1 Typology of Recursion

In this section, building on Roeper and Snyder (Reference Roeper, Snyder, Di Sciullo and Delmonte2005) and Roeper (Reference Roeper2011), we propose a new typology of recursion. In particular, three types of recursion are introduced, as in (6).

Roeper (Reference Yang, Roeper and Boeckx2011) has argued that Direct Unstructured Recursion (DUR) adjoins XPs in a linear manner, while Indirect Recursion (IR) introduces XPs in a hierarchical way mediated through an additional category YP.Footnote ² Direct Structured Recursion (DSR) is the new type of recursion proposed in this chapter and displays an intermediate complexity between DUR and IR in that XPs are introduced hierarchically, but not through an additional category YP. Although full theoretical formalization of this typology of recursion is beyond the scope of this chapter, syntactic behavior of each type of recursion is described below.Footnote ³

1.1 Direct Unstructured Recursion

Direct Unstructured Recursion (DUR) is the “default” type of recursion and adds an indefinitely large number of XPs in a linear manner without generating hierarchical structures. DUR would be formulated with the phrase structure rule (7).Footnote ⁴

(7)	Direct Unstructured Recursion:
	YP → YP XP*
	(where “*” means zero or more)

Example (8) instantiates DUR, where YP = VP and XP = PP, and what Langendoen et al. (Reference Langendoen, McDaniel and Langsam1989) call “coordinating.”

(8)	Put an apple [PP in the kitchen], [PP in the bedroom], and [PP in the balcony].

Semantically, DUR has a conjunctive interpretation. For example, example (8) means that each PP is individually predicated of the object “an apple” and PPs are not predicated as a unit (Chomsky Reference Chomsky2013). Consequently, DUR shows no compositional relationships among recursive XPs, so that permutation yields no semantic differences, as in (9).

(9)	Put an apple [PP in the balcony], [PP in the kitchen], and [PP in the bedroom].

Syntactically, since recursive XPs are coordinated in a linear manner, extraction out of them is impossible due to the Coordinate Structure Constraint (Ross Reference Ross1967), as in (10).

(10)	*What did John put an apple in the kitchen, in the bedroom, and in <what>?

In sum, DUR is semantically conjunctive and syntactically linear. This type of recursion is equivalent to “parataxis” in non-literate languages observed by Hale (Reference Hale and Dixon1976), Everett (Reference Everett2005, Reference Everett2009), and Evans and Levinson (Reference Evans and Levinson2009). This corroborates the view that DUR is the “default” type of recursion available universally and predicts that children begin with producing and comprehending recursive XPs as DUR.

1.2 Direct Structured Recursion

Our initial observations in Pirahã and English all motivate this second new type of recursion: Direct Structured Recursion (DSR), which appears similar to DUR but quite different in involving hierarchical structure, rather than linear structure. The phrase structure rule responsible for DSR can be formulated as in (11).

(11)	Direct Structured Recursion:
	XP[+F] → XP[+F] XP[+F]

Unlike DUR, the phrase structure rule is binary and crucially generates hierarchical structure; namely, more than two sisters are impossible. This is achieved by the shared feature [+F] between XPs (Chomsky Reference Chomsky2013). Typical examples of DSR are what Langendoen et al. (Reference Langendoen, McDaniel and Langsam1989) call “stuffing” (12), where XP = PP.

(12)	a.  Put an apple [[[PP in the house] [PP in the kitchen]] [PP in the cabinet]].Footnote 5
	b.  Bill saw Mary [[[PP on Saturday] [PP in the morning]] [PP at nine]].

DSR, unlike DUR, is semantically compositional. For instance, in the example (12a), three PPs are jointly predicated of the object “an apple,” but PPs do not modify the preceding NPs (i.e., the house is not in the kitchen). In other words, PPs collectively saturate the obligatory locative argument of “put” and can be interpreted in a single event, unlike example (8). Similarly, in example (12b), three PPs together express one specific time (i.e., Saturday is not in the morning). Therefore, in contrast with DUR, permutation of recursive XPs does affect semantic interpretations, making the example ungrammatical or at least infelicitous, as shown in (13).

(13)	#Put an apple [[[PP in the cabinet] [PP in the house]] [PP in the kitchen]].

Importantly, extraction out of DSR is possible, indicating that PPs here must be hierarchically organized and not coordinated in a linear manner.

(14)	What did John put an apple in the house in the kitchen in <what>?

This observation is reminiscent of asymmetric coordination, where extraction is generally permitted (Nonato, this volume). In summary, DSR is different from DUR in that the former is compositional and hierarchical, while the latter is conjunctive and linear, as revealed by permutation and extraction facts. Nevertheless, DSR and DUR are similar in that both can stack adjacent identical XPs without an intervening category YP. This “direct” nature distinguishes DSR and DUR (i.e., recursion by one rule) from the third type of recursion (i.e., recursion by two rules), to which we now turn.

2 Acquisition Path of Recursion

In this section, we explore the psychological reality of the proposed typology of recursion by showing that three types of recursion are reflected in the acquisition path of recursion. Since those types of recursion differ in syntactic complexity, the following time course of acquisition is predicted by the theory:

Furthermore, this particular order of the acquisition path is quite natural under the theory of the acquisition engine with automatic self-revision (Roeper Reference Roeper2014). Since adjacent identical XPs attested in Direct Unstructured Recursion and Direct Structured Recursion are not preferred by the “anti-identity” condition (Leivada Reference Leivada2015), the acquisition engine seeks to revise those dispreferred types of recursion to Indirect Recursion, which does not involve adjacent identical XPs. One consequence is that some speakers find “put the jar on the table in the box” (Direct Structured Recursion) to be worse than “put the jar in the box on the table” (Indirect Recursion), which is actually the case from informal investigation.

3 Recursion in Pirahã?

Everett (Reference Everett2005) has argued against Hauser, Chomsky, and Fitch (Reference Hauser, Chomsky and Fitch2002) that Pirahã lacks sentential embedding, one major instance of IR, arguing instead that recursion is not universal but rather cultural in nature. However, Sandalo et al. (this volume) carefully show with various experimental tasks that Pirahã does have PP recursion, another instance of IR. Again, in the acting-out experiment, the following example of IR was first presented and understood perfectly by the monolingual speaker of Pirahã:

Interestingly, in spontaneous production, that Pirahã speaker inverted the order of two other PPs, creating DSR:

This fact not only serves as a strong existence proof of PP recursion in Pirahã, but also squarely fits with the theoretical claim that DSR is less complex than IR.

Critical independent confirmation came in the elicitation experiment reported by Sandalo et al. (this volume), where the following example of IR was elicited:

Here there are two verbs, main xihi ‘store’ and auxiliary ho ‘be,’ but there is only one tense marker on the auxiliary verb, which crucially rules out the possibility of parataxis, contrary to Everett’s (Reference Everett2005) claim.

In addition, DUR occurs in Pirahã, as expected under the view that DUR is the default and simplest mode of recursion:

This example is interpreted by the Pirahã speaker conjunctively, not compositionally, and requires the conjunct piai ‘and’ exactly as in English.

It follows that Pirahã does have recursion, at least in the domain of PP. But what about the alleged absence of recursion in the domain of CP? In fact, Sauerland (this volume) and Rodrigues et al. (this volume) have shown that Pirahã also does have recursion in the domains of CP (sentential embedding) and VP (obligatory control). In addition, Salles (Reference Salles2015) has shown that recursive possessives are found in Pirahã as well:

Even without these pieces of evidence, the lack of recursion with specific categories is not surprising. As articulated by Watumull et al. (Reference Watumull, Hauser, Roberts and Horstein2014), the absence of recursion in particular domains simply means that there are some lexically specific constraints, not the absence of recursion in the grammar itself. For example, as documented by Roeper (Reference Roeper2011), German lacks recursive possessives as in (34).Footnote ⁷

In the same vein, there are no recursive compounds in Romance languages, no recursive prenominal adjectives in French, no recursive serial verbs in English, no sentential embedding in Warlpiri, and so on. In this light, the alleged absence of recursion in Pirahã is simply explained away by lexically specific constraints. From the acquisition perspective, this fact entails that children should not automatically extend recursion in one domain to another without language-specific experience; otherwise, impossible recursive XPs would be over-generated.

We also note that these results do not match the domain-general approach to recursion: for those who consider recursion to be domain general and not specific to human language (Corballis Reference Corballis2011), then lexically specific constraints on recursion are not expected, as in German recursive possessives. If recursion is derived from cognition outside human language, why are there language-specific constraints on the depth of recursive possessives? All of these linguistic arguments are incompatible with the claim that recursion is a domain-general capacity that is applicable across all forms of cognition.

4 Conclusion

Our proposal for how recursion is represented with the three primary types of recursion – beyond Merge – reflects increasing structural complexity. They are in turn reflected in the acquisition path: (1) DUR, (2) DSR, and (3) IR. We have found preliminary suggestive evidence at every possible data point (introspective acceptability judgments, child spontaneous production, child laboratory comprehension, electrophysiological measurement) to support our perspective (though much remains to be carefully explored).

The history of the generative enterprise has had enormous success in demonstrating that principles of grammar serve to describe grammars of natural languages around the world. The fact that the same experimental methodologies can be applied across Brazilian languages with parallel questions and comparable results strongly supports this enterprise. This not only provides important evidence for theoretical assumptions, but also demonstrates that experimental techniques developed in language acquisition can naturally transfer to fieldwork. Despite the diversity of languages, histories, cultural circumstances, and social environments, deep universal principles of grammar emerge repeatedly with surprising clarity.

1 Introduction

Our specific goal in this chapter is to use experimentation developed in acquisition work to identify the presence of self-embedding recursion in Pirahã.Footnote ¹ Our broader goal, in concert with other chapters in this volume, is to jointly explore formal theoretical issues and extend experimental methodology to indigenous languages. We shall provide evidence that recursive self-embedding is present in Pirahã PPs and explore the consequences for the larger tapestry of recursive structures in human language in general. As a result, we reconsider the provocative claim by Everett (Reference Everett2005, Reference Everett2009, Reference Everett2012) that Pirahã lacks recursive syntactic structures altogether, showing that this view most likely results from a misunderstanding about the underlying grammatical system of Pirahã.

2 Recursion Types

The universal form of Merge has been defined by Chomsky (Reference Chomsky2013) in the following terms:

That is, recursive Merge refers here to a structure-building algorithm where only set formation ({α,β}) is combined, without a built-in label assigned to nodes.

In this recursive procedure, every step in structure-building is an operation of Merge that takes as its input (α and β) two lexical items and merges them, delivering as its output a more complex object ({α,β}). In the next step, Merge may take a new phrase as input and combine it with the complex object formed in step 1.Footnote ⁴

When we turn to self-embedding recursion, it is easy for us to conceive it in terms of node labels, which abstractly are maximal projections, represented as XP or YP, projected from heads, as X or Y. From there, we can differentiate three types of structures with rules that operate upon labelled nodes. Each entails a different formal representation, although their ideal formal representation will no doubt undergo further evolution. Snyder and Roeper (Reference Roeper and Snyder2004) and Roeper (Reference Roeper2011), building upon work in computer science, have identified Direct Recursion (DR) and Indirect Recursion (IR). Roeper and Oseki (this volume) have further divided Direct Recursion into Direct Unstructured Recursion (= Conjunctive) (DUR) and Direct Structured Recursion (DSR).Footnote ⁵

DUR delivers a conjunction, which can be generated in accordance with the rewriting rule in (4a):

The signature characteristic of DUR can be represented as in (1) and it is interpreted as conjunction or “and.”

Everett (Reference Everett2005) calls this elementary form “parataxis,” and claims that all phrases in Pirahã are interpreted in this straightforward way. Arsenijević and Hinzen (Reference Arsenijević and Hinzen2012)Footnote ⁶ suggest that this default form actually lies outside of grammar itself and it applies to every structural level (XP-level, sentence-level, word-level).Footnote ⁷ Classic evidence for this kind of structure comes from forms like (4b), where order has no interpretive effect and little evidence of binary structure is present:

A second form of recursion, Indirect Recursion, involves an extra derivational step, or an extra rewriting rule (5):

According to this, a category Z may emerge from the combination of other categories. In this second step of the derivation, X, created in step 1, is optionally re-introduced, resulting in a structure with self-embedding or “mutual recursion” in some accounts. The core forms of self-embedding in grammar are expressed through IR because they entail interpretive dependencies. An interesting case for the present discussion is DP-PP recursion (6), where PPs are introduced within DPs, creating a loop:

This can produce forms like (7) (marking the maximal projections: DP, NP, PP):

In (7), we have a cascade of referential DPs containing a NP with a PP specifying the reference of the DP. This means that the DP the jar is defined by the PP on the shelf, and the shelf is defined by the PP in the closet, which is further defined by the PP in the kitchen. The significant fact here is, ultimately, the complex way in which recursion controls reference or interpretation dependencies. Pérez-Leroux et al. (this volume) provide discussion of the syntax/semantics interface entailed by this type of structure.

A third form of recursion involves linked or “stacked” PPs or relative clauses and has been called feature-sharing by Chomsky (Reference Chomsky2013). Roeper and Oseki (this volume) call it DUR because it is formed in accordance with the rules in (6), in which a category PP emerges from merging a PP with a *PP, but the result involves referential dependencies and structural domination. This is best illustrated through VP recursion

(notation adapted from traditional Kleene* system):

It is evident in cases of phrases describing motion following a path:

It can also generate examples like (10) with order opposite to (7):

Notably these forms allow wh-extraction, which requires c-command:

(10) and (11) involve a series of locative interpretations dependent upon each other, and is, therefore, not conjunctive, as it would be for (12), where conjunction would allow multiple jars to be placed:

Therefore, DUR behaves syntactically and semantically differently from DSR, as in (13):

The PP* shares the [+LOC feature] and represents one argument of the verb ‘put.’ It also reflects the direction of motion and the fact that a single action of putting is usually entailed. That is, one does not first put the jar in the kitchen, then move it into the closet, and then move it onto the second shelf.

IR

through DP, however, is the more common form:

Or a more fully expanded DP:

Roeper and Oseki (this volume) show very early spontaneous use of PP recursion in language acquisition, which suggests that it is less difficult for a child to recognize it. Maia et al. (this volume) also observe that DUR is a more accessible default form, which does not exclude the presence of Indirect Recursion.

3 Pirahã Recursion

Now we have to adjust our structures to account for the left-branching nature of DP-PPs in Pirahã. The structures run the opposite way, but with the same relations:

Based on the example in (16), where hio apo likely represents a complex preposition akin to English into, we could represent the internal structure of the DP in (16) as in (17):

What would happen to the internal structure of the construction if Pirahã accepted multiple PP embedding? The example above suggests that should Pirahã speakers be able to understand multiple embedded PPs under DUR, then sentences like the one in (18) would be preferred over IR, as it is along the acquisition path from DUR to DSR to IR. The left-branching reverses the order: ‘coin on paper on chair on board’ to ‘on board on chair on paper coin’:

Notice that the sentence in (18) allows for a representation following the Indirect Recursion example presented in (15) above for English. The main distinction would be based on the fact that Pirahã is a head-final language, which would give us the structure in (19):

This also allows PP DUR with the implied conjunctive ‘and.’ If PP DSR is available in Pirahã, then speakers would be able to interpret DPs like those in (20), with the structure in (21):

We should, therefore, seek all three forms of recursion in Pirahã, although it is conceivable that Indirect (and, consequently, Structured) Recursion might be less evident, since it seems to be rarer among languages in general. Nevertheless, as we shall see, there are indications that they are all present. It might be that Pirahã blocks some forms of IR, as so many languages do. For instance, it is impossible to have recursive possessives in German (of the type, ‘John’s friend’s father’s house’), but Franchetto (this volume) and Lima and Kayabi (this volume) find them in Kuikuru and Kaiweiwete, respectively. Pirahã also allows recursive possessive DPs as shown in Salles (Reference Salles2015), who collected data containing three levels of self-embedding within possessive DPs. Can we predict where this type of recursion will be found? It is not obvious where one should look, and in fact any language might have a form of syntactic recursion never seen before. For Pirahã, in addition to sentence recursion, PP recursion is a natural choice to investigate.

Thus far, there are no known criteria for what links recursive structures in a given language, but it is very noticeable that, although English has both left and right-branching recursion, Romance languages with SVO structures appear to favor right-branching, while languages with SOV structure allow more left-branching recursion. The question of whether different forms of recursion are linked typologically and along the acquisition path is the next frontier in this research.

3.2 Pilot Study 1: Teasing Direct and Indirect Recursion Apart

Method: Participants, Materials, and Design

  Iaoá and Yapohen Pirahã, our participants, are native speakers of Pirahã with no apparent knowledge of Portuguese. They were exposed to a series of six pictures, like the ones shown in Figure 15.1, and after hearing a sentence in Pirahã (pronounced by one of the experimenters) they were expected to point towards the picture that best fit the description provided in the sentence.Footnote ¹⁴

Figure 15.1 Pictures in pilot study 1

Pictures 1 to 6 in Figure 15.1 were borrowed from Maia (Reference Maia2012) and Maia et al. (this volume) and were crucial to this experiment, as they visually describe the following grammatical possibilities:

i.	No recursivity or coordination of PPs (pictures 3 and 4)
	alligator on the beach on the stone   =/=> not on stone on the beach (picture 3)
	=/=> not on stone and beach

ii.	Coordination of two PPs (picture 1)
	alligator on stone on beach => alligator on stone and on the beach

iii.	Coordination of three PPs (picture 4)
	alligator on blanket on stone on beach => on blanket and on a stone and on a beach

iv.	Recursivity of two PPs (picture 2) (pictures 1, 2, 4, 5)
	alligator on stone on beach = alligator is on the stone that is on the beach

v.	Recursivity of three PPs (picture 5)
	alligator on blanket on stone on beach = alligator that is on the blanket that is on the stone that is on the beach

We started the procedure with lexical elicitations. Each of the objects composing the pictures in Figure 15.1 was first introduced to the speakers, and the corresponding lexical items were elicited. Then, we pointed to each picture and asked the speaker to describe it for us. Note that it was mandatory for this study that a picture representing direct and IR (e.g., pictures 5 and 6) be shown together in contrast to highlight a minimal pair.

Through controlled elicitations, we collected the following target sentences where apo ‘on’ re-appeared with reference to recursive pictures.

(24)	a.	koxoahai   bege   apo   xaxai apo
		alligator   floor   on     stone on
	b.	koxoahai   bege apo xaxai   apo    tahoasi apo
		alligator    floor on stone     on   mat      on

The second part of our procedure was an interpretation task, which reversed the tasks done in the first procedure. The experimenter pronounced out loud each one of the elicited sentences to the participant, and asked him to show the situation (a picture in Figure 15.1) described by the sentences he heard. This was done sentence by sentence, situation by situation, and the trials were randomly ordered in order to prevent saturation.

If the participant treated the target sentences in (24) as involving conjoined PPs, then he was expected to point towards picture 1 or 4. If, however, the prepositional phrases were treated as a case of self-embedding, then the participant should point towards either picture 2 or 5.

3.3 Results and Discussion

The results of this first experiment suggest that Pirahã speakers are able to process, comprehend, and differentiate ambiguous prepositional phrases. The speaker consistently paired the target sentences with the recursive pictures, as shown in the following:

To describe pictures with coordination, the speaker modified the target sentences, introducing an additional word, piai, a coordinative particle translated as ‘also’ by Everett (Reference Everett1990).Footnote ¹⁵

These results clearly show that Pirahã speakers are capable of teasing coordination and recursion apart. It suggests that the target sentences, (24a) and (24b), might not even be ambiguous. If they are, however, the results presented here indicate that: (a) a recursive structure (IR) is available for these sentences; (b) speakers have a preference for treating (24a) and (24b) as containing IR PPs; and (c) the ambiguity is resolved by inserting an overt conjunction, reinforcing a coordinative reading.

In formal terms, we conclude, thus, that Pirahã, similar to English, Portuguese and many other known languages, has both DUR (Direct) and IR.

3.4 Pilot Study 2: Spotting Indirect Recursion

Methods: Participants, Materials, and Design

This test followed test 1. Iaoá was our only participant. The test consisted of an acting-out game, with the participation of two players. The player in charge would give commands that the other had to execute. The picture (Figure 15.2) shows one of the scenarios involved in the activity. Two chairs were placed on the floor, one above a wooden board. There were two cups, one placed on the wooden board, and the other placed on the chair, which was placed on the wooden board.

Figure 15.2 A scene from pilot study 2 in which the experimenter gives commands to the participant

As in the first test, we started with lexical elicitations. Each of the objects composing the scene above was first introduced to the speakers, and the correspondent lexical items were elicited. Then we executed actions of putting coins in/on different objects present in the scene. This procedure allowed us to elicit target sentences, such as (25), which describes a scene in which a coin is placed inside the cup on top of the wooden board to the left and another coin is placed on the blue chair to the right, and (26), which describes a scene in which a coin is placed inside the cup on the chair on the wooden board.Footnote ¹⁶

(25)	ihiaipati   gigohoi   kopo   ko   tiapapati   apo   piai
	put         coin      cup      in    chair             on       also

(26)	ihiaipati gigohoi   kopo ko   tiapapati   apo
	put          coin            cup       in       chair         on

Once the participant felt comfortable with the game, we changed the scenario to include situations involving three pieces of paper, one sitting on the top of the chair placed on the wooden board, one on the top of the other chair, and another one on the wooden board. This scene allowed us to test the following target sentences:

(27)	ihiaipati   gigohoi kapiiga apo   tiapapati     apo   (piai)   tabo   apo   piai
	put         coin    paper   on    chair         on    (also)   board  on     also

(28)	ihiaipati   gigohoi   kapiiga   apo   tiapapati   apo     tabo   apo
	put         coin       paper      on     chair        on      board on

These four target sentences are samples of the following type of structures:

(29)	a.	Coordination of two PPs	(25)
	b.	Recursivity of two PPs	(26)
	c.	Coordination of three PPs	(27)
	d.	Recursivity of three PPs	(28)

In the first part of the game, the experimenter provided the participant with a handful of Brazilian coins, and asked him to put coins in different places. The commands were the target sentences in (25)–(28).

In the second part of the game, the roles of the participants were reversed, and Iaoá became the one in charge. He provided the experimenter with a handful of Brazilian coins and gave him commands about places to put the coins. This procedure allowed us to verify if Pirahã speakers were capable of comprehending and producing structures with multiple levels of PP embedding. Thus, similar to the first experiment, this experiment was originally designed to examine the availability of Direct (Unstructured Recursion) versus Indirect Recursion.

4 Conclusion

These pilot studies constitute informal, experimental evidence that Pirahã allows recursive syntactic structures of three types. Once again, the speakers who participated in our pilot studies demonstrated no difficulties in comprehending and producing self-embedding postpositional phrases (IR), in contrast to conjunctive, or paratactic, structures, which Everett claimed were the only available structures.

Although Everett’s strong claim (Reference Everett2005, Reference Everett2012) is not upheld, it had the merit of provoking fruitful discussion on Pirahã grammar and recursion in general. Based partly on data published by Everett and Nevins, Pesetsky, and Rodrigues (Reference Nevins, Pesetsky and Rodrigues2009b) developed an interesting cross-linguistic study, showing that Pirahã is in no way exceptional with respect to recursion.

Their work has now initiated new fieldwork beyond this study, as has the work by Sauerland (this volume) for sentential self-embedding and Rodrigues, Salles, and Sandalo (this volume) for self-embedding VPs in control configurations. Silva (Reference Silva2014), looking at constructions with focus and topicalization, points out that movement is possible out of self-embedding/recursive PPs, in contrast with coordinated PPs. Additionally, Salles (Reference Salles2015) demonstrates clear cases of recursive possessive DPs. The studies here and throughout this book demonstrate that the extension of acquisition experimentation to fieldwork is quite straightforward. It has created a new vista of possibilities for experimental fieldwork.

As such, support for UG has emerged from fieldwork with isolated indigenous languages. With such compelling support, we maintain that the same type of complex grammatical phenomena and formal constraints upon them are found in all known languages in the world.

1 Simplicity and Complexity in Children’s Language

Children’s early utterances lack complexity (Brown and Hanlon Reference Brown, Hanlon and Hayes1970; Brown Reference Brown1973; among others.). Much of the process of development can be described as growth of complexity, and much of it might be due to growth of processing capacities (Bloom Reference Bloom1990). Complexity itself, however, has not been given a coherent definition in acquisition. It has been operationalized in terms of mean length of utterance (MLU), subordination, or diversity of grammatical markers and constructions in children’s sentences. All of these phenomena correlate with complexity but are distinct from it. Alternatively, complexity has been described in terms of derivations and locality conditions (Friedmann, Belletti, and Rizzi Reference Friedmann, Belletti and Rizzi2009; Friedmann and Costa Reference Friedmann and Costa2010; Jakubowicz Reference Jakubowicz2011).

