, Hoffmann and Trousdale2013: 244) and the workings of unification are still a slightly underdeveloped concept in CxG.

9.4.1 Types of Horizontal Links

The first kind of lateral links is drawn to establish the relations in a system of differential oppositions. This is an insight that goes back to structural linguistics: A constructional form–meaning pair can often be understood only by comparing it to formally related constructions that minimally differ. For example, the position of the main verb in continental Germanic languages like Dutch and German forms such a system. If the verb is placed in second position (V2), we have a declarative main clause. If the verb is placed at the end, we have a subordinate clause (V-late). If the verb is in first position (V1), we have a non-assertional context, like imperatives, questions, or an asyndetic conditional clause. This system is meaningful by its internal contrasts. This is visualized in Figure 9.5, where the various templates have been horizontally connected.

Figure 9.5 The position of the finite verb in Dutch clauses as a constructional network with horizontal relations

(Van de Velde Reference Van de Velde, Boogaart, Colleman and Rutten2014: 150)

We can also apply the notion of horizontal connections to the network diagram presented in Figure 9.3. There, all the semi-specific templates with the different possessive pronouns (my, your, her, …) can be linked horizontally as well. They are considered sisters which are paradigmatically related.

A second kind of lateral link, reminiscent of the differential opposition relation, are links between alternating constructions, like the prepositional dative and the double-object dative (a.k.a. the dative alternation). These alternations typically express near-synonymous meanings and are felt as belonging to a set (mostly a pair) – see for example Szmrecsanyi et al. (Reference Szmrecsanyi, Grafmiller, Bresnan, Rosenbach, Tagliamonte and Todd2017) and Pijpops (Reference Pijpops2020) – and can be thought of as ‘allostructions’ (Cappelle Reference Cappelle and Schönefeld2006). Evidence for lateral links between allostructions and between their slot-fillers comes from lexical biases (Perek Reference Perek2015; Pijpops Reference Pijpops2019): For example, in the dative alternations some verbs associate more with the double-object construction and other verbs are more likely to occur in the prepositional dative. Typically, the verbal slot-fillers within one of the variants will semantically cluster.

Allostructions are linked through super-constructions or ‘constructemes’. The abstract constructeme on the top layer in Figure 9.6 only encodes those elements that are shared by both variants; the horizontally connected allostructions on the lower level specify those details which make the constructions differ from each other, in this case the different particle (‘Prt’) placement in the variants pick up the book vs. pick the book up.

Figure 9.6 Cappelle’s superconstruction/constructeme

(Cappelle Reference Cappelle and Schönefeld2006: 18)

The difference between these allostructions and the differential oppositions, then, is that allostructions are related primarily through their meaning and the differential relations through their form. The distinction is not always clear-cut, though. One could argue that active vs. passive verbs form a paradigm but it is equally possible to see the opposition in terms of an alternation, with a meaning difference.

A third kind of lateral link is used to express the fact that constructions that bear a formal similarity exert influence on one another, in processes like analogization or constructional contamination (Lorenz Reference Lorenz2013, Reference Lorenz, Sommerer and Smirnova2020; Pijpops & Van de Velde Reference Pijpops and Van de Velde2016; Pijpops et al. Reference Pijpops, De Smet and Van de Velde2018), that is, the process whereby etymologically related or unrelated constructions formally influence each other. Hilpert and Flach (Reference Hilpert, Flach, Krawczak, Lewandowska-Tomaszczyk and Grygiel2022) give an elucidating example of this process in English: Adverbial modification of be-passives displays word order variation, with the adverb either in front of the participle (the book was widely read) or after the participle (the book was read widely). Different adverb–participle combinations alternatively prefer one or the other order. The preference is laterally influenced by the frequency of occurrence in another construction, namely, adverbially modified attributive participles, which almost exclusively occur in the preposed variant (a widely read book). These loose connections that can even be etymologically unwarranted show that linguists’ analyses may diverge from the associations in actual usage, which easily violate constructional boundaries. In that sense, ordinary speech has multifarious lateral connections that surpass the parsimony-driven approach in many computational implementations of Construction Grammar.

A fourth kind of lateral link expresses polysemy and metonymical and metaphorical links between related constructions. This is, in fact, the semantic counterpart of the third kind of lateral link just mentioned. Polysemy does not occur only in the lexicon but also at the level of morphosyntax. For instance, the different s-genitives in English do not all express possession in its strict sense but form a set of polysemous meanings. Suzanne’s car, Suzanne’s father, Suzanne’s habits, Suzanne’s downfall, Suzanne’s support, Suzanne’s height have a common denominator of ‘association’ as metaphorical extensions of pure possession, and the extension is even more pronounced in cases like yesterday’s events (Taylor Reference Taylor1989). These polysemous instances are linked to one another on the basis of their semantic association. The reality of such lateral links is evidenced by the fact that the extension can proceed stepwise, in lateral directions, instead of shooting off separately from the mother node. That is, the various extensions are not individually sanctioned by one central meaning, but one extension can lead to the next, from sister to sister, so to speak.

A full-fledged analysis is provided by Geeraerts (Reference Geeraerts, Van Langendonck and Van Belle1998) on the Dutch Indirect Object, from which we reproduce Figure 9.7. Here we see that the Indirect Object in its core expresses a beneficial transfer of a concrete object to a recipient (the circle in the middle), from which various extensions radiate. The nodes in this network are connected by links, representing lateral relationships. A lateral relation can be posited between the nodes that are not directly connected to the core meaning (encircled in the diagram). So ‘stative relations instead of transfers’ are a form of generalization of ‘preconditions and resultant states instead of transfers’.

Figure 9.7 Radially expanding polysemy in the indirect object

A fifth kind of lateral link exists ‘in praesentia’, that is, syntagmatically. This is the situation in which a meaning is expressed by several forms, for example, 2sg meaning marked as an inflectional ending on the verb and as a pronoun, as in Gumawana Komu ku-mwela ‘you 2sg-climb’ (Siewierska Reference Siewierska2004: 120–127). Redundant expression can also occur within one single word, as in the expression of past time reference by a prefixed ‘augment’ e- and a suffixed sigmatic marker -s- in Ancient Greek and Old Indic aorists (Ancient Greek é-lu-s-a ‘I unbound’). Such multiple exponence (Harris Reference Harris2017) or multiple expression of a grammatical category often goes under the rubric of agreement. This kind of lateral link may seem to install redundancy and as such to amount to a violation of the one-form-one-meaning isomorphism. On the other hand, this kind of lateral redundancy offers evolutionary advantages, making a system robust against perturbations and allowing for evolvability (Whitacre & Bender Reference Whitacre and Bender2010; Van de Velde Reference Van de Velde, Boogaart, Colleman and Rutten2014; Winter Reference Winter2014). For an example of evolvability, see Van de Velde (Reference Van de Velde and Booij2018) on the fate of the Indo-European ŏ-grade in Germanic.

9.4.2 Many-to-Many Mappings

The previous section introduced a number of different kinds of horizontal relations. As mentioned, the first two types (i.e., differential oppositions and allostructions) are related. Both have to do with alternating ways of expressing related signifiés but the former type is form-based and the latter type is meaning-based. As constructions are pairings of form and meaning, the interaction between differential oppositions and allostructions will typically yield a constellation of many-to-many mappings, which, like multiple exponence (see above) makes language systems robust and evolvable. To elucidate what we mean, the visualization by Van de Velde et al. (Reference Van de Velde, Maekelberghe and Fonteyn2021), introduced here as Figures 9.8 and 9.9, may shed light on the matter.

Figure 9.8 Symbolic relations and lateral differential relations. Solid lines denote symbolic relations; dotted lines denote lateral differential relations.

Figure 9.9 Synonymy in symbolic-and-lateral relations

In the representation in Figure 9.8, lateral relations between both functions and forms are recognized. Function_A could for instance be the expression of semantic roles (Function_Ai: agent; Function_Aii: patient; Function_Aiii: recipient; etc.). Form₁ could be different cases (Form_1i: nominative; Form_1ii: accusative; Form_1iii: dative; etc.). The lateral links between the constructions are the paradigmatic links. This is the situation in the case of differential oppositions.

For a full view of linguistic interaction, we need to acknowledge the second kind of lateral relationships introduced above, namely, those between the allostructions in a system of differential oppositions. In Figure 9.9, the diagram shown in Figure 9.8 is enriched by Form₂, an alternate expression of Function_A. Form₂ could be expressed by, for example, prepositions or by word order. The lateral connections between Form_1i and Form_2i are allostruction links. In the dative alternation, for instance (Bresnan et al. Reference Bresnan, Cueni, Nikitina, Baayen, Bouma, Krämer and Zwarts2007; Röthlisberger et al. Reference Röthlisberger, Grafmiller and Szmrecsanyi2017; Zehentner Reference Zehentner2019; among many others), Form_1i would be the alternant with the bare object and Form_2i would be the prepositional dative.

This is the situation in the case of synonymy. The reverse situation applies in the case of homonymy (pleiotropy), where one form is used for the expression of multiple functions. Often, however, we have a network where there are many-to-many mappings between forms and functions (see Van de Velde Reference Van de Velde, Boogaart, Colleman and Rutten2014 on ‘degeneracy’): One function, say, argument realization, may be expressed by different forms, say, a case system, prepositions, or word order, whereas these forms may play a role in the expression of different functions; the case system and the prepositions do not express only argument realization but also locative relations, and word order may be linked to illocution or information structure.

Weakening or strengthening the vertical many-to-many links between Forms and Functions, while maintaining the lateral links, is a way to keep differential oppositions in position in terms of language change. As such, a network view is useful for coming to terms with the way languages gradually change, which brings us to diachronic Construction Grammar and how it models language change.