2.1. The Projection Problem

Before delving into abstractness and opacity, I want to emphasise the obvious point that what is easy or hard to learn depends entirely on what learners bring to the task. In generative grammar, what has been called ‘the logical problem of language acquisition’ (Hornstein & Lightfoot Reference Hornstein, Lightfoot, Hornstein and Lightfoot1981) can be schematically depicted as in (2):

The diagram illustrates a learner born into a community that speaks a language L, who is exposed to a sampling of data, D_L, from L, and somehow acquires a grammar of L, G_L. What the learner has to do is known as the Projection Problem (Peters Reference Peters and Peters1972; Baker Reference Baker1979), because the learner is required to project (i.e., induce) a grammar G_L from D_L. This projection is made possible by the innate set of cognitive principles that learners are equipped with, which can convert D_L into G_L. In generative grammar, these principles have been called UG. Some understand UG in a narrow sense to refer to an innate cognitive endowment that is specific to language. However, it has sometimes been used to refer to the collection of cognitive principles that allow learners to acquire a language, whether these are specific to language or not, and this is the sense in which I will use it. While it is an interesting question how much of UG is particular to language or even phonology, this may not be easy to determine. Even principles that appear to be very specific to phonology, such as the ones presented in §2.2, might, at a higher level of abstraction, turn out to be phonological manifestations of more general principles. For example, it has been shown (Gershman & Niv Reference Gershman and Niv2010; Courellis et al. Reference Courellis, Minxha, Cardenas, Kimmel, Reed, Valiante, Daniel Salzman, Mamelak, Fusi and Rutishauser2024) that abstract neural representations arise in all kinds of learning. What is important for my purposes here is that, by definition, UG is not learned, but is rather what the learner brings to the task of acquiring a grammar. In Bayesian terms, UG is the hypothesis space and the set of priors in the learning scenario, leaving open which innate principles are unique to language.

The diagram in (2) abstracts away from many issues surrounding the acquisition and use of language: it is manifestly unequipped to represent the time course of language acquisition, or language acquisition in a multilingual or multidialectal environment. Rather, the diagram is an idealisation (not a hypothesis!) that is meant to focus our attention on the two questions in (3):

The first goal of generative grammar (3a) is to determine G_L for each L. A correct grammar of L – one that represents the grammar internalised by speakers of L – achieves descriptive adequacy, in the term used by Chomsky (Reference Chomsky1965). Some questions phonologists want to answer are given in (4).

These are all questions that phonologists argue about, but they cannot be issues for learners. The basic form of each G_L, and of all possible G_Ls, is determined by UG. In Chomsky’s (Reference Chomsky1965) term, a correct theory of UG achieves explanatory adequacy.Footnote ³

Having to project a grammar from incomplete data requires a type of induction that inevitably involves a poverty-of-the-stimulus problem: without some constraints on possible hypotheses, there are too many potential ways one can generalise from any finite amount of data. Moreover, the data D_L does not by itself tell the learner what the units or operations of mental representation are. UG must be rich enough to bridge the qualitative gap between D_L and G_L. Therefore, when one asks how hard it is for a learner to acquire G_L given exposure to D_L, any answer we give must make some assumptions about UG: what may be hard to learn given UG₁ might be easy to learn given UG₂. Linguists’ intuitions as to what might be easy or hard to learn thus presuppose some often unspoken assumptions about the nature of UG. In this article, I will try to make some of these assumptions explicit.

2.2. Assumptions about phonological grammars

I make the basic assumptions in (5):

Assumptions (5a) and (5b) are common to most theories of phonology. The status of (5c) was at the core of a much-discussed example of what Bloch (Reference Bloch1941) called the partial overlapping of phonemes. This situation arises when occurrences of the same sound under the same conditions must be assigned to different phonemes. An example involves the word-final devoicing (WFD) of obstruents in German (Trubetzkoy Reference Trubetzkoy1939; Moulton Reference Moulton1962), as shown in (6).

In (6a), WFD applies to the underlying /d/ of Bund /bund#/ ‘federation.sg’, causing it to surface as [t], like the [t] in (6b) bunt ‘colourful.m.sg’, which derives from an underlying /t/.Footnote ⁴ Thus, two occurrences of phonetic [t] that derive from different phonemes occur in identical phonetic contexts. If we are allowed to take into account the lexical identities of these forms and the evidence of other members of their paradigms, we can see that the final [t] of ‘federation’ alternates with [d], as in [bundə], whereas the final [t] in ‘colourful’ is always [t], as in [buntə]. Bloch, like many of his fellow post-Bloomfieldians, assumed that learners may not make use of such evidence when establishing their phonemic systems, and would therefore have no way to know that the final [t]s in these words belong to different phonemes. Therefore, Bloch (Reference Bloch1941) proposed that this kind of overlapping should be excluded from phonemic analysis. It then follows that the [t] in both instances of bunt would have to be assigned to the phoneme /t/; the relation between [t] and [d] in the forms of ‘federation’ would have to be accounted for at a higher, morphophonemic, level of analysis.

Halle (Reference Halle1959) showed that this restriction on phonemic analysis results in a loss of a generalisation when applied to Russian; Chomsky (Reference Chomsky1964) argued that the assumptions undergirding this restriction have no empirical support. Their arguments thus undermined the empirical and psychological bases of what they called the ‘taxonomic phoneme’ (see further Dresher & Hall Reference Dresher and Hall2022; Ladd Reference Ladd2022).

This example shows how learnability considerations have always been at the heart of debates over abstractness in phonology. It also illustrates how assumptions about what resources learners bring to the task of acquiring phonology govern our estimate of how easy or hard underlying forms are to acquire. If learners do not have access to the facts that [bunt] ‘federation.sg’ is related to [bundə] ‘federation-pl’ and that [bunt] ‘colourful.m.sg’ is related to [buntə] ‘colourful-f.sg’, then it is impossible for them to correctly assign the [t] of any given instance of [bunt] to /d/ or to /t/; if they do have access to this information, then it becomes easy to imagine how they might do this. Following Chomsky and Halle, most analyses in a generative framework have assumed the correctness of (5c).Footnote ⁵

Assumption (5d) has been assumed by many, but not all, phonological theories, particularly within generative phonology; see Krämer (Reference Krämer2012) for a history of underlying representations. For example, the grammar in (6) posits that the morpheme ‘federation’ has a single underlying representation /bund/. If we deny (5d), we could assign it two underlying representations, /bunt/ for when the stem is word final and /bund/ for when it is followed by a suffix. But such an analysis fails to capture the transparent generalisation that both [bunt#] and [bund-] follow predictably from /bund/ and WFD. Hyman (Reference Hyman2018: 595), who argues in support of this assumption, calls it the morphophonemic principle: ‘one should derive allomorphs from the same UR, wherever possible and “motivated”.’ Sometimes, no plausible phonological account can be constructed, as in cases of suppletive allomorphy, and learners may be unable to arrive at a single underlying form. Bermúdez-Otero (Reference Bermúdez-Otero2018a) argues that underlying representations adhering to (5d) are required in order to distinguish between regular phonology and suppletive allomorphy.Footnote ⁶ Sanders (Reference Sanders2003) and O’Neill (Reference O’Neill and Aronoff2024), who oppose (5d), call it the principle of lexical minimisation. It is clear from all the above writers that the utility and validity of this principle depend on what other machinery one attributes to UG. Sanders (Reference Sanders2003) and O’Neill (Reference O’Neill and Aronoff2024) posit different theories of phonology and morphology from the one adopted here.