Utterance length provides a limited perspective on the development of complexity in child language. Modified NPs can illustrate precisely why this is so. At the age of five, most children have MLUs that roughly approximate those of adults (Brown Reference Brown1973); yet, their spontaneous and elicited speech seems to lack NP modification. Complex NPs in child language have low productivity. Until the age of five, NPs consist mostly of single, unmodified nouns. PPs and adjectives are commonly produced, but rarely in NP-internal position. Eisenberg et al.’s (Reference Eisenberg, Ukrainetz, Hsu, Kaderavek, Justice and Gillam2008) analysis of narrative samples shows that less than 60 percent of English-speaking 5 year olds produce any nouns modified by a PP (e.g., aliens with legs). NP-internal adjectives (e.g., the yellow ball) are more common (around 80 percent of children). Double adjectival modification (e.g., big yellow thing) is not (25 percent of 5 year olds). Full productivity with nominal modification is achieved in the school years. According to Eisenberg et al., 11 is the age when most children are able to use PP modifiers and double adjectival modifiers in elicited narratives. Recursive PP modifiers such as those targeted in this study are altogether absent.

This observation cannot be explained in terms of functional development. Possession (sister > Elmo’s sister) and modification (dog > big dog) are among the earliest semantic primitives identifiable in children’s speech (Bloom, Lightbown, and Hood Reference Bloom, Lightbown and Hood1975). The grammatical connectors (such as genitive ’s and prepositions) are learned early in many languages (Brown Reference Brown1973; Hernández Pina Reference Hernández Pina1984; Aguado Reference Aguado2000; Eisenbeiss Reference Eisenbeiss, Rizzi and Friedemann2000), but there is a lag between their first uses and their use as NP-internal modifiers. It seems unlikely that 5-year-old children do not understand the grammatical function of modification. NP modification is a response to specific referential demands. Young speakers are sensitive to context when deciding to produce modification. Nadig and Sedivy (Reference Nadig and Sedivy2002) found that 5 year olds produced adjectives (the small glass) only when a referential competitor was present in the context (for instance, a large glass). Children also demonstrated their ability to use adjectives according to the referential perspective of their conversation partners.

There are various accounts of how structural complexity develops in children, mostly focused on the acquisition of sentence subordination. Diessel and Tomasello (Reference Diessel and Tomasello2001) and Diessel (Reference Diessel2004) argue that structural complexity grows through expansion. From a usage-based perspective, these authors propose that in children’s early subordinates (such as I think my Daddy took it (Sarah 3;07), I bet I can (Sarah 3;09)), the main verb acts as an epistemic or deontic marker for the second proposition. Under this view, early subordinates are not considered biclausal. Later, children learn that matrix and embedded verbs belong in separate clauses. Thus, development from a monoclausal to a biclausal structure proceeds through analysis. Other perspectives focus on children’s use of appositive sequences in lieu of sentences with more complex structure. Children are known to produce unintegrated clauses linked by a coordinating use of the complementizer, in lieu of object relatives, as in (3).

Under the alternative accounts, development proceeds by synthesis, i.e., by the grammatical integration of paratactic configurations over time (Abbedduto and Rosenberg Reference Abbeduto and Rosenberg1985; Lebeaux Reference Lebeaux1988; Givón Reference Givón2009).

Examining the same data as Diessel and Tomasello (Reference Diessel and Tomasello2001), Givón (Reference Givón2009) reached the opposite conclusion. In his account, the first step in syntactic development is for single words to combine by fusion into simple clauses. Next, simple clauses combine into clausal chains, linked paratactically. Finally, clausal chains become proper embedded clauses, which are hypotactically linked. This proposal is not that different from work by Lebeaux (Reference Lebeaux1988, Reference Lebeaux2000), within the generative framework, identifying parataxis as a precursor to embedding. Lebeaux proposed that at some early stages, children’s representation of complex clauses does not necessarily involve structural subordination. When their analysis of a complex structure fails, they resort to a default conjunction operation. According to Lebeaux, these two operations (adjoin and conjoin) describe the course of development, as well as the distinction between languages with DP internal relative clauses and languages where relatives are peripheral to the main clause, as in the Hindi correlative construction.

The emergent literature on recursion in children suggests that depth of embedding is constrained. According to Roeper and Snyder (Reference Roeper, Snyder, Di Sciullo and Delmonte2005), children do not use recursive NPs in spontaneous interactions or understand them in parental speech. Comprehension experiments confirm this for a range of recursive structures, including locatives (Up on the shelf in the closet in the kitchen), compounds (Christmas tree cookie), and possessives (Roeper Reference Roeper2011; Limbach and Adone Reference Limbach and Adone2010; Amaral and Leandro Reference Amaral and Leandro2013). In one sense, it is natural that children have to learn the recursive step, given that languages vary as to which categories iterate (Roeper and Snyder Reference Roeper, Snyder, Di Sciullo and Delmonte2005). A language can have a form of embedding while blocking further self-embedding of that category. For instance, German has a possessive marker that is historically related to the English Saxon genitive. The English case is recursive (John’s friend’s father’s hat), but the German is not (Marias Haus, *Marias nachbars Haus; Roeper Reference Roeper2011). Similarly, Spanish noun-noun compounding (mujer araña ‘spider woman’) only happens once (*mujer araña móvil ‘spider woman mobile’). Such variation indicates that, although a fundamental feature in language, recursion must be learned beyond the initial step of acquiring the connectives (Roeper and Snyder Reference Roeper, Snyder, Di Sciullo and Delmonte2005; Roeper Reference Roeper2011; Pérez-Leroux et al. Reference Pérez-Leroux, Castilla-Earles, Béjar and Massam2012). Acquisition evidence such as in Terunuma and Nakato (this volume) supports the idea of recursion as a distinct step in acquisition.

The only production study to date supports available comprehension data. Pérez-Leroux et al. (Reference Pérez-Leroux, Castilla-Earles, Béjar and Massam2012) elicited recursive possessives (4) and PP modifiers (5) in children between the ages of 3 and 5.

Adults used recursive PPs quite frequently, but few children did. One third of the children under 5 could produce the first level of NP embedding. Second-level embedding appeared after 5, with only 43 percent of children at that age producing them. Children often understood the referential demands of the task, producing elaborate answers that expressed the desired meaning but which lacked recursive syntax (This baby, look, the mother got flowers). Coordinate structures, however, were easy to produce even for the youngest children.

2 The Question of Performance: PP Attachment Ambiguities, Processing, and Children

Understanding embedding problems in children can make use of a body of work on children’s comprehension of temporarily ambiguous PP structures. Children fail to reanalyze garden-path sentences such as (6) (Trueswell et al. Reference Trueswell, Sekerina, Hill and Logrip1999), but have less difficulty with their unambiguous counterparts, as in (7):

Sentences such as (6) are temporarily ambiguous. At the moment in which listeners hear the first PP (on the napkin), they might treat it as the goal of the motion verb put. As the sentence progresses and the second PP (in the box) is heard, adult listeners realize that the first PP is in fact a modifier within the direct object NP (the frog on the napkin). Children behave unlike adults both in explicit action (which object they reached to move), and in their patterns of looking preferences to one referent or the other. With temporarily ambiguous sentences, looking preference data suggest that children maintain the high attachment of the initial locative PP as goal argument to the ditransitive verb put, and fail to correct this interpretation. The presence of a second frog in the context allows adults to treat the first PP as a modifier and converge faster on the target frog. It makes no difference for children, who continue to assign a goal interpretation to the first PP. Furthermore, children persevere in this initial incorrect parsing to the extent that in 60 percent of the trials they actually ignore the second PP and go on to perform the action of moving the frog to the napkin.

Trueswell et al. (Reference Trueswell, Sekerina, Hill and Logrip1999) interpret the data within a constraint satisfaction framework. They propose that children’s parsing problems relate to their inability to coordinate lexical and contextual cues. They reject the possibility that children’s performance could be based on structural economy strategies such as the Principle of Minimal Attachment (Clifton, Speer, and Abney Reference Clifton, Speer and Abney1991). Subsequent work has pointed out that these effects can result from either minimal attachment or early overreliance on lexical cues (the ditransitivity of put). To disambiguate the two possibilities, Snedeker and Trueswell (Reference Snedeker and Trueswell2004) subsequently studied how lexical verb bias affected PP attachment.

Children remained biased towards instrument (high-attachment) responses. However, the effect appeared only with instrument-bias and equipollent verbs. In other words, children’s high-attachment preference does not override lexical constraints. The high-attachment preference is thus due to ignoring the contribution of the referential context. Snedeker and Trueswell (Reference Snedeker and Trueswell2004) concluded that children do not show a general preference for high attachment, but over-rely on lexical cues.

Kidd, Stewart, and Serratrice (Reference Kidd, Stewart and Serratrice2009) explored how the structural distance between ambiguity point and target constituent affected children’s errors. For this purpose, they combined verbs with high bias for instruments (such as to cut), with potential instruments of low plausibility (such as a candle):

Adults allowed both interpretations, realizing that with a candle could function as either modifier of the cake or as instrument for cutting. Children looked at the plausible instrument at the initial region of the sentence and again at the end. They also followed up with using the final NP as instrument. Kidd, Stewart, and Serratrice (Reference Kidd, Stewart and Serratrice2009) did not consider minimal attachment as a possibility, concluding instead that children favor high attachment because they over-rely on bottom-up, lexical cues for interpretation. They favored a probabilistic parser model, that relies on multiple comprehension cues from the start, while acknowledging that not all cues are present or are as strongly represented at the outset of language development. Snedeker and Trueswell (Reference Snedeker and Trueswell2004) carefully noted that such theories, unlike general domain theories of cue competition, assume representational modularity. Semantic, syntactic, and phonological information are independently represented, but are available to interact with other sources of information.

Meroni and Crain (Reference Meroni and Crain2011) objected on the grounds that this violates continuity. They proposed that children are sensitive to the same referential and thematic constraints that guide adult parsing, but are unable to revise an analysis once started. Because children’s responses are less automatic than adults’, due to their lesser verbal memory capacities, they tend to act out parts of the analyses generated before all planning is complete (see McDaniel, McKee, and Garrett Reference McDaniel, McKee and Garrett2010). Meroni and Crain’s experiments demonstrated that as long as children are forced to process the entire sentence before acting, they can treat the first PP as modifier.

3 Articulating the Challenge of Recursion: Acquisition, Processing, and Theory

The previous section suggests that children can acquire different components of a grammatical system without putting their full power to use. By the age of four, children have a strong grasp of syntax, including the ability to use a variety of pre- and post-nominal modifiers, and to produce multi-clausal sentences. However, at that age, children still process complex structures differently from adults (Snedeker and Trueswell Reference Snedeker and Trueswell2004). The processing evidence has been attributed to differences in the ability to integrate various sources of knowledge. However, it is still the case that, beyond the lexical facts, children produce more high-attachment responses overall. This is compatible with the view that children have a minimal attachment bias and that such bias is driven by processing economy. Within the range of possibilities given by lexical constraints, children consistently choose VP attachment at rates higher than adults. Both perspectives fit well with the general view that resource limitations shape children’s language processing.

We now summarize the three observations about children’s grammar and processing of complex nominal structures:

1. 1. complex nominals are rarer in children’s speech than they perhaps ought to be;

2. 2. children prefer less embedding, when it comes to PP attachment, within the range of possibilities allowed;

3. 3. children seldom produce recursively embedded possessives or modifiers, and have substantive difficulty comprehending them.

Recursive structures appear to present a specific learning problem for children. Before discussing the implications of this, let us clarify the concept of recursion. Watumull et al. (Reference Watumull, Hauser, Roberts and Horstein2014) critiqued the common misunderstanding that equates linguistic recursion with embedding, or particular forms of it (Levinson Reference Levinson2013). Recursion depends on properties of the formal system (computability, definition by induction, mathematical induction), not on properties of the actual strings of language it outputs. In their words:

Any language, insofar as it is not a list of utterances, is generative, and arises as the result of recursive procedures. Whether the utterances it generates contain actual embedded or recursively embedded sentences is beside the point. Recursion is a property of the intensional system, not of the e-language extensions.

In this broad conception, recursion refers simply to the fundamental operation of asymmetric merge. Children possess this form of recursion from the onset of word combinations. Children unfailingly map utterances into hierarchical structure as soon as they can produce multiword utterances. This ability is the gift of the language faculty. While there is a position within the developmental field that explicitly argues against generativity in the earliest utterances produced by children (Tomasello Reference Tomasello2000; Ambridge, Pine, and Lieven Reference Ambridge, Pine and Lieven2013), the argument against productivity has not withstood the empirical tests (Valian Reference van Hout, Kamiya and Roeper2009; Yang Reference Yang2010, Reference Yang2013; Ninio Reference Ninio2011). Hunsicker and Goldin-Meadow (Reference Hunsicker and Goldin-Meadow2012) documented evidence that deaf children without access to sign language develop hierarchical nominal constituents in their home sign systems. Endocentric NPs appear in the language created by these children in the absence of a conventional language model.

There is also a narrower notion of recursion as iterative self-embedding of phrasal categories, such as a DP within a DP, or a CP within a CP (Arsenijević and Hinzen Reference Arsenijević and Hinzen2012). In this narrow sense, we have seen that recursion is both a locus of language variation and a specific challenge in acquisition (Roeper Reference Roeper2011; Pérez-Leroux et al. Reference Pérez-Leroux, Castilla-Earles, Béjar and Massam2012). Roeper and Pérez-Leroux et al. pointed out that since all human languages have hierarchical, asymmetrical concatenated structures, one would expect continuous access to this fundamental property. Therefore, it should be easy for children to acquire recursive embedding, but it is not. Why is that?

Herein lies the relevance of the processing data. The parsing system, although highly sensitive to lexical demands, shows a bias against embedding. When thematic constraints are pitted against referential contrast, children first satisfy the thematic constraints.This is in accordance with the prediction of minimal attachment, which attributes more complexity to embedded adjunct PPs than to argumental PPs. Probabilistic input also goes against low attachment. Recursive modification, such as elicited in Pérez-Leroux et al. (Reference Pérez-Leroux, Castilla-Earles, Béjar and Massam2012), is rather rare. It is only used in contexts where a speaker must disambiguate from multiple competing referents. To illustrate, we turn to (10) and (11), where the initial head noun baby is followed by two prepositional modifiers.

Such sentences will be produced only when speakers need to distinguish between babies in two ways: one, on whether they are paired with women, and two, on the basis of an additional property applicable to either baby or woman. Neither property can uniquely identify the given baby. In (10), there might be babies that have lollipops but are not with their mothers. In (11), it could be that there are two babies held by women, but only one of the women is holding flowers. The amount of information to be coordinated is substantial. It is not surprising that children can produce three coordinated NPs, which are both common and semantically simple, but fail to produce recursively modified NPs. If we want to evaluate the challenge of embedding, we need to compare recursive embedding with non-recursive double modification, i.e., on the contrast between (10) and (11). In (10), each modifier independently restricts the head noun. We describe these cases as two instances of level 1 modification. In principle, (11) has two interpretations, but we focus here on the one where it is the mother who is carrying the flowers, which is an instance of recursive modification, wherein the nominal under the first PP is itself restricted by a second PP modifier, presumably requiring more complex coordination of information. By comparing these two types of complex nominal, we isolate the question of children’s embedding preferences from that of the competition between lexical constraints and referential constraints.

4 Study

4.1 Methods and procedure

We designed an elicited production study to test whether children differentiate between recursive and non-recursive double modification, as in (1) and (2). In principle, since both of these targets involve two modifiers, they should represent comparable degrees of difficulty for children and adults. Alternatively, if embedding, in and of itself, introduces complexity, we predict an asymmetry in the productivity of the two types. If the tendency to avoid embedding is related to planning capacities, we also predict that working memory might be part of the asymmetry. Last, we examine whether the effect of recursive embedding is comparable in children and adults. These hypotheses can be summarized as follows:

• Null Hypothesis: No difference in the frequency of complex modification in contexts where successful reference requires recursive and non-recursive double modification

• Alternative Hypothesis: Asymmetry in productivity of recursive and non-recursive doubly modified DPs.

• Performance Hypothesis: Working memory plays a role in the difficulty presented by embedding.

• Continuity Hypothesis: If children have access to the same processes and mechanisms as adults, they should treat doubly modified NPs in an analogous manner.

We employed a referential elicitation task similar to the one in Pérez-Leroux et al. (Reference Pérez-Leroux, Castilla-Earles, Béjar and Massam2012). A visual context with multiple referential competitors is arranged so an adequate description of the target referent required two different modifier PPs in order to uniquely refer to the target. Examples are given in (12) and (13).

(12)

(13)

These phrases are surface-ambiguous. The context alone determines the underlying structure. In (12), the bird itself is not in the water; just the alligator is. The speaker must specify which bird got the worm, since another bird also stands on another alligator, crucially standing outside the pond. Similarly, in (13), the visual context shows that the plate has oranges and the table does not, and the other plate with oranges differs from the target in terms of location: it is not under the table.

4.3 Coding

Responses were classified according to depth of embedding in the NP produced (level 2 embedding > level 1 embedding > single NP), as in Pérez-Leroux et al. (Reference Pérez-Leroux, Castilla-Earles, Béjar and Massam2012). We additionally coded the structures in terms of referential success, as summarized in Figure 16.1. This coding system determined whether (i) the target referent was successfully described (by whatever means); (ii) the description included the target semantic predicates; (iii) the description was descriptively incomplete or complete (i.e., it made reference to three contrasting referents, i.e., alligator, bird, water); or (iv) the description was integrated syntactically as a complex NP, which provides the most felicitous and economical response to the question presented by the experimenter.

Figure 16.1 Decision tree for referential coding of responses

Children gave responses where they were able to uniquely identify the target referent, while failing to embed the modifiers into a single complex NP. Such cases of referential success with syntactic failure include various strategies, including coordination and distribution of the modifiers in different clausal constituents.

(14)	Target: The worm in an apple on the plate
	Response: The worm inside the apple and the apple is on the plate and the worm is green. (DA, 5;10)

(15)	Target: The worm in an apple on the plate
	Response: The worm that’s in an apple and on the plate. (IR, 5;08)

(16)	Target: The toothbrush in the cup on the shelf
	Response: The big toothbrush is in the cup on the shelf. (MD, adult)

(17)	Target: The bird on the crocodile in the water
	Response: The birds that’s on top of the crocodiles the crocodiles that’s in water. (AL4, 5;04)

Note that only the target complex NP constitutes a proper answer. Cases that approach referential success, while lacking the target syntax, remain suboptimal. A clausal response such as (16) does not address the question under discussion, about which toothbrush is the largest. Such clausal responses (which effectively eliminate recursive embedding) provide truthful but infelicitous responses.

For the non-recursive condition, reordering the modifiers has no effect, but it degrades a response to the target condition. Responses such as (18) and (19) are not quite right, since one of the other toothbrushes is on the surface of the shelf, but the target is not.

(18)	Target: The toothbrush in the cup on the shelf.
	Response: The toothbrush on the orange shelf in the bowl. (DA9, 5;10)

(19)	Target: The toothbrush in the cup on the shelf
	Response: A big one on the orange shelf with a little cup. (JS21, 5;04)

Reordering in the recursive NP forces the application of the second modifier to the head noun. The resulting description might now be false: in The bird in the water on the alligator, the bird is not in the water; the alligator is. Of course, we can charitably assume that children giving such responses know what they intend to describe but have sentence planning difficulties. These difficulties might range from mild to severe. For instance, the nouns might be part of the structure but not articulated as required, including cases of predicate-argument reversals and various prepositional choices that render the description nonsensical, as in the following examples:

(20)	That one [=bird] is in the water and that one is on a crocodile. (JS20, 5;01)

(21)	Prompt: Which worm is green?
	Target: The worm on the apple in the plate
	Response: The one [=apple] that has yellow plate but that has the green um the green worm. (AN, 5;11)

(22)	Prompt: Which books are blue?
	Target: [The books [inside the (green) box] [under the chair]]
	Response: The ones [=books] under the chair that has a green box on them. (PS42, 5;01)
	Response: With the blue box on it and it’s under the table. (SS, 4;04)

We also observed a pattern of responses that were syntactically quite complex but semantically incomplete. Children produced some responses that incorporated supplementary nominal structure by further specifying the modifier, such as adding a relational noun over one of the modifiers. In (23), the use of on top of and eye effectively increases the level of embedding of the response. However, lack of mention of the second contrasting modifiers renders the response referentially unsuccessful. Children also produced sentences where the most embedded NPs redundantly made reference to a higher referent, as shown in (24):

(23)	The bird on the top of the alligator’s eye. (DA, 5;10)

(24)	The yellow plate with the apple on it. (LM, 4;09)

Here, the speaker merely introduced two of the nouns (plate, apple), iterating the reference to the second noun. The result is tautological: if there is an apple on the plate, the plate has an apple on it (see Peterson et al. Reference Peterson, Pérez-Leroux, Castilla-Earls, Béjar and Massam2015)

4.4 Results

Table 16.1 presents the overall frequencies of responses, classified according to the referential schema.

Table 16.1 Number of responses by group and condition, classified according to the referential schema

Coding	Description	Example	Children		Adults
			Recursive	NonRec	Recursive	NonRec
Incomplete	Single NP or level 1 embedding	The plate The bird on the alligator	204	182	25	21
Alternative	Appropriate but alternative description that does not include the target modifiers	The one on the left The smallest statue	25	8	13	6
Sequential	Sequences of independent NPs that together contain the three target predicates	The bird on the alligator. The one in the water.	32	56	3	3
Unembedded	Referentially complete, single utterance without embedded NP syntax	The worm inside the apple and the apple is on the plate and the worm is green.	15	32	9	25
Target	Specified level 2 or two level 1 N PP PP sequence: These have both target syntax and referential success	The plate with oranges under the table. The bird on the alligator in the water.	24	22	28	23

Children produced few target responses. Not all the non-target responses were referential errors. However, since our focus is on examining children’s ability to articulate complex NPs, we concentrate only on responses that contain the three target nouns. These semantic predicates were introduced in the story, which highlighted them as the source of contrast between referents. We group these as descriptively complete attempts: unembedded, sequential, and target responses. Figure 16.2 groups the various response patterns into incomplete (including incomplete and alternative responses), complete but non-target, and target. The data show that children can produce more descriptively complete responses and more target responses for non-recursive than recursive NPs.

Figure 16.2 Frequency of children’s responses classified as descriptively incomplete, descriptively complete but non-target, and target, across conditions

Our next step was to compare overall frequencies of target responses across groups. Adults were far from ceiling. This is not entirely surprising in an open elicitation task, which allows a certain degree of expressive freedom. The majority of non-target responses in the adults were either incomplete, as participants at times failed to notice one of the contrasting referents, or an alternative description (which is not helpful to our comparison but still correct). Figure 16.3 shows that adults produced the target structures much more frequently than children, at about a ratio of four to one. Individually, twelve of the thirteen adults produced the recursive target, while only eighteen out of fifty children were able to do so. Both groups produced target responses approximately twice as frequently for the non-recursive as for the recursive condition.

Figure 16.3 Proportion of target responses across children and adults

Frequencies of target responses were submitted to a logistic regression analysis with group and conditions as fixed effects and participants as a random effect. The results show significant differences in the frequency of target responses across groups (β=2.21, Z=4.56, p<.001) and across conditions (β=1.38, Z=3.84, p<.001). The lack of interaction (β=0.45, Z=1.00, p=.31) shows that the recursive condition was not comparatively harder for the children.

Age was not a strong predictor of target production in children, unlike in other studies, such as Terunuma and Nakato (this volume) and Corrêa et al. (this volume). To investigate the role of phonological working memory, we tested the association between children’s scores in the non-word repetition task and the two NP conditions. A partial (Kendall’s) correlation controlling for the small but positive effect of age showed no effect of working memory in the non-recursive condition (τ=.07, p=.45), but a small but significant correlation of phonological working memory on targets produced in the recursive condition (τ=.20, p=.047).

5 Discussion

Recursive modification does not require that children learn additional functional vocabulary nor special operations beyond those present at the first level of embedding (the bird on the alligator). The semantic ingredients and operations are also the same for first and second level of embedding: the definite determiner; selecting a unique individual that fits the descriptive content of the relevant predicates; the semantic predicates (noun and PPs); and the semantic derivations which include predicate modification. Syntactically, there is no reason why one additional step in recursion should introduce complexity. From a competence perspective, we would predict no differences between level 1 and recursive modification. What about performance factors? The processing literature suggests a possible initial preference for high attachment. One potential explanation for such preference is performance limitations in children.

Our results show that recursive modification is specifically more difficult. Children produced target descriptions twice as often for non-recursive than recursive targets. Surprisingly, so did adults. Thus, the null hypothesis, that there are no differences between types, is rejected. Our data concur with other studies in this volume in showing that the second level of embedding is a distinct acquisition step from the first level (see Hollebrandse, this volume; Terunuma and Nakato, this volume).

How the difference is stated is no trivial matter. Given that the two types of nominal involve the same bits of syntax and semantics, the differences in complexity should be characterized at the interface of the syntax and the semantics. In the non-recursive description, when the highest DP is composed, a fully intersective interpretation is available between all three predicates: the unique thing that is a plate and is under the table and has oranges. The truth conditions that show commutativity are given in (25):

The same variable linked to the head noun plate and the other two predicates derived from the constituent PPs is accessible to the definite function. In the recursive case, however, there is no simple Boolean intersect that describes the domain to which the definite functionapplies. The phase [the alligator in the water] introduces an opaque domain. In the highest NP, the water is not predicated of the bird, just of the alligator; the lower modifier does not relate to the head noun because its variable is closed off when it becomes part of the larger characteristic function λu. u is an alligator and u is in the water. Intersection is only possible between the simple predicate λu. u is a bird and the complex predicate λu. u is on an alligator in the water. These truth conditions are given in (26):

Recursive structures require that speakers, at the moment of composing the higher NP, attend to a referent (the alligator in the water) that has become inaccessible in the active derivational workspace. At the point when the active predicates intersect, the lowest predicate is now just part of the descriptive restriction on the characteristic function of the higher predicate. In the terms of Arsenijević and Hinzen (Reference Arsenijević and Hinzen2012), it has become intensionalized. The difference in complexity can be described in terms of the referential demands at the interface.

In other words, recursively modified DPs are challenging because the speaker is required to attend to material embedded in a closed phase. The referential task conflicts with phasal architecture. Referential intention drives the process: the syntactic phases construct a path from referent to referent until the target is identified. This analysis situates the cost at the interface, similar to Corrêa et al.’s (this volume) proposal that computational costs arise from the number of syntactic objects to be processed in parallel derivational spaces. We predicted that if children’s avoidance of embedding was related to planning capacities, working memory and the ability to embed would be correlated. In fact, we found the correlations for recursive modification, but not for non-recursive modification.

Maia et al. (this volume) propose a role of learning in processing. Their adult comprehension experiments show an initially higher processing cost for self-embedded PPs. However, embedding becomes less costly with iteration. The N400 amplitudes elicited by PP processing (an indicator of processing difficulty) decrease sharply for the third embedded PP. This is interpreted as progressive facilitation from the processing of the first embedded PP, to the second and to the third. Maia et al. suggest that the algorithm in recursion is costly to launch, but once established, it can be easily redeployed. Their online measurements demonstrate facilitation in processing, whereas the off-line measures showed the cumulative effect of referential complexity (in comparison to coordinated structures).

Our findings are not compatible with approaches positing discrete changes in the syntactic representation in the acquisition of the recursive structure. Terunuma and Nakato (this volume) propose a distinct representational shift, where the label assigned to the possessive phrase changes in the grammar of children. The initial non-recursive possessive has a less specified type (MODP) than the recursive target (POSSP). Subsequently, the label content is further refined and the configuration can recur. We believe that the same findings can be accounted for in terms of processing capacities without proposing discontinuous syntax. Because the cost of embedding is comparable for children and adults, our results support continuity approaches.

In sum, we have examined a unified account for the various paratactic trends in the acquisition literature, including the preference for minimal attachment in the processing of PP attachment ambiguities, the modification gap in production and the general difficulty with recursive structures. As we found that the predicted asymmetry is associated with recursive embedding, we conclude that embedding introduces an additional degree of complexity beyond the referential demands of modification. The data reviewed here are naturally more compatible with the development as synthesis approach, at least for nominal modification.

1 Relevant Generalities about Kuikuro Grammar and Prosody

As mentioned above, Kuikuro is ergative. Internal arguments (of postpositions, nouns, Patient/Experiencer of a verb) are morphologically unmarked for (absolutive) Case and they always form a phonological-prosodic unit with their heads. All intransitive verbs are unaccusative, as shown by examples (1) and (2). The sentence in (3) is an example of a transitive sentence: the External Argument (external Cause/Source/Agent of an event/action) is marked by heke, which is a postposition used to mark ergative case (ERG), though semantically can be thought of roughly as expressing the spatial distance between two points measured from the perspective of one of them (Franchetto Reference Franchetto, Gildea and Queixalós2010):Footnote ²

Kuikuro has one single set of bound (prefixed) pronominal forms, which encode the absolutive pronominal argument of a verb, the possessor of a noun or the argument of a postposition. There are no auxiliaries and there is no explicit agreement on verbs or nouns.

For a fuller understanding of the prosodic patterns discussed in Sections 2 and 3, a brief introduction to Kuikuro phrasal prosody is necessary, summarizing the findings presented in an earlier publication (Silva and Franchetto Reference Silva and Franchetto2011). The main stress is generally on the penultimate syllable of the isolated word; stressed syllables are basically distinguished by high pitch (and associated with lengthening). As previously stated, internal arguments (of postpositions, nouns, Patient/Experiencer of a verb) always form a phonological-prosodic unit with their heads. Then, as a first level of prosodical integration, any head constitutes with its direct or internal argument an intonation unit: the phrasal main stress is on the juncture, manifested on the last syllable of the argument or on the first syllable of the head (Silva and Franchetto Reference Silva and Franchetto2011). Consider the following examples in order to understand the two patterns of Kuikuro phrasal prosody. Main stressed syllables are in bold and marked with [ˈ]. First of all, observe that in the isolated words tahinga (‘cayman’ in (4a)) and kangamuke (‘child’ in (5a)) the main stress is, as expected, on the penultimate syllable. When the nominal word becomes the argument of a head, like a verbal head, however, something happens in the prosodic domain. Compare tahinga when it is the internal argument (direct object) of the transitive verb ‘to see’ in (4b) and the internal argument (actor or theme) of the intransitive verb ‘to fall’ in (4c).

In (4b) and (4c), the syllable perceived by the native speakers and researchers as carrying the main stress is the last one of the argument, but it is the first syllable of the head (the verb) that has the prominent F0 peak of the whole VP (σ). This is the first pattern of Kuikuro phrasal prosody:

• Pattern 1: [ˈσ # σ]

If we place focus on the external argument in the transitive sentence (5b), where unlike (4b) which has a postposed pronominal subject, this full DP with a postpositional phrase comes before the VP, the syllable perceived as prominent is the last one of the (internal) argument of the PP heke, and, in fact, it is this syllable that is marked by the prominent F0 peak of the whole PP [kangamuˈke heke].

The left-hand phrase in (5b) is an example of the second pattern of the Kuikuro phrasal prosody:

• Pattern 2: [ˈσ # σ]

The environments of the two patterns of prosodic integration, briefly described here, are verb phrases, nominal phrases and postpositional phrases, and we will see that they occur in the data recorded during our study of Kuikuro DP and PP recursive constructions. The problem is to understand how and where they are at work when we have multiple embedding.

2 DP Recursion in Kuikuro: Possessives

In recursive DP constructions, the two prosodic patterns described above characterize the first argument/head relation. Any embedded N to this first merge maintains its own lexical stress on the penultimate syllable, but the prosodic pattern of the whole phrase reveals a clear recursive structure. The same recursive constructions are productive for alienable and inalienable Ns. Recursion and coordination are thus clearly distinguishable through their distinct phrasal prosodies.

2.1 DP Recursive Possessives with Alienable Nouns

In the following examples, the genitive suffix on the ‘possessed’ N – glossed as GEN – marks the dependence between NPs. Stressed syllables are marked with a preceding [ˈ]; the syllable perceived as bearing the main stress of the whole construction is marked with [ˈ] and in bold. The relational marker –gü undergoes assimilation to –gu when following an /u/ in the preceding syllable.

• Alienable N:

(6a)	eˈtene         ‘paddle’
	ˈiku              ‘decoration’

(6b)	[eteˈne iˈkusü]
	etene     iku      -      sü
	paddle decoration-gen
	‘paddle’s decoration’

(7a)	aˈnetü   ‘chief’
	ˈehu        ‘canoe’

(7b)	[aneˈtü eˈhugu]
	anetü   ehu -   gu
	chief    canoe-gen
	‘chief’s canoe’
(8)	[[[[aneˈtü eˈhugu] eteˈnegü] iˈkusü]]
	anetü ehu-gu	etene-gü	iku-sü
	chief canoe-gen    paddle-gen decoration-gen
	‘chief’s canoe’s paddle’s decoration’

Declination reset (Ladd Reference Ladd1986, Reference Ladd1988; see also Mithun Reference Mithun, Givón and Shibatani2009) is used as a diagnostic of prosodic domain delimitation. The pitch movement or intonation of the recursive construction in (8) is shown in Figure 17.1 and is coherent with the first pattern of prosodic integration between argument and head. A rising intonation reaches the highest pitch of the whole construction exactly on the internal juncture in [anetü ehugu], ‘chief’s canoe.’ After this, the following stressed syllables are characterized by a sequence of increasingly lower pitches or declination resets, until the final fall.

Figure 17.1 Pitch movement of the recursive construction in (8)

(9b) results from adding one more level of embedding to (8).

(9a)	ngiˈkogo         ‘(wild) Indian’

(9b)	[[[[ngikoˈgo   aneˈtü-gü]      eˈhu-gu]      eteˈne-gü]      iˈku-sü]
	ngikogo anetü-gü      ehu-gu            etene-gü        iku-sü
	indian   chief-gen   canoe-GEN paddle-gen decoration-gen
	‘Indian’s chief’s canoe’s paddle’s decoration’

Figure 17.2 shows the prosodic profile of (9b).

Figure 17.2 The prosodic profile of (9b)

Examples (8) and (9b), with the pitch tracks shown in the figures below, reveal just one higher pitch exactly on the juncture of the first merge between head and argument, and then declination during the entire course of the complex DP. This can be directly contrasted with an example of coordination, which contains two syntactically independent DPs, and as a result, no declination reset and two declination domains, as shown in Figure 17.3.

(10)	[ngikoˈgo eteˈne-gü]   õ [aneˈtü eˈhu-gu] iˈmbe-lü geˈhale iˈheke
	ngikogo etene-gü       õ anetü       ehu-gu       imbe-lü gehale i-heke
	Indian paddle-gen & chief      canoe-gen bring   also   3-erg
	‘he brought the Indian’s paddle and the chief’s canoe’

Figure 17.3 No declination reset and two declination domains

Two equal higher pitches and two falling intonations constitute evidence that DP coordination is distinct from DP recursive structure, a crucial piece of evidence from the intonation domains as correlates of syntactic domains.

2.2 DP Recursive Possessives with Inalienable Nouns

The phrasal prosodic pattern of possessive recursive constructions containing inalienable nouns is not different from that described in Section 2.1 for alienable nouns. The following data result from the expansion of the recursive construction by adding, one by one, more levels of embedding.

(11a)	uaˈkongo
	u-akongo
	1-companion
	‘my companion’

(11b)	uhameˈtigü
	u-hameti      -      gü
	1-brother-in-law-gen
	‘my brother-in-law’

(11c)	[uakoˈngo hameˈtigü]
	u-akongo           hameti      -      gü
	1-companion      brother-in-law-gen
	‘my companion’s brother-in-law’

(11d)	[uhametiˈgü hisü]
	u-hameti -            gü         hi      -      sü
	1- brother-in-law-gen younger.brother-gen
	‘my brother-in-law’s younger brother’

(11e)	[[uakoˈngo hisü] ˈhitsü]
	u-akongo         hi-                    sü         hi-tsü
	1-companion    younger.brother-gen wife-gen
	‘my companion’s younger brother’s wife’

The first level of embedding exemplified in (11e) results in a construction with the highest pitch on the first syllable of the head (ˈhisü) of the first syntactic-prosodic integration and then a partial reset with a lower peak on the first syllable of [ˈhitsü]. This can be seen in Figure 17.4.

Figure 17.4 Pitch profile of (11e)

The example in (12) has one more level of embedding:

(12)	[[uakoˈngo       hameˈtigü] ˈhisü] ˈhitsü]   etijiˈpügü]
	u-akongo         hamet     i-         gü                   hi-sü
	1-companion    brother-in-law- gen      younger.brother-gen
	hi-tsü              etiji-pügü
	wife-gen         sprout-perf
	‘my companion’s brother-in-law’s younger-brother’s wife’s children’

Figure 17.5 Pitch profile of (12)

As shown in the Figure 17.5, the single highest pitch is exactly at the juncture between the complement and the head of the first merge: uakongo (or uakango) and hametigü. This highest pitch is followed by a ladder of lower pitches, each one corresponding to the stressed syllable of hisü, hitsü, and etijipügü.

The example in (13) results from a further level of embedding:

(13)	[[[uakoˈngo hameˈtigü] ˈhisü] ˈhitsü] etijiˈpügü] muˈkugu]
	u-akongo         hameti         - gü                        hi-          sü
	1-companion     brother-in-law-gen       younger.brother-gen
	hi-tsü               etiji-pügü          muku-gu
	wife-gen         sprout-perf       son-gen
	‘my companion’s brother-in-law’s younger-brother’s wife’s children’s son’

Figure 17.6 Pitch profile of (13)

No matter how many possible embeddings, the expanded recursive DP, as exemplified in (13) and in Figure 17.6, shows a striking prosodic integration with just one highest pitch on the first merge and then a declination of continuously lower pitches on the stressed syllables of the following embedded possessed nouns.

3 PP-Level Recursion

If the production of DP recursive constructions, like those exemplified in Sections 2.1 and 2.2, is an easy task for Kuikuro speakers, we cannot say the same for the production of PP recursive constructions with more than one or two levels of embedding. For the time being, we do not have a clear answer to the question of why recursive PPs would be more difficult to process and to produce than recursive possessive DPs. We encountered two main difficulties during the elicitation of recursive PP constructions. On the one hand, our Kuikuro consultants took longer: several attempts were discarded as unsatisfactory or unacceptable, until they reached a construction consensually considered as “good (atütü).” On the other hand, our own perception of prosodic integration was far from clear if compared with the immediate apprehension of the whole intonation of recursive DPs. It is the pitch movement, however, that came to inform our analysis, showing, as we will see, intonation patterns similar to those already found in complex recursive DPs.

As this is an initial investigation of these structures, for now we only deal with locative PPs expressing spatial relations between objects. In this case, in order to elicit specific locative PPs, we used, together with verbal instructions, visual stimuli such as the direct or indirect manipulation of familiar objects (bench, gourd, mat, platform, fish, turtle, etc.), in order to obtain precise descriptions. Since the speaker could produce a sentence that he considered as “good,” he made a drawing representing exactly the specific spatial arrangement of the objects, generally one inside or on another, as described by the complex construction. The Appendix contains the drawings associated with the examples selected.

In the apparently less complex constructions, as in (14b), the matching between syntax, perception, and the intonation contour displayed in the figure generated using PRAAT is apparent. We found just one higher pitch and then declination during the entire course of the complex PP [uagisuˈgu agiˈsugu aˈtalü ˈata], both delimiting one single phrasal domain, as shown by the pitch track in Figure 17.7. Note that the last two words ainde kuihi are not part of the recursive PP structure and hence the last pitch peak, i.e., the one on ainde, is not relevant to the question at hand.

Figure 17.7 Pitch profile of (14b)

More complex recursive cognition of spatial relations is expressed by different and apparently non-recursive syntactic strategies.

(15a–c) present a first set of examples, with the aim to produce the translation of ‘the turtle on the stone on the beach of the lagoon’:

A first attempt by our Kuikuro consultants, in order to describe ‘the turtle on the stone on the beach of the lagoon,’ was judged as “not good” (atütühüngü, good-NEG), even if not ungrammatical (kütsü, ‘bad’):Footnote ³

Then, they consensually considered the construction in (15c) as finally ‘good’ (atütü):

A full sentence was immediately uttered as an appropriate syntactic context:

(15b) was considered just a translation of the Portuguese corresponding construction. The “heavy” recursive PP in the less “good” construction (15b) was split in two parts by hikutaha (‘turtle’) in order to have (15c), the “good” one. As the consultants explained, a “good” sentence would be one which expresses the right sequence of the objects in contact, in a kind of bottom-up cognitive apprehension of a vertical spatial relation: on the left side of the sentence, the base or the ground, and on its right side of what is on the base.Footnote ⁴

(16b), an even more complex PP, is an example of one of the usual solutions, in Kuikuro, for avoiding ‘heavy’ syntactic objects, splitting the whole into two units tied by an anaphoric pronoun, üle:

The match between prosody, syntactic and cognitive integration is evidence that (16b) is not a paratactical construction. The pitch trace of example (16b), shown in Figure 17.8, is evidence of a single intonation unit, a clear manifestation of prosodic integration.

Figure 17.8 Pitch trace of (16b)

Looking at Figure 17.8, we see that the higher pitch of the whole complex construction is at the juncture of the first merge (syllable in bold in [oˈgo ugupongo]), followed by descending partial pitch resets on the stressed syllables in [üˈle ugupo], [tuaˈhi ugupo] and [tüheˈnkinhü]. Then, we have an overall intonation contour that includes three prosodic sub-contours with prosodic breaks between them (similar to the kind of evidence adduced in Mithun (Reference Mithun, Givón and Shibatani2009)).

Before they reached the ‘good’ construction in (16b), the Kuikuro consultants produced two attempts (16c–d), with the first one judged as less ‘good’ than the second one, but this latter one less good than (16b), manifesting a kind of growing gradient of acceptability:

Once more, as we saw before, a full sentence was uttered as the appropriate syntactic context for the situation described by (16b) and depicted by the correspondent drawing (see Appendix):

Once more, our consultants clarified the reason why (16b) is the best construction, reproducing the same cognitive apprehension of the bottom-up order of a vertical spatial relation between objects in contact, as we saw in (15c).

Contrasting with (16b) and parallel to the coordinate structure in (10) and Figure 17.3, (17b) could be considered an example of dissolution of complex spatial cognitive relations between objects into two syntactic units, loosely tied by the anaphoric üle.

Figure 17.9 Pitch trace of (17b)

Looking at Figure 17.9, we see that between ogo ugupo akandoho and üle ugupo atange ata kanga, there is a total pitch reset on the main stressed syllable of [üˈle ugupo]. Thus, we have two distinct prosodic units or phrases, revealing a coordination in a way that is perfectly parallel to what we saw in Figure 17.3, corresponding to the canonical coordination exemplified by (10). Partial resets are visible inside each intonation domain. Note that the one in the second domain points to a first-level recursive structure (üle ugupo / atange ata, ‘(fish) inside the pot on the platform’). Could this coordination-like construction be interpreted as a mismatch between cognitive integration and syntactic/prosodical integration?

The ‘not good’ constructions produced by the Kuikuro consultant on the path to the ‘good’ one are yet again interesting. (17c) was considered a direct translation from Portuguese:

Consequently, they produced (17d) after the comment: “it’s not right to say this, you must take off something,” but it was judged as ‘not good’ because the ‘platform’ does not come first, as in the ‘good’ (17e):

(17f) was offered as a ‘good’ sentential context:

4 Final Remarks

The incorporation of finely graded phonological knowledge into syntactic properties allows a much better understanding of the DP and PP recursive constructions in Kuikuro, not only when the match between prosodic integration and syntactic structure is manifestly clear, as we discovered in our first incursion in Kuikuro phrasal prosody where the syntactic merge between head and complement was nicely mirrored by their prosodic integration.

The prosodic contrast between two syntactically parallel sentences, e.g., (16b) and (17b), shows two different strategies in order to simplify a complex PP. The paratactical coordination in (17b) could be a case of an apparent mismatch between syntactic and prosodic structures, contrasting with the clear prosodic integration in (16b), shown by Figure 17.8. This led me to mention the idea of a matching between prosodic and cognitive integration following Mithun (Reference Mithun, Givón and Shibatani2009). We saw the paths followed by Kuikuro speakers in order to avoid unnecessary and unmotivated complexity and then reach the ‘good’ construction when dealing with multiple spatial embedding. However, this points to the need for a new and deeper syntactic analysis. This would be a more cautious descriptive and theoretical step forward,Footnote ⁵ rather than to accept immediately the conclusions presented by some authors (see Mithun Reference Mithun, Givón and Shibatani2009; Hunyadi Reference Hunyadi and van der Hulst2010; Hulst Reference Hulst, van der Hulst, Koster and van Riemsdijk2010).Footnote ⁶ These authors state that if we are facing phenomena at the interface between prosody and semantics or cognition, then syntax must be discarded as the central computational device generating structures interpreted at the phonological and the conceptual interfaces. By contrast, I contend that prosody is the key for the understanding of recursive structures, but it pushes us back to syntax.

1 The Psycholinguistic Sentence/Picture Matching Experiments

To investigate the hypothesis that recursively embedded PPs should be harder to processFootnote ² than their coordinated counterparts both in Karajá and in Portuguese, we applied an auditory sentence/picture matching experiment in three groups of subjects: Karajá speakers tested in their native Karajá; Karajá speakers tested in their L2 Portuguese; and monolingual BP speakers. The objective of the experiments was to assess whether the processing of PP embedding was costlier than the processing of PP coordination. The independent variables of the study were, therefore, 2- and 3-PP/DP embedding and coordination and the dependent variables were the accuracy rates and decision times.

Materials

There were six conditions in the experiments, as exemplified in the Karajá and BP constructions in Figures 18.1–18.6. These figures, as well as all the other sets used in the experiment, displayed situations in which different locative PPs (e.g., in the basket, on the beach, etc.) may be either embedded or juxtaposed, as shown in the following six conditions:

• Condition 1. Recursion with two embedded PPs

utura       ijõdire      weriri-roki       ynyra   tyre-ki

fish      there is   basket-inside beach   on

Tem peixe na cesta na praia.

“There is fish in the basket on the beach”

Figure 18.1 Recursion with two embedded PPs

• Condition 2. Recursion with three embedded PPs

utura       ijõdire      weriri-roki   myna   tyre-ki   ynyra-ki

fish      there is      basket          inside rock on      beach-on

Tem peixe na cesta na pedra na praia

“There is fish in the basket on the rock on the beach”

Figure 18.2 Recursion with three embedded PPs

• Condition 3. Coordination with two PPs

utura   ijõdire    myna   tyre-ki      ijõ      ynyra   tyre-ki

fish      there is   inside   rock on   other   beach   on

Tem peixe na pedra e na praia

“There is fish on the rock and on the beach”

Figure 18.3 Coordination with two PPs

• Condition 4. Coordination with three PPs

utura   weriri-roki   ijõdire   ijõ      myna   tyre-ki   ijõ      ynyra   tyre-ki

fish      basket-in    there is   other   rock   on         other   beach   on

Tem peixe, na cesta, na pedra e na praia

“There is fish in the basket, on the rock, and on the beach”

Figure 18.4 Coordination with three PPs

• Condition 5. Coordination with two NPs

utura	weriri	wyna	ynyra-ki	ijõdire
fish	basket	and	beach-on	there is

Tem peixe e cesta na praia

“There is (a) fish and (a) basket on the beach”

Figure 18.5 Coordination with two NPs

• Condition 6. Coordination with three NPs

utura   weriri     myna     ynyra-ki     ijõdire

fish      basket   rock      beach-on   there is

Tem peixe, cesta e pedra na praia

“There is (a) fish, (a) basket, and (a) rock on the beach”

Figure 18.6 Coordination with three NPs

Notice that recursive embedding of PPs is not morphologically marked in Karajá or in BP (Conditions 1 and 2). Nevertheless, the conjoining of PPs in Karajá is operated by the quantifier ijõ ‘other’ (Conditions 3 and 4), whereas the conjoining of NPs may be obtained through the optional conjunction wyna‘and’ (Conditions 5 and 6). In BP, as exemplified in the glosses of Conditions 3, 4, 5, and 6, the same conjunction e, which means ‘and,’ is employed both for the PP and NP conjoining.

Results

The results indicated that recursively embedded PP constructions were more difficult to process than PP and NP conjoined constructions, both for Karajá tested in Karajá and in BP as well as for the monolingual BP participants. Even though decision rates were not different across conditions, average reaction times were significantly higher for three embedded PPs than for two embedded PPs or for any coordinate constructions in all subject groups. Reaction times for constructions with two embedded PPs were significantly higher than reaction times for constructions with two coordinate PPs or NPs. Reaction times for coordinate PPs were not significantly different than for coordinate NPs. Table 18.1 and Figure 18.7 summarize these results.

Table 18.1 Average reaction times (ms) in the oral sentence/picture matching experiment

Group/Condition	R2PP	R3PP	C2PP	C3PP	C2NP	C3NP
Karajá tested in Karajá	1614	2990	1142	2004	1040	1553
Karajá tested in BP	1557	2694	1206	1570	1393	1780
BP tested in BP	1496	2018	916	1191	1388	1297

Figure 18.7 Average reaction times (ms) in the oral sentence/picture matching experiment

A three-way analysis of variance (ANOVA) was applied to the PP conditions, crossing two within-factors and one between-factor. The within-factors were Syntax (recursive embedding × conjoining) and Number of PPs (two × three). The between-factor was the group of participants (KK, Karajá judging Karajá; KP, Karajá judging Portuguese; and BP, monolingual Brazilian Portuguese speakers judging Brazilian Portuguese). There was a highly significant main effect of the factor Syntax in the expected direction, indicating that PP embedding is harder to process than PP conjoining in the three groups (F(1,46) = 51.2 p<0.000001***). The factor Number of PPs also yielded a significant main effect, indicating that increasing the number of PPs increases response times regardless of the syntactic process (F(1,46) = 40.1 p<0.000001***) in the three groups. However there was no significant interaction of the factors Syntax and Group of participants (F(2,92) = 0.200 p<0.818722), indicating that the three groups did not differ in their pattern of responses: all participants decided faster in PP coordination than in PP embedding. Likewise, there was no significant interaction of the factors Syntax, Number, and Group (F(2,92) = 0.183 p<0.833306), confirming the similarity of response patterns across all the factors. Pairwise t-tests were also conducted across the conditions, supporting the hypotheses, as indicated in Table 18.2.

Table 18.2 Pairwise t-tests comparing conditions in the three groups of participants

	R2PP x C2PP	R3PP x C3PP	R2PP x R3PP	C2PP x C3PP
KK	t(46)=2.31 p<0.025	t(46)=2.50 p<0.015	t(23)=3.19 p<0.004	t(23)=5.5 p<0.000
KP	t(46)=2.44 p<0.018	t(46)=3.52 p< 0.0010	t(23)=2.20 p<0.038	t(23)=1.41 p< 0.17
BP	t(46)=2.73 p< 0.009	t(46)=5.55 p< 0.0001	t(23)=2.62 p< 0.015	t(23)=2.12 p< 0.04

We interpreted these results as an additional piece of evidence that performance systems are habitual and may lie beyond narrow syntax in the domain of third-factor effects. As proposed by Trotzke, Bader, and Frazier (Reference Trotzke, Bader and Frazier2013), performance systems must be taken as essential in the challenge to understand the boundaries of grammar. Note that Perez-Léroux et al. (this volume) offer acquisition evidence in line with our finding that PP embedding introduces an additional degree of complexity, in comparison with conjoined PPs.

2 The Neurophysiological Assessment of Karajá Participants

With such interesting behavioral results in the sentence/picture matching, we set out to conduct an event-related brain potential (EEG-ERP) test, aiming at grasping subtler on-line effects that could be related to the reading of specific chunks of the stimuli. We carefully organized stimuli to be able to compare the electrophysiological responses (i.e., brain waves) related to the reading of SOV sentences containing three PPs, either conjoined or embedded in Karajá.

Stimuli and Presentation

In Karajá, a sequence of PPs are embedded by juxtaposition, while a way of structuring conjoined PPs or DPs is by means of the particle ijõ ‘other.’ Tables 18.3 and 18.4 show a sample of the sixty-four experimental sentences (thiry-two with coordinated items and thirty-two with embedding). There were also 128 distracting fillers (sixty-four were grammatical and sixty-four contained a nonword).

Table 18.3 Embedding

Kua habu		↓   Trigger 1	↓   Trigger 2	↓   Trigger 3
	utura	womati-ràbi	berysyna-roki	mana-tyretxi	riwyra
That man	fish	can from	bucket in	stone on top	took
“That man took fish from the can in the bucket on top of the stone”

Table 18.4 Conjoined

1		↓   Trigger 1	↓   Trigger 2	↓   Trigger 3
Kua habu	utura	womati-ràbi ijõ	berysyna-roki ijõ	mana-tyretxi	riwyra
That man	fish	can from other	bucket in other	stone on top	took
“That man took fish from the can and from the bucket and from the stone”

Before starting the test, participants had to go through a training session to get used to the kind of sentences being tested. The idea was to clearly signal to the participant, as of the appearance of the first PP, that the sentence would have one of two structural possibilities: either a sentence with conjoined items (those that had the word ijõ) or a sentence with embedding (without ijõ). The sentences appeared on the screen in chunks, as can be seen in the experiment timeline (Figure 18.8).

Figure 18.8 The experiment timeline

Participants would first see a fixation cross for 500 ms. Then, after a 50 ms interval, the first word group displayed the sentence subject for 500 ms. After another interval of 50 ms, the second word group, displaying the object, appeared for 500 ms. Then, the three critical PPs, triggered so as to be time-locked to the ERP measurement, appeared on the screen for 500 ms each. Finally, there was a question prompt in relation to the grammaticality judgment of the sentence. The response was linked to a time-out routine of 1500 ms.

Results

Figure 18.9 presents a comparison of stimulus sections corresponding to the three PPs. For the sentences with PP embedding, the waves from a central electrode (C3) are shown comparing the first embedded PP to the second one and the first to the third. The dependent measures, i.e., the voltages within the N400 mean voltage time-window, were analyzed by the Wilcoxon test and it was possible to eliminate the null hypothesis. The visual inspection of the N400 wave at trigger 3 clearly shows lower amplitude and shorter latency components than those of the two other triggers. These two attributes, lower amplitude and shorter latency, are usually interpreted as less complex computations. The first PP has a larger amplitude and longer latency than those of the others. This, in turn, indicates that higher structural complexity demands more energy and time.

While the two graphs relating to embedded structures show statistically different waves, the ones related to the coordinated structures show an overlapping pattern at 400 ms and were not statistically significant (p=0.6).

Figure 18.9 The waves corresponding to the different PPs both for the embedded conditions and for the coordination ones, sensed from a central-left electrode (C3)

Despite the fact that the number of participants was not ideal in this experiment, it was possible to verify a number of aspects of the comparison between coordinated PPs and recursively embedded ones: (1) coordination computations seemed faster than those of embedding; (2) at each PP layer, the recursive embedding gets progressively easier and faster. Since there is an open morpheme signaling coordination in Karajá, a parametric comparison with a language that does not have an open morpheme marking coordination is desirable to understand the importance of this characteristic, computationally speaking.

3 The Neurophysiological Assessment of Brazilian Portuguese Participants

To understand the parametric difference between Karajá and BP, the former marking the coordination with an open morpheme (ijõ) but not the latter, we decided to run another EEG-ERP test, this time in BP, again comparing PP embedding with conjoining.

Experimental Design

In a 2×2 design, we manipulated two variables: (i) coordination versus embedding, and (ii) congruence versus incongruence. Coordinated sentences presented a sequence of three PPs in which the second and third could only be interpreted as being coordinated, since they presented the coordinating conjunction ‘and,’ whereas in the embedded sentences, the second and third PPs could only be interpreted by means of an embedded reading. Congruence was manipulated by adding an adverbial phrase at the end of the sentence, at the region known to give rise to the wrap-up effect. Manipulation made the sentences either make sense or not. Thus, lists of stimuli were compiled, each with ten items for four conditions (Table 18.5), as well as eighty fillers of which forty were congruous and forty incongruous, resulting in a total of 120 sentences per experimental list.

Table 18.5 Sample items

Condition	Congruous	Incongruous
Coordination	O zelador limpou as lixeiras da escada e do pátio e do prédio com cuidado (n=10) The janitor cleaned the trashcans on the stairs and on the patio and in the building carefully	O contador calculou os lucros da drogaria e da livraria e da ótica depois de amanhã (n=10) The accountant figured the profit of the drugstore, and of the bookstore and of the eyeglasses store the day after tomorrow
Embedding	O contador calculou os lucros da drogaria da filial da empresa anteontem (n=10) The accountant figured the profit of one of the branches of the drugstore of the holding, the day before yesterday	O zelador limpou as lixeiras da escada do pátio do prédio amanhã (n=10) The janitor cleaned the trashcans on the stairs and on the patio and in the building tomorrow

Participants were instructed to judge whether the sentence made sense or not at the end of each sentence, by pressing a key for YES and another one for NO. Sentences were presented in chunks of up to two words, respecting syntactic boundaries. Each chunk of the sentence was presented for 250 ms, followed by an interval of 100 ms. Before each sentence, a fixation cross was shown for 1500 ms, and after each sentence, participants had 2500 ms to respond. Sentences were presented on a computer screen, chunk by chunk, following the events depicted in Figure 18.10.

Figure 18.10 The experiment timeline

Each test started with a training session with eight sentences mixing the two experimental conditions and fillers. The training session could be repeated in case the participant was not completely sure of the procedures.

The test came immediately after the training, following a within-subject experimental design. Participants were tested in a single session lasting about one hour (including about 30 minutes of experimental preparation). Participants were randomly assigned to one of the two lists used, so as not to repeat tests across participants and to counterbalance participants across lists.

Data Acquisition and Analysis

The EEG signals were recorded continuously from sixty-four sintered Ag/Ag–Cl electrodes attached to an elastic cap in accordance with the extended 10–20 International System (Nuwer et al. Reference Nuwer, Comi, Emerson, Fuglsang-Frederiksen, Guérit, Hinrichs, Ikeda, Lucas and Rappelsburger1998). Several of these electrodes were placed in standard International System locations, including five sites along midline (FPz, Fz, Cz, Pz and Oz) and sixteen lateral/ temporal sites, eight over each hemisphere (FP1/FP2, F3/F4, F7/F8, C3/C4, T3/T4, T7/T8, P3/P4, and P7/P8). Also, another forty-three extended 10–20 system sites were used (AF3/AF4, F1/F2, F5/F6, FC1/FC2, FC3/FC4, FC5/FC6, FT7/FT8, C1/C2, C5/C6, CP1/CP2, CP3/CP4, CP5/CP6, TP7/TP8, P1/P2, P5/P6, P7/P8, PO3/PO4, PO5/PO6, PO7/PO8, CB1/CB2, O1/O2).

Figure 18.11 The gray shaded circles highlight the six regions of interest (ROIs) bilaterally distributed among a 64-channel scalp-electrode array, used for visual inspection and statistical analysis: frontal-left, frontal-mid, frontal-right, central temp-left, central-mid, central temp-right, parietal-left, parietal-mid, parietal-right, occipital-left, occipital-mid, occipital-right

The EEG was referenced on-line to left and right mastoid channels. Impedances were maintained below 10 kΩ. EEG was amplified and digitized at a sampling frequency of 500 Hz. After recording, data was filtered with a bandpass of 0.1–30 Hz. ERPs were averaged off-line within each experimental condition (coordination, embedding, congruous and incongruous) for each subject at each electrode site in epochs spanning −200 to 1000 ms relative to the onset of the target stimulus. Epochs characterized by eye blinks or excessive muscle artifacts were dependent on the experimenter’s visual inspection. Accuracy was computed as the percentage of correct responses (min 95 percent).

ERP components of interest were identified based on visual inspection of ERPs, ROIs (regions of interest) and topographic maps, as well as prior findings. For each of the channels, we quantified ERPs for analysis as mean voltages within windows of 300–500 ms (capturing a broad negativity). Grand-averages were formed by averaging over participants.

These dependent measures, i.e., the voltages within the N400 mean voltage time-window, were analyzed with repeated measures ANOVAs. ANOVAs were performed separately at each electrode side, and then also averaged for analysis within six-channel-groups (see Figure 18.11). A three-way ANOVA model was used, and the factors were sentence-type (coordination, embedding), interval (1st PP, 2nd PP, and 3rd PP) and ROI (frontal-left, frontal-mid, frontal-right, central temp-left, central-mid, central temp-right, parietal-left, parietal-mid, parietal-right, occipital-left, occipital-mid, occipital-right).

The Greenhouse-Geisser correction for inhomogeneity of variance was applied to all ANOVAs with greater than one degree of freedom in the numerator. In such cases, the corrected p value was reported. Significant main effects were followed by simple-effects analysis.

Results

In an ERP test, visually inspecting the waves related to well-streamlined conditions gives an idea of how different these conditions are. Figure 18.12 is just a sample of the difference between embedded and conjoined PPs perceived at a central-parietal site. It is possible to follow each stimulus chunk in the two conditions, during the time-window of 1800 ms, that encompasses the five chunks of each stimuli. It is also possible to visualize both conditions running in parallel: the black line represents the electrical flow of coordination and the dark grey line, that of embedding. The light grey line represents the difference between the two conditions.

As can be seen, the light grey line flows relatively close to 0 µV, in the segments related to the second and third chunks of the stimuli that correspond to the first and second PPs. This means the conditions are not very different from each other. But at the fourth chunk, relating to the third PP, there is a more prominent difference, meaning the greatest contrast is between coordination and embedding of the third PP.

Figure 18.12 Grand-average ERPs recorded at central-parietal electrode midline sites. The onset of the critical DP and the three PPs is indicated by the vertical bars. Positive voltage is plotted down.

Beyond visual inspection, contrasts can be more accurately depicted in the statistical analysis of the waves, considering their main aspects: latencies and amplitudes. Starting with latencies, Table 18.6 shows the main effects. There is a main effect for the ROI comparisons. This means that when we subtract the waves related to the embedded stimuli from those of the conjoined ones, we can assume that each of the regions evaluated is different from zero.

Table 18.6 Main effect for mean latency: (a) comparison between two intervals (200–400 ms and 400–600 ms) was analyzed according to four different statistical criteria, with the most restrictive one being a Sphericity Assumption; (b) ROI with the same criteria; (c) Coordination versus Embedding (notated as Coor × Rec)

Source		Type III Sum of Squares	df	Mean Square	F	Sig.	Partial Eta Squared	Noncent. Parameter	Observed Powera
Interval	Sphericity Assumed	53339.457	2	26669.729	1.030	.363	.033	2.060	.222
	Greenhouse-Geisser	53339.457	1.901	28053.576	1.030	.360	.033	1.958	.217
	Huynh-Feldt	53339.457	2.000	26669.729	1.030	.363	.033	2.060	.222
	Lower-bound	53339.457	1.000	53339.457	1.030	.318	.033	1.030	.166
Error (interval)	Sphericity Assumed	1553585.773	60	25893.096
	Greenhouse-Geisser	1553585.773	57.040	27236.545
	Huynh-Feldt	1553585.773	60.000	25893.096
	Lower-bound	1553585.773	30.000	51786.192
ROI	Sphericity Assumed	147778.316	12	12314.860	3.579	.000	.107	42.951	.998
	Greenhouse-Geisser	147778.316	3.681	40151.011	3.579	.011	.107	13.174	.836
	Huynh-Feldt	147778.316	4.259	34696.974	3.579	.007	.107	15.245	.877
	Lower-bound	147778.316	1.000	147778.316	3.579	.068	.107	3.579	.449
Error (ROI)	Sphericity Assumed	1238617.684	360	3440.605
	Greenhouse-Geisser	1238617.684	110.417	11217.648
	Huynh-Feldt	1238617.684	127.773	9693.864
	Lower-bound	1238617.684	30.000	41287.256
Coor x Rec	Sphericity Assumed	10994.349	1	10994.349	1.449	.238	.046	1.449	.214
	Greenhouse-Geisser	10994.349	1.000	10994.349	1.449	.238	.046	1.449	.214
	Huynh-Feldt	10994.349	1.000	10994.349	1.449	.238	.046	1.449	.214
	Lower-bound	10994.349	1.000	10994.349	1.449	.238	.046	1.449	.214
Error (Coor × Rec)	Sphericity Assumed	227669.651	30	7588.988
	Greenhouse-Geisser	227669.651	30.000	7588.988
	Huynh-Feldt	227669.651	30.000	7588.988
	Lower-bound	227669.651	30.000	7588.988

Tests of Within-Subjects Effects

Measure: latency

Despite the fact that there was a main effect for latency in the ROIs, no other main effect could be observed in the interval or in the comparison between coordination and embedding as a whole. That is not critical, as the computations being compared here are qualitatively different and should not be relevant when all electrodes are averaged as a whole. Thus, an effect should not be expected in this kind of general comparison.

Figures 18.13 and 18.14 plot the coordination and embedding latencies, respectively, at different ROIs.

Figure 18.13 Coordination latencies of the N400 at relevant ROIs

Figure 18.14 Embedding latencies of the N400 at relevant ROIs

Embedding-related N400 latencies at relevant ROIs contrast with those related to PP layers connected by coordination at the second and the third PPs. While the coordinated PPs yielded in N400 latencies of similar value in the most relevant ROIs, the N400 latencies related with the embedding condition could be statistically differentiated at central, temporal, and parietal electrodes concerning the layers. Moreover, the third PPs show shorter latencies in all of the relevant ROIs. These results replicate those of the Karajá test. The PP embedding seems to be facilitated after the first layer, that is, after one enters the recursive embedding mode.

The amplitude differences that can be visually observed in the electric flow between coordinated PPs plotted together with embedded ones could be statistically testified by the main effect results plotted in Table 18.7.

Table 18.7 Main effect for mean amplitude: (a) comparison between two intervals (200–400 ms and 400–600 ms) was analyzed according to four different statistical criteria, with the most restrictive one being a Sphericity Assumption; (b) ROI with the same criteria; (c) Coordination versus Embedding (notated as Coor × Rec)

Source		Type III Sum of Squares	df	Mean Square	F	Sig	Partial Eta Squared	Noncent. Parameter	Observed Powera
Interval	Sphericity Assumed	326.945	2	163.473	9.093	.000	.233	18.186	.969
	Greenhouse-Geisser	326.945	1.845	177.214	9.093	.001	.233	16.776	.959
	Huynh-Feldt	326.945	1.960	166.783	9.093	.000	.233	17.825	.967
	Lower-bound	326.945	1.000	326.945	9.093	.005	.233	9.093	.831
Error (interval)	Sphericity Assumed	1078.656	60	17.978
	Greenhouse-Geisser	1078.656	55.348	19.489
	Huynh-Feldt	1078.656	58.809	18.342
	Lower-bound	1078.656	30.000	35.955
ROI	Sphericity Assumed	2955.186	12	246.266	16.018	.000	.348	192.211	1.000
	Greenhouse-Geisser	2955.186	2.671	1106.516	16.018	.000	.348	42.778	1.000
	Huynh-Feldt	2955.186	2.956	999.642	16.018	.000	.348	47.352	1.000
	Lower-bound	2955.186	1.000	2955.186	16.018	.000	.348	16.018	.972
Error (ROI)	Sphericity Assumed	5534.903	360	15.375
	Greenhouse-Geisser	5534.903	80.121	69.081
	Huynh-Feldt	5534.903	88.687	62.406
	Lower-bound	5534.903	30.000	184.497
Coor × Rec	Sphericity Assumed	3.372	1	3.372	.032	.859	.001	.032	.053
	Greenhouse-Geisser	3.372	1.000	3.372	.032	.859	.001	032	.053
	Huynh-Feldt	3.372	1.000	3.372	.032	.859	.001	.032	.053
	Lower-bound	3.372	1.000	3.372	.032	.859	.001	.032	.053
Error (Coor × Rec)	Sphericity Assumed	3160.276	30	105.343
	Greenhouse-Geisser	3160.276	30.000	105.343
	Huynh-Feldt	3160.276	30.000	105.343
	Lower-bound	3160.276	30.000	105.343

Tests of Within-Subjects Effects

Measure: meanAmp

The main effects for mean amplitude were observed in relation to interval (all electrodes as a whole) and ROIs, concerning the comparison between coordinated PPs and embedded ones. Nevertheless, a general comparison of latencies between coordination and embedding was not statistically relevant. This is probably due to the fact that the effect is qualitatively different among the three PP layers.

Figures 18.15 and 18.16 plot the coordination and embedding latencies, respectively, at different regions of interest (ROIs).

Figure 18.15 Coordination mean amplitudes of the N400 at relevant ROIs

Figure 18.16 Embedding of PPs’ mean amplitudes for the N400 at relevant ROIs

The results at relevant ROIs show that it is possible to differentiate among the PP layers connected by coordination by means of the statistically significant N400 amplitudes of the first, second and third PPs, an effect that is stronger on the left hemisphere ROIs. Since amplitudes are related to computational complexity, these results seem to point to a progressive facilitation at each PP within the coordination mode. The interesting aspect of this finding is that, as seen in Figures 18.13 and 18.14, this facilitation does not result in time advantage, since coordination of PPs presented the same latency times for each PP. As could be imagined, coordination must involve more memory resources,Footnote ⁵ often linked to increased processing time, but not necessarily more complex operations. It is possible that this effect was not found in Karajá because of the coordination morpheme that might make processing simpler.

Similar to the coordinated PPs, but not as strong and not as widespread, the N400 latencies for embedded PPs yielded different values in the most relevant ROIs. Therefore, the N400 latencies related with the embedding condition could be statistically differentiated, showing a smaller amplitude at each PP. This progressive facilitation is followed here by time advantage. This result seems to replicate the results we found in Karajá, which made us conclude that the processing of the PPs seems to be facilitated after one enters the recursive embedding mode.

4 Conclusions

Despite the fact that the tests differed in methodology, i.e., a chronometric off-line psycholinguistic test with oral stimuli versus on-line electrophysiological ERP tests with visual stimuli, the results showed a marked facilitation of coordination compared to embedding.

Both Karajá and BP PP coordination and embedding, tested off-line and on-line, yielded compatible results in two aspects: (i) the three types of stimuli listing one, two, and three coordinated words had similar RTs and ERP latencies; (ii) coordination yielded earlier RTs and N400s than those of embedding; and (iii) strikingly, as to the embedded stimuli, there was a progressive facilitation going from the constructions with one PP layer, to two and three PPs. Thus, since marked N400s are connected with difficulties in word integration with the working context, according to this view, the more salient the N400, the harder the combinatorial process (Kutas and Hillyard Reference Kutas and Hillyard1980, Reference Kutas and Hillyard1984; Brown and Hagoort Reference Brown and Hagoort1993; França et al. Reference França, Lemle, Cagy, Constant and Infantosi2004; Lau, Phillips, and Poeppel Reference Lau, Phillips and Poeppel2008).

Our interpretation is, therefore, that embedding is the result of a syntactic algorithm that is costly to be launched, but once established, does not pose any extra significant effort to the system.

This result is striking also in view of the fact that the embedding condition has an inherent supplement of complexity, which is semantic restrictiveness. However, it can be explained because, within the ERP sensitivity, syntax is accessed earlier than semantics. Very early ERPs, within the 100–200 ms timeframe, are known to be sensitive to phrase structure building (Lau et al. Reference Lau, Phillips and Poeppel2008; Kim and Gilley Reference Kim and Gilley2013).

Additionally, the N400 in fact also reflects the minute semantic manifestation of syntax, the kind of semantics that derives anticipating meaning from syntactic configuration and not from root meaning (Lau, Holcomb, and Kupperberg Reference Lau, Holcomb and Kupperberg2012). If this is the case, then maybe the N400 does not result from lexical-level processes, but might be related to the effort to perform a combinatorial process: the syntactic head-complement combination.

Thus, we argue here that our ERP results reflect the basic syntactic algorithm of embedding, in contrast with the off-line psycholinguistic test, which probably captured cumulative semantic effects of restrictiveness.

Finally, it should be clear that we are not arguing here that embedding can be reduced to a processing effect, since such a conclusion could not be granted by the very findings in two sets of experiments conducted: our coordination results yielded faster RTs and shorter latency ERPs than those of recursively embedded PPs. More importantly, we assume that the two kinds of Merge that are necessary to coordinate and to embed PPs are not extra-grammatical, but primitive narrow faculty computations. However, the subtlety of the ERP results, disentangling syntactic and semantic computations, allowed us to ponder that since syntactic facilitation does appear in the subsequent embedding, a performance or third-factor phenomenon might be connected to this facilitation. Embedding is hard to deploy, but once engaged in its algorithm, subsequent embedding is facilitated.