Assumption (5e) is standard in theories that adopt (5d). Since the evaluation measure proposed by Chomsky & Halle (Reference Chomsky and Halle1968), what ‘the simplest and most regular grammar’ is and how learners arrive at it has been a central issue in phonological learnability (see the introduction by Katzir et al. Reference Katzir, O’Donnell and Rasin2021 to a special issue of the Journal of Language Modelling on simplicity in grammar learning and the papers therein). My focus is to show how learners guided by the proposed UG principles could plausibly arrive at abstract representations and opaque rules in the cases to be discussed. See §2.3 for some proposals for how simplicity might be computed by learners in a general way.

Assumption (5f) expresses the idea that phonological analyses preferably employ phonological terms rather than non-phonological terms. Of course, there are morphologically governed alternations that may look phonological but which do not have a purely phonological solution. However, it may not be evident to learners at first what sort of case they are dealing with. Therefore, even in such cases, logic requires learners to first look for a phonological solution, and only resort to non-phonological terms when none is available. Otherwise, they risk overlooking a phonological solution when there is one, contrary to (5f).

Diacritics are here considered to be non-phonological by definition; in practice, however, whether a term is classified as phonological or diacritic depends on one’s theory. For example, Nespor & Vogel (Reference Nespor and Vogel2007) consider the prosodic hierarchy and its constituents (the phonological phrase φ, the intonational phrase I, etc.) to be native to the phonology, but Scheer (Reference Scheer, Hartmann, Hegedüs and Riemsdijk2008) considers them to be diacritics. For our purposes, I consider a ‘diacritic’ to be an ad hoc symbol that has no phonological/phonetic interpretation in itself, but which has phonological consequences. For example, if one were to distinguish two types of i in a language by designating them i ₁ and i ₂, then the numerical subscripts are diacritics. I understand ‘the diacritic use of phonological features’ (Kiparsky Reference Kiparsky and Fujimura1973) to mean that features are being used in an ad hoc, arbitrary way that has no connection to their purported phonological/phonetic interpretation. Conversely, ‘the phonological use of diacritic features’ (Kiparsky Reference Kiparsky and Fujimura1973: 18) refers to diacritics that function as phonological features; according to (5f), learners would posit actual phonological features rather than diacritics that have the same effect.

Finally, I assume that underlying representations are related to surface representations by means of ordered rules (5g), as in classical generative grammar. I adopt this model for concreteness and do not intend to exclude refinements such as Autosegmental Phonology (Goldsmith Reference Goldsmith1976), Metrical Phonology (Liberman & Prince Reference Liberman and Prince1977; Halle & Vergnaud Reference Halle and Vergnaud1987) or levels as in Lexical Phonology and Morphology (Kiparsky Reference Kiparsky, Hulst and Smith1982a,Reference Kiparsky and Yangb, Reference Kiparsky1985). Many phonologists assume rather that phonological processes take the form of ranked constraints, as in various versions of Optimality Theory (OT; Prince & Smolensky [1993] Reference Prince and Smolensky2004). Some of the basic assumptions carry over to versions of OT that allow for synchronic opaque interactions, including Stratal OT (Kiparsky Reference Kiparsky2000; Rubach Reference Rubach2003; Bermúdez-Otero Reference Bermúdez-Otero2018b; Jaker & Kiparsky Reference Jaker and Kiparsky2020) and Harmonic Serialism (McCarthy Reference McCarthy2007, Reference McCarthy2008; Elfner Reference Elfner, McCarthy and Pater2016; Rasin Reference Rasin2022; Pruitt Reference Pruitt2023).Footnote ⁷

There are differing views as to the nature of the basic primes that constitute phonemes. What form they take is an empirical issue; for concreteness, I will assume that they are binary features as in (7). Privative (unary) elements or structures have also been proposed; see van ’t Veer et al. (Reference van ’t Veer, Botma, Breit and van Oostendorp2023) for a recent survey. Many of the learnability considerations discussed here carry over to these other representations.

By ‘language-particular’ (7b), I mean that I accept the arguments by Mielke (Reference Mielke2008), Samuels (Reference Samuels2011) and others that features are not universal, but are constructed by learners based on the evidence supplied by their language. Positing that features are emergent in this sense does not lessen the need for a rich set of innate UG principles; on the contrary, if individual features are not innately supplied it is all the more important to have principles that constrain how many features there can be and what properties they have. I assume that perceptual and physical systems put constraints on what a possible feature is (Heffner et al. Reference Heffner, Idsardi and Newman2019). I also assume that constraints are imposed by considerations of phonological contrast (Cowper & Hall Reference Cowper and Hall2014; Dresher Reference Dresher2014; Hall Reference Hall2023), as discussed further below.

It should be emphasised that the kind of markedness assumed in (7) is language-particular, in the spirit of Trubetzkoy (Reference Trubetzkoy1939); see further Rice (Reference Rice, Cheng and Sybesma2003, Reference Rice and Lacy2007), Battistella (Reference Battistella2022: 229–231) and Dresher & Hall (Reference Dresher and Hall2022: 373–374). On this conception, just as each feature has a positive and a negative pole, it also has a marked and an unmarked one. This kind of markedness is a formal property of feature theory and is therefore not subject to the critiques that markedness is a prime example of ‘substance abuse’ (Hale & Reiss Reference Hale and Reiss2000; Reiss Reference Reiss2018) or vagueness (Haspelmath Reference Haspelmath2006; Martins Reference Martins and Samuels2017). Assumption (7d) is based on the observation by Rice (Reference Rice and Lacy2007) that susceptibility to assimilation or deletion is characteristic of unmarked elements, which tend to be targets of phonological processes, whereas segments with marked features tend to be triggers of processes.

I further assume that features are assigned in accord with Contrastive Hierarchy Theory (CHT), whose main tenets are shown in (8):

These principles of CHT constrain the number of features that can be posited for any given inventory (Dresher Reference Dresher2018). Since the ordering of features is language-particular, learners need a way to determine which features are contrastive and how they are ordered. According to (8c), only contrastive features can be active; therefore, by hypothesis, an active feature must be contrastive. In CHT, then, an important source of evidence for learners is phonological activity, which can be defined as in (9).

CHT together with the assumptions in (5) and (7) posits that phonology is serial and rule-based, and that only contrastive features are phonologically active. The analyses I will present presuppose this framework, but it is possible that their essential elements can also arise in other theories.

Dresher (Reference Dresher, Baker and McCarthy1981) considers how learners might arrive at abstract grammars. He suggests that ‘the most common phonetic rules involve the assimilation of one feature to a feature in its environment’ and proposes that a rule of the general form in (10) is a highly-valued rule that learners would be drawn to construct.

According to (10), if a segment S = takes on a certain feature value in the presence of another segment T, the learner will suppose, unless there is evidence to the contrary, that T also bears the same specification and is the cause of the change in S. A similar (perhaps too strong) constraint has been proposed by Danesi (Reference Danesi2022) under the name of the No Ex Nihilo Hypothesis:

2.3. Relationship to learning models

The principles presented in §2.2 are not intended to provide a step-by-step acquisition procedure or computational algorithm. As stated in §2.1, they are intended to address the logical problem of language acquisition; in particular, they are an attempt to provide a set of learning principles that can lead a learner to the abstract representations that I argue for in the subsequent sections. Thus, I abstract away from early or intermediate stages of learning and look at what crucial principles of UG a learner supplied with all the relevant data would need to arrive at the proposed grammars.

Various models have been presented that aim at aspects of learning that the principles in §2.2 do not address (see Jarosz Reference Jarosz2019 and Belth Reference Belth2023a for reviews). Some of these models are claimed to be able to learn some types of opaque rules and/or abstract underlying representations. To the extent that they do not conflict with the principles assumed here, they can be viewed as complementing the current proposal.

In a series of publications (Rasin & Katzir Reference Rasin and Katzir2016, Reference Rasin and Katzir2020; Rasin et al. Reference Rasin, Berger, Lan and Katzir2018, Reference Rasin, Berger, Lan, Shefi and Katzir2021; Rasin Reference Rasin2022), Roni Katzir, Ezer Rasin and their collaborators have argued in favour of a learning approach that follows the principle of minimum description length (MDL; Rissanen Reference Rissanen1978; Rissanen & Ristad Reference Rissanen, Ristad and Ristad1992). They show that it is capable of learning at least some types of opacity in both constraint-based and rule-based phonology.Footnote ⁸

MDL enforces a type of locality in phonology, and locality is the main principle of the Parsimonious Local Phonology (PLP) learner proposed by Belth (Reference Belth2023a). He shows that PLP can learn abstract underlying forms and certain opaque rules. This approach complements principles such as (10) and (11), which focus on the relation between the target and the context of a rule; PLP focuses on the locality of the context (the ‘X’ in (10)), but not on the relation between the target and the context. Belth (Reference Belth2026) extends the approach to long-distance tier-based interactions (cf. Nevins’s [Reference Nevins2010] notion of relativised locality).

Yang (Reference Yang2005, Reference Yang2016) has proposed the Tolerance Principle, which posits the maximum number of exceptions that a rule can withstand before a learner is required to revise or abandon it. Belth (Reference Belth2023a,Reference Belth, Hunter and Prickettb) incorporates it into his learning model, and nothing prevents it from being a part of the UG outlined in §2.2.

Chandlee et al. (Reference Chandlee, Heinz and Jardine2018) characterise opaque interactions computationally in terms of input strictly local (ISL) maps (Chandlee Reference Chandlee2014). They argue that ‘the various types of interactions which researchers have identified as opaque all share the computational property of being ISL’, which comes with strong learnability results (Chandlee et al. Reference Chandlee, Heinz and Jardine2018: 172). They conclude that such opaque interactions ‘are not necessarily more complex than single processes’.

Computational learning models within OT have been shown to be able to learn some types of opaque interactions. One influential approach uses Maximum Entropy Grammar (Goldwater & Johnson Reference Goldwater, Johnson, Spenader, Eriksson and Dahl2003; Hayes & Wilson Reference Hayes and Wilson2008); see O’Hara (Reference O’Hara2017), Nazarov & Pater (Reference Nazarov and Pater2017) and Wang & Hayes (Reference Wang and Hayesin press) for applications.

Though the models mentioned in this section may differ conceptually and empirically from my approach, the fact that different types of learning models succeed in learning opaque interactions, when supplied with appropriate principles, shows that opacity is not the stumbling block to learnability that it has often been supposed to be.

In the following sections, I will show how the principles in §2.2 apply to several cases of abstractness. In each case, I will argue that abstractness and opacity pose no special problems that would require the learning theory to depart from the normal phonological principles that apply to transparent rules. Moreover, I will contend that the proposed alternative non-opaque analyses are not any easier to learn, and that learnability considerations do not militate against abstract phonological representations and opaque rules in these cases.

3.1. Strong and weak [i]

Many Inuit dialects make a distinction between ‘strong i’ and ‘weak i’.Footnote ⁹ For example, in Barrow (North Alaskan) Inupiaq (Kaplan Reference Kaplan1981b: 81–82), the suffixes -lu ‘and a N’, -nik ‘obl.pl’, and -tun ‘like a N’ follow a stem whose last vowel is u, as in (12a).

These suffixes all begin with an alveolar consonant which is palatalised after some i, as shown in (12b): l becomes ʎ; n becomes ɲ and t becomes s, which is the usual Inuit palatalisation (actually assibilation) of t. This is called ‘strong i’ in the literature. After other i (‘weak i’) as in (12c), there is no palatalisation, and the suffixes appear as they do after u in (12a) (and also after a, not shown here). Following Kaplan (Reference Kaplan1981b), Compton & Dresher (Reference Compton and Elan Dresher2011) propose that whereas strong i is underlyingly /i/, weak i derives from an underlying vowel that is distinct from /i/.Footnote ¹⁰

This abstract analysis reflects the historical provenance of strong and weak i from Proto-Inuit-Yupik (PIY) as reconstructed by Fortescue et al. (Reference Fortescue, Jacobson and Kaplan1994): strong i mostly derive from PIY *i, as in (13b), and weak i mostly derive from a fourth vowel reconstructed as PIY *ə, as in (13c).Footnote ¹¹ Cognates of these words in Central Alaskan Yupik (CAY) dialects, which retain a phonetic contrast between /i/ and /ə/, usually have [i] corresponding to strong i and [ə] corresponding to weak i (13).Footnote ¹² Child learners of modern Inuit dialects have no access to the PIY origins of these words or to the CAY cognates. The abstract analysis is not motivated by PIY or by CAY, but by the synchronic data that learners have access to.

3.2. A learning theory for the abstract vowel in Inuit dialects

How hard is it, in Inuit dialects, to acquire an underlying vowel that has no distinct surface realisation? It depends on the contents of UG. If UG limits the learner to underlying representations that exist as such at the surface, then there is no path to acquiring an abstract vowel. But I know of no evidence for this limitation. It would perhaps have some rationale if UG treated phonemes as undecomposable primes. If that were the case, one could perhaps argue that it would be difficult, if not impossible, for learners exposed only to allophones of /i/, /u/, and /a/ to posit a fourth phoneme, say /ə/, in lexical representations. But the theory adopted here assumes that phonemes are composed of features, as in (7). If so, then it is these primes that are the material of phonological computation. I will argue that this kind of computation can easily lead to abstract phonemes.

Recall that one of the ‘strong claims’ of the Compton & Dresher (Reference Compton and Elan Dresher2011) analysis, according to Mayer et al. (Reference Mayer, Major, Yakup, Jurgec, Duncan, Elfner, Kang, Kochetov, O’Neill, Ozburn, Rice, Sanders, Schertz, Shaftoe and Sullivan2022a: 1), is ‘that speakers have localized the source of the idiosyncrasy to a distinction between two sounds that are identical on the surface’. In this case, it is very clear from (12) that some stem-final i are what cause palatalisation of the suffix-initial consonants, which does not occur in their absence.Footnote ¹³ It is not so obvious what the palatalising feature is; for now, let’s call it [+P]. Thus, i in (12b) carries this feature, and stem-final u in (12a) and i in (12c) do not. Further, by our assumption in (10), learners prefer to posit a rule that assigns [+P] in the context of [+P], suggesting that palatalisation assigns [+P] to the palatalised consonants. Identifying one feature [P] for both cause and effect is simpler than identifying two different features [P] and [Q], if palatalisation is not the result of the assimilation of a feature. Adapting the template in (10) to our case, we suppose that learners would posit a rule like (14) to account for palatalisation.Footnote ¹⁴

Whereas stem-final u in (12a) clearly lacks [+P] and the stem-final i in (12b) clearly has it, (12c) presents conflicting signals: stem-final i is phonetically the same as i in (12b), hence [+P]; but the suffixes that follow it suggest that it is not [+P]. The learning theory tells the learner how to resolve this conflict. In classical generative phonology, the resolution occurs via a derivation: though stem-final i in (12c) has [+P] at the surface, it must lack it underlyingly and at least until after palatalisation has applied.

3.3. Assigning features to weak i

How does a learner assign features to weak i? The same way that features are assigned to every other phoneme. Let us consider first Inuit dialects with three underlying vowels, /i, a, u/. These dialects have completely lost any contrast between PIY *i and *ə. Interestingly, none of these dialects have palatalisation after /i/. Compton & Dresher (Reference Compton and Elan Dresher2011) propose that this is because the Inuit-Yupik feature hierarchy has [low] ordered over [labial] (notated [low] $\gg $ [labial]), as shown in (15).Footnote ¹⁵ As only two contrastive features are needed in a three-vowel system, /i/ in these dialects has no contrastive palatalising feature; it’s the unmarked vowel. Compton & Dresher (Reference Compton and Elan Dresher2011: 223) observe that /i/ in these dialects is the epenthetic vowel inserted to satisfy phonotactic constraints in adapting loanwords: ‘This use of /i/ as the default vowel supports its unmarked status in the inventory of three-vowel dialects.’

Now consider dialects which have retained a contrast between strong and weak i, that is, between /i/ and a fourth vowel, which for now we can call /V/. By assumption (5f), the contrast between /i/ and the fourth vowel /V/ requires a phonological feature, which must be the palatalising feature [P]. Several considerations converge to the conclusion that this feature should be added to the hierarchy as shown in (16).

In support of (16), the fourth vowel merges with /i/ (in most cases; some other outcomes are discussed in the next section), suggesting that its features apart from [P] are the same as those of /i/. Second, there is no evidence that the fourth vowel is either [+low] or [+labial]. Third, we will see evidence that the fourth vowel is unmarked in these four-vowel dialects, supporting its lack of marked vowel features.

What is [P]? Compton & Dresher (Reference Compton and Elan Dresher2011) proposed that [P] is [coronal], following studies that argue that V-place [coronal] causes palatalisation of consonants (Clements Reference Clements1976, Reference Clements1991a; Hume Reference Hume1994), even those with C-place [coronal] (see Kochetov Reference Kochetov, Oostendorp, Ewen, Hume and Rice2011 for a review). If strong /i/ is [+coronal], then weak i must be [−low, −labial, −coronal], that is, a non-low, non-rounded, non-front vowel we could call /ə/ or /ɨ/.

Kaplan (Reference Kaplan1981b) followed Chomsky & Halle (Reference Chomsky and Halle1968) in proposing that the palatalising feature is [+high]. This view is supported by Lahiri & Evers (Reference Lahiri, Evers, Paradis and Prunet1991) and Lahiri (Reference Lahiri, Hyman and Plank2018), who argue that the palatalisation of /l/ to [ʎ] and /n/ to [ɲ] amounts to the change of [−high] to [+high].Footnote ¹⁶ Suppose we assume that the third feature is [high]. On this view, weak /i/ must be [−low, −labial, −high], a mid non-rounded vowel which again could be considered to be /ə/ (or perhaps /e/).

In our case, it doesn’t much matter what we call the palatalising feature. Whether feature theory has C-place and V-place tiers is determined by UG; it’s not something the learner has to figure out. Nor does it matter what exactly we call the fourth vowel. In CHT, segments are underspecified in the phonological component, and phonetic detail is added in the phonetics; but the fourth vowel has no independent phonetic realisation. There is no harm in identifying it with a particular segment like [ə] or [ɨ] or [e], but we should keep in mind that its actual identity is the set of contrastive features it is assigned, which strictly speaking have no phonetic realisation (being underspecified).Footnote ¹⁷

We can now address another critique of the abstract analysis by Mayer et al. (Reference Mayer, Major, Yakup, Jurgec, Duncan, Elfner, Kang, Kochetov, O’Neill, Ozburn, Rice, Sanders, Schertz, Shaftoe and Sullivan2022a: 1), that it is an instance of ‘the diacritic use of phonological features’. As discussed in §2.2, I understand this expression to refer to the use of phonological features in an ad hoc, non-phonological manner. However, there is nothing ad hoc or arbitrary about the features employed in this analysis: rather, phonological features are motivated by phonological processes and contrasts.

3.4. Weak i and opacity

I have now presented the outline of a learning theory that can lead an Inuit learner to identify weak i with an underlying set of features that can be written /ə/ (with the above caveats). To complete the story, let’s consider sample derivations with strong and weak i. In (17a), palatalisation applies to /l/ that follows underlying (strong) /i/. In (17b), palatalisation does not apply to /l/ that follows underlying /ə/ (weak i). The neutralization of /ə/ to [i] must follow the application of palatalisation. The relative ordering of palatalisation and /ə/ → [i] makes the former rule opaque.

The examples in (12c) make palatalisation an example of the type of opacity defined in (1a): palatalisation appears to have underapplied in (17b) in ini-lu (*ini-ʎu), and similarly in ini-nik (* ini-ɲik ) and ini-tun (*ini-sun). The underapplication is only apparent, however; at the point in the derivation where palatalisation applies, the relevant forms are , and , and the context for palatalisation is not met.

Does this opacity thereby make the palatalisation rule hard to learn? No! In our learning scenario, learners have already acquired palatalisation (14), as well as the underlying contrast between /i/ and /ə/. Ordering palatalisation before /ə/ → [i] – that is, creating opacity – is a solution to the problem of conflicting signals sent by weak i.

Even if it is agreed that the abstract analysis is learnable, one might ask whether it should be preferred to a diacritical analysis. What would be wrong with positing a single /i/ in palatalising dialects, and marking the so-called weak i as exceptionally not triggering palatalisation? Or alternatively, marking palatalising /i/ with a diacritic, say , that triggers palatalisation? Is it not somehow simpler, more conservative, closer to the null hypothesis, to posit a diacritic than an abstract phoneme?

No! The impression that a diacritic solution is the default option is an illusion based on thinking of phonological computation as accessible to conscious introspection. In our case, we have an example of palatalisation of consonants triggered by an i, a cross-linguistically very common process that is uncontroversially mediated by a phonological feature. As this account is available in our case – indeed, preferred, given the learning assumptions we are following – it follows that the burden of proof is rather on those who wish to argue that this approach does not apply here.

Compton & Dresher (Reference Compton and Elan Dresher2011) survey different Inuit dialects that distinguish strong and weak i. In some dialects, palatalisation is no longer productive and is limited only to the change of /t/ to [s]. In such dialects, the explanatory work done by positing a fourth vowel is limited, whatever analysis we adopt. Other dialects display more robust evidence for a fourth vowel, and in those dialects there are indeed significant differences between these approaches. Thus, Kaplan (Reference Kaplan1981b: 31) writes that although all Inupiaq dialects have a phonetic three-vowel system, ‘there are strong arguments’ based on phonological processes for the underlying existence of a fourth vowel.

Learners of North Alaskan Inupiaq would have several reasons in addition to palatalisation to distinguish two types of [i] (Kaplan Reference Kaplan1981b: 116–149). Unlike strong i, weak i (which Kaplan transcribes as ï) alternates with a in certain contexts, as before the copula -u- in (18b); compare the strong i in (18a), which does not alternate. In other contexts, weak i but not strong i alternates with u, as well as with $\varnothing $ ; the latter alternation is evidence for either epenthesis or syncope, depending on the analysis.

Now the advantages of an abstract (i.e., phonological) analysis over a diacritic one are more evident. The various kinds of phonological activity that the two i enter into are all consistent with strong i being more marked than weak i: palatalisation suggests that strong i has an active feature that weak i lacks; and the fact that weak i is easily assimilated and either deleted or epenthetic suggests that its features are relatively unmarked, as per (7d). Indeed, in Yupik, which retains an overt four-vowel system /i, a, u, ə/, the schwa does not have the same status as the other vowels. According to Kaplan (Reference Kaplan and Collis1990: 147), it ‘cannot occur long or in a cluster with another vowel’, instead undergoing dissimilation or assimilation when adjacent to full vowels. Miyaoka (Reference Miyaoka2012: 38) writes that Yupik schwa ‘frequently occurs as an epenthetic vowel (EV) to break up an unallowable consonant cluster’. This is exactly the behaviour of weak i in Inupiaq, which follows from the abstract analysis. On a diacritic analysis, however, there is no reason to expect that a non-palatalising i should also be subject to assimilation and deletion or epenthesis, unless we ascribe to the diacritic the properties of an unmarked phonological feature, essentially adopting the abstract analysis.

4.1. Backness harmony in Uyghur

The vowel inventory of Uyghur is shown in Table 1.Footnote ¹⁸

Table 1

Uyghur vowel inventory (Hall & Ozburn Reference Hall and Ozburn2019).

Table 1 Long description

The table is organized into four main columns under two primary headings: Front and Back. Each of these is further divided into Unrounded and Rounded sub-columns.

* The High row contains the vowel i in the Front Unrounded cell, y in the Front Rounded cell, and u in the Back Rounded cell. The Back Unrounded cell is empty.

* The Mid row contains the vowel e in the Front Unrounded cell, ø in the Front Rounded cell, and o in the Back Rounded cell. The Back Unrounded cell is empty.

* The Low row contains the vowel æ in the Front Unrounded cell and ɑ in the Back Unrounded cell. Both the Front Rounded and Back Rounded cells are empty.

Uyghur displays backness harmony, whereby the vowels of suffixes harmonise with the final vowel of a stem, as in (19) and (20). Some consonants also participate in this harmony: the dative front -gæ (or -kæ) in (19c) alternates with back -qɑ (or -ʁɑ) in (20c).

The vowels i and e have no back counterparts (*ɯ, *ɤ). They can co-occur with both front and back vowels, and transparently allow backness harmony to affect following suffixes, as in (21) and (22).Footnote ¹⁹

Given the data up to here, when Uyghur [i] co-occurs with back vowels, one might suppose that it is the surface realisation of an abstract back /ɯ/. In Uyghur, however, there is another way to interpret the varying signals sent by surface [i]: rather than representing two underlying vowels, one could also conclude that there is a single /i/ that is neutral with respect to backness harmony. This interpretation is supported by the fact that, unlike the other front vowels in Uyghur, /i/ and /e/ lack a back counterpart, raising the possibility that they have no contrastive backness feature at all. If we generate contrastive features hierarchically, we find that there are many feature orderings in which /i/ and /e/ do not receive a specification for [front/back]. An example is (23).Footnote ²⁰

On this interpretation, which is not available in Inuit dialects, the harmonic [front] feature originates from the non-neutral stem vowels that bear a contrastive [front] feature. However, there is more to it than that.

Stems containing only /i/ and /e/ are of two types: some take front suffixes, as in (24), and some take back suffixes, as in (25).

These examples cast doubt on the analysis whereby /i/ is neutral, and appear to favour the abstract analysis that posits an underlying /ɯ/ in (25). Additional data, however, puts these forms into a wider context which shows other types of disharmony between stems and suffixes. Mayer et al. (Reference Mayer, Major, Yakup, Jurgec, Duncan, Elfner, Kang, Kochetov, O’Neill, Ozburn, Rice, Sanders, Schertz, Shaftoe and Sullivan2022a) and Mayer et al. (Reference Mayer, McCollum and Eziz2022b) adduce several cases, some of which are shown in (26). These include: (26a) disharmony with k, a [+front] consonant that is expected to take -lær (cf. (19c)), and (26b) the converse disharmony with [−front] q, which should take -lɑr (cf. (20c)); (26c) disharmony following the non-neutral vowel ɑ; and (26d) variation in the suffix following sowet.

These examples show that the source of a harmonizing [ $\pm $ front] feature may be associated with a stem and not with a specific vowel or consonant. That is, the feature may be floating, or on a separate autosegmental tier. In the analysis of Hall & Ozburn (Reference Hall and Ozburn2019), the contrastive feature on non-neutral vowels and consonants is privative palatal that is a dependent of V-Place; lacking that feature, they surface as back by default. Similarly, Mayer (Reference Mayer2021: 121) proposes that [+back] is unmarked in Uyghur. Dresher et al. (Reference Dresher, Hall, Idsardi and Raimy2024) use a formalisation in terms of phonological events, features, and precedence drawn from Raimy (Reference Raimy2000), Papillon (Reference Papillon2020) and Idsardi (Reference Idsardi2022).

Here, I will assume that a contrastive autosegmental [ $\pm $ front] feature associates with vowels and consonants that are contrastive for this feature and can also be lexically associated in floating fashion with the end of a stem, as in the example in (27). The vowels of the stem sinip have no contrastive [front] feature, and the end of the stem has a floating [−front] feature that associates to the vowel and back consonant of the suffix (K and A represent a back consonant and low vowel unspecified for backness; braces represent morpheme boundaries), yielding qɑ.

4.2. Learning exceptional harmony in Uyghur

In comparison to some other examples of abstractness, there is nothing ‘abstract’ about the harmonising feature [ $\pm $ front], which is observed in the speech signal. Nor are there any opaque processes in the data surveyed in the previous section: suffixes transparently receive a [+front] or [−front] feature in the presence of certain stems.Footnote ²¹ Rather, the challenge for learners, as Mayer et al.’s (Reference Mayer, Major, Yakup, Jurgec, Duncan, Elfner, Kang, Kochetov, O’Neill, Ozburn, Rice, Sanders, Schertz, Shaftoe and Sullivan2022a) remark suggests, is to localise the source of the [ $\pm $ front] feature that is affecting the suffixes. In examples like those in (19) and (20), it is clear that the source of the feature is in the vowel of the stem, but in other examples, the source is not so clear. In examples like (25), it is apparent that the source cannot be the stem vowels, which seem to have the opposite value of the feature affecting the suffix. So where is the feature coming from?

Learners following the learning theory outlined in §2 would see that the backness of alternating suffixes is dependent on the stems they attach to. According to the template in (10), they would assume that the [ $\pm $ front] feature observed on the suffix originates in the preceding context. Where there is an overt vowel or consonant with the harmonising feature, they would locate the source there. If there is no such overt segment, and absent evidence that such a segment has been deleted or altered, the next hypothesis would be that the feature is associated with the stem itself. In the version of the theory assumed here, this association takes the form of a floating [ $\pm $ front] feature. Invariant suffixes like -tæk in (26c) have their own prespecified [ $\pm $ front] feature, which can spread to following suffixes (Mayer Reference Mayer2021: 188).

Mayer et al. (Reference Mayer, Major, Yakup, Jurgec, Duncan, Elfner, Kang, Kochetov, O’Neill, Ozburn, Rice, Sanders, Schertz, Shaftoe and Sullivan2022a), following Mayer (Reference Mayer2021), propose an OT analysis using lexical diacritics. On this analysis, when the source of harmony is an overt vowel, harmony is governed by the Agree constraints in (28), a standard OT implementation of feature spreading or agreement. But roots with neutral vowels are marked with an index indicating whether they induce front or back harmony, and these roots are subject to the indexed Harmonise constraints in (29).Footnote ²²

Mayer (Reference Mayer2021: 140) writes:

This analysis is an example of ‘the phonological use of diacritic features’ (Kiparsky Reference Kiparsky and Fujimura1973: 18), because the diacritic here (the index) is functioning exactly like the phonological feature [ $\pm $ back] or [ $\pm $ front]. Indeed, the index will at some point have to be converted into one of these feature values to actually accomplish the harmony. The learning challenge in the case of neutral and otherwise exceptional morphemes is to learn which stems (or roots) induce what kind of harmony, absent an overt harmonising vowel or consonant. Once learners have met this challenge, the question is how they encode that information in their grammar. That depends on UG.

According to the learning assumptions set out in this article, they would prefer to do so phonologically, using a phonological feature to trigger harmony in exceptional cases just as it does in regular cases. Concern about an abstract */ɯ/ in Uyghur is misplaced: the same learning theory that leads a learner to posit abstract /ә/ in Inuit dialects leads a Uyghur learner to posit that /i/ is not contrastively specified for [ $\pm $ front] and that there are morpheme-level [ $\pm $ front] features. We would need a convincing reason to complicate the learning theory, as well as the phonology, to require two entirely different systems to accomplish backness harmony: one using features for when the source of harmony is overt, and a second using indices for when the source of harmony is not overt. As Dresher et al. (Reference Dresher, Hall, Idsardi and Raimy2024: 4) conclude, ‘[t]o all appearances, Uyghur harmony and disharmony are phonological. Lacking evidence to the contrary, we maintain that phonological representations are phonological.’

5.1. Emergent Grammar and Universal Grammar

As Archangeli & Pulleyblank tell it, the EG hypothesis competes with the UG hypothesis in these terms: Do infants learn grammar ‘due to an innate capability specific for language, the Universal Grammar hypothesis (UG), or are they simply the abilities that infants use to learn about all aspects of their world, the Emergent Grammar hypothesis (EG)?’ They propose that language learners make use of basic cognitive principles, listed in (30), which are not special to language:

That’s it! Recall that these principles have to determine what phonological grammars are like; they have to answer the questions in (4). The principles in (30) are indeed fundamental and are presupposed by every learning theory, including the one adopted in this article. But that means that they are compatible with any conceivable theory of phonology. They are thus far too weak to support the acquisition of phonology, which must be based on innate principles that will guide learners to a specific type of phonological grammar. Whatever the exact nature of the phonological grammar, overcoming the poverty of the stimulus requires a contentful theory of UG.

Archangeli & Pulleyblank single out opacity as a problem that UG analyses have and that their EG analysis does not. I will show, however, that opacity is a red herring that obscures the real learning problem.

Esimbi has an unusual restriction on root vowels and an interesting set of prefix alternations. Only three vowels can occur in Esimbi roots, and they are all high: [i, ɨ, u]. Moreover, if a root contains more than one vowel, they must be identical. Esimbi prefixes have more vowels, as shown in (31).

The two prefixes we will be looking at first each have three allomorphs whose choice depends on the root they attach to. Roots with [i] are shown in (32), and roots with [u] are shown in (33); the numerals 3 and 9 represent noun classes.

The patterns in (32) and (33) are general: prefixes alternate among either [i, e, ɛ] or [u, o, ɔ].Footnote ²⁵ The examples show that roots with [i] and [u] come in three types: those that occur with prefixes [i, u]; those that occur with [e, o]; and those that occur with [ɛ, ɔ]. There are also roots with [ɨ], as shown in (34). There are only two types of such roots; prefixes [i, u] are missing.

The generalizations we have observed up to here are:

• • A given prefix is always front or always round.

• • The height of a prefix depends on the root it attaches to.

At first sight, these prefix alternations appear puzzling. Many languages have height harmony, where the height of a prefix vowel must match the height of the root vowel. But in Esimbi, all root vowels are high!

5.2. The basic learnability argument in Esimbi

Building on work by Kenneth Stallcup (see Stallcup Reference Stallcup and Bouquiaux1980a,Reference Stallcupb), Hyman (Reference Hyman1988) proposes that the restriction of roots to high vowels at the surface masks the fact that in underlying representations there is a wider variety of vowels that trigger height harmony in the prefixes. For root vowels that surface as [i] and [u], the vowels of the prefixes mirror the height of the underlying root vowels. The vowels that surface as [ɨ] evidently derive from two central vowels: a mid vowel that co-occurs with prefixes [e-] and [o-], which Hyman represents as /ə/, and a low vowel that co-occurs with [ɛ-] and [ɔ-], represented as /a/. The ingredients of his analysis are summarised in (35).

Some sample derivations that illustrate this analysis are given in (36). Note that RVR makes PHA opaque: after the root vowels raise, we can no longer see the rationale for why the prefixes have the height that they do.Footnote ²⁶

Archangeli & Pulleyblank (Reference Archangeli and Pulleyblank2015: 10–11) are critical of this analysis; they write:

The suggestion here – not stated explicitly – is that learners may not have evidence for positing height distinctions in the lexical forms of the roots. Moreover, they observe that the analysis results in surface opacity and propose alternative generalisations that ‘resolve the opacity problem’, without explaining why opacity is a problem.

Archangeli & Pulleyblank (Reference Archangeli and Pulleyblank2015) present an analysis with no opacity and no abstract underlying vowels that are different from the surface vowels. In their analysis, the words for ‘goat’, ‘antelope’ and ‘animal’ (32) all have the same high vowel in their lexical representations: /bi/, /kibi/ and /nyimi/, and similarly for all the other root vowels [u] and [ɨ]. So how do they account for the fact that roots take prefixes of different heights: [i-bi], [e-kibi], [ɛ-nyimi]? Here is how they do it: in the lexical entry of each root, they indicate – in terms of features – what sort of prefix the root prefers. Some sample representations are shown in (37).

In (37), the notation indicates that /bi/ ‘goat’ in Set A prefers a prefix that is [high] and [ATR], and /simi/ ‘grain’ in Set C prefers a prefix that is [low] and [RTR]. Set B roots have no specified preference; Archangeli & Pulleyblank propose that they take the unmarked prefixes, which in their analysis are [e-] and [o-]. The reasons why prefix selection is framed as preferences, why two features are needed for Sets A and C, and why Set B preferences are left unstated, have to do with the realisations of the third prefix, discussed in §5.3.

Comparing this analysis to one such as Hyman’s, Archangeli & Pulleyblank (Reference Archangeli and Pulleyblank2015: 10–11) write (emphasis added):

Archangeli & Pulleyblank’s analysis and discussion raise some questions:

• • Why is opacity an issue? What is the issue? What is gained by eliminating it?

• • How do we draw the line between phonological and lexical generalisations when the latter are stated entirely in terms of phonological features?

• • Are features easier to learn if they are represented as small capital subscripts?

I mention the notation because I think it obscures some similarities between the UG and the EG analyses. The UG analysis of a word like simi ‘grain’, which takes [ɛ, ɔ] prefixes, attributes to the root vowel two different feature specifications: one is underlying, whose height (and tongue root) feature is spread to the prefix, and the other is for the root after raising, as shown in (38a). The EG analysis of this word also attributes to the root vowel two different feature specifications: one is for the root vowel and the other is for the prefix, as in (38b).Footnote ²⁷

What does the learner have to discover in order to arrive at either the UG or the EG analysis? The learner has to recognise that, though the root [simi] has vowels that appear as [high, ATR], it carries somewhere, in some fashion, [non-high] and [RTR] specifications. What sort of principles will enable Esimbi learners to discover this? Esimbi learners must have a learning mechanism that directs them to look for a solution in terms of features associated with the roots to account for the height of the prefixes.

Consider first the UG analysis: Do we have a learning theory that does this? Yes, we do! In the learning theory outlined in §2.2, the first two assumptions in (5) are that segments are analysed into features and that segments interact through features. Recall also our template for a highly valued rule in (10). Applied to our case, if learners see the form [ɔ-simi] ‘sg 3-grain’, where the height features of the prefix (but not its roundness) are determined by the root, they will attribute those height features to the root.

Like weak i in Inuit dialects, root vowels are sending conflicting signals. In (38a), the surface form of the root vowel [i] in [simi] signals that it is high, but the prefix vowel [ɔ] signals that it is not high. The conflict is resolved by assigning both [high, ATR] and [non-high, RTR] to the root vowel [i]. UG tells the learner how to accommodate these contradictory specifications. In derivational generative phonology, the accommodation takes the form of a derivation with ordered rules, as in (36). [−high, RTR] is assigned to the underlying representation and spreads to the prefix by PHA; the root vowel then raises to [+high, ATR] by RVR.

Is there a learning theory for the analysis presented in Archangeli & Pulleyblank (Reference Archangeli and Pulleyblank2015)? The EG as presented there would have to be greatly enriched beyond the general abilities in (30) in order to arrive at their analysis of Esimbi. We don’t know what such a theory would look like when fully spelled out. In terms of the representations it ends up with, it is not very different – so far! – from the abstract UG analysis. However, whereas the UG theory posits a single unified mechanism of feature transmission for transparent and opaque situations, the EG theory posits two entirely different mechanisms, thereby requiring more, not less, phonology-specific innate machinery, or so it appears. Be that as it may, Archangeli & Pulleyblank (Reference Archangeli and Pulleyblank2015) have not shown that there is a UG opacity ‘issue’ that needs to be resolved, or how EG resolves it.

Some questions about the analysis have yet to be answered:

• • Why do Archangeli & Pulleyblank (Reference Archangeli and Pulleyblank2015) write that roots ‘prefer’ certain prefixes? Why not ‘select’ or ‘assign’?

• • Why are the Set B prefix preferences left unmarked?

• • Finally, what exactly are the phonological features of Esimbi vowels?

To answer these questions, we have to look at a third Esimbi prefix, which Hyman (Reference Hyman1988) calls the A- prefix. This prefix considerably complicates the analysis of Esimbi vowel phonology. And here we will see a considerable difference in the adequacy of the UG analysis compared to the EG analysis.

5.3. Further intricacies of the Esimbi vowel system: the A- prefix

As Hyman (Reference Hyman1988) observes, the A- prefix appears one height degree lower than the vowels of the I- and U- prefixes which occur with the same root. For example, the sg 3 U- prefix in (39a) has the allophones shown. In (39b) are the same roots with the pl 6 A- prefix: [u] in (39a) corresponds to [o] in (39b); [o] corresponds to [ɔ] and [ɔ] corresponds to [a].

Unlike the I- and U- prefixes, the A- prefix does not consistently appear as front or round, nor does it consistently receive these features from the root. As shown in (40), A- appears as [o] with /i, u/; as [ɔ] with /o, ə/; as [ɛ] with /e/ and as [a] with /ɛ, a, ɔ/. Hyman (Reference Hyman1988) writes that the frontness and rounding of the A- prefix are presumably determined by secondary processes.

We will be mainly concerned with the A- prefix specifications that have the effect of lowering the height assigned by the root vowels by one step. This is not a trivial problem! Let’s first look at Archangeli & Pulleyblank’s approach, which is very different from any UG account. They do not characterise the three prefixes in terms of features, but rather as sets of allomorphs. Their analysis is summed up in Table 2.

Table 2

Descriptive summary of Esimbi prefixes (Archangeli & Pulleyblank Reference Archangeli and Pulleyblank2015: 6; adapted from their Table 8)

Table 2 Long description

The table consists of four columns: Class, Prefix, Vowel Height, and Examples.

Row 1: Class 1. Prefix u. Vowel Height High. Examples include u plus b i meaning person and u plus t i meaning tree.

Row 2: Class 2. Prefix a. Vowel Height Low. Examples include a plus b i meaning people and a plus t i meaning trees.

Row 3: Class 3. Prefix u. Vowel Height High. Examples include u plus l i m i meaning tongue and u plus k o b o meaning skin.

Row 4: Class 4. Prefix i. Vowel Height High. Examples include i plus l i m i meaning tongues and i plus k o b o meaning skins.

Row 5: Class 5. Prefix i. Vowel Height High. Examples include i plus s u meaning eye and i plus k u meaning death.

Row 6: Class 6. Prefix a. Vowel Height Low. Examples include a plus s u meaning eyes and a plus k u meaning deaths.

Row 7: Class 9. Prefix i. Vowel Height High. Examples include i plus n a m a meaning animal and i plus g b a meaning rope.

Row 8: Class 10. Prefix i. Vowel Height High. Examples include i plus n a m a meaning animals and i plus g b a meaning ropes.

Recall that Archangeli & Pulleyblank (Reference Archangeli and Pulleyblank2015) specify the Set A roots, which Hyman considers to be underlyingly high, as preferring prefixes that are [high] and [ATR] (e.g., {bi _{hi, atr} } ‘goat’). The highest prefixes in the front and round classes, [i] and [u], are both [high] and [ATR]. The highest prefix in the non-high class, [o], is [ATR] but not [high]. This is why prefix selection is framed as preferences: Set A prefers prefixes that are [high] and [ATR], but will accept only one of these if necessary. In Archangeli & Pulleyblank’s (Reference Archangeli and Pulleyblank2015) analysis, [o] is the only non-high prefix that is [ATR]; [ɛ, ɔ, a] are all [RTR].

The Set C roots, which Hyman considers to be underlyingly /ɛ, ɔ, a/, prefer prefixes that are [low] and [RTR] (e.g., {zu _{lo, rtr} } ‘snake’). In Archangeli & Pulleyblank’s analysis, [ɛ, ɔ] are the only front and round prefixes that are [RTR] (though not [low]). In the non-high prefix, [ɛ, ɔ] are [RTR] but lose to [a] which is also [low].

Now consider the Set B roots, which Hyman considers to be underlyingly /e, o, ə/. In Archangeli & Pulleyblank’s analysis, these roots have no specified preferences (e.g., $\{ $ ki $\} $ ‘tail’) but take the ‘unmarked’ member of each prefix, stipulated to be the middle member. Now we can see that they are forced to this solution because there is no way to state the Set B preferences in a positive way. One would need to say that Set B prefers [non-high] and [ATR] to account for the front and round prefixes, but this selects the wrong vowel [o] in the non-high prefix. The non-high allomorphs that need to be selected are [ɛ, ɔ], which are [RTR]; but then the front and round prefixes will select the wrong vowels [ɛ] and [ɔ].

Let’s reflect for a moment on how Archangeli & Pulleyblank (Reference Archangeli and Pulleyblank2015) specify the variants of each prefix. Each prefix consists of a list of allomorphs, as in Table 2. Why these particular allomorphs? In this analysis, there is no reason why the heights of the front and round allomorphs correspond to each other. And it appears to be a coincidence that the non-high allomorphs are exactly one step below them. Thus, the EG analysis has no explanation for why the prefix allomorphs are the way they are.

By contrast, here is what Hyman (Reference Hyman1988: 260) considered to be the criterion for a successful analysis of the Esimbi prefixes (emphasis added):

The EG analysis abandons this aim: it simply stipulates the vowel heights of each prefix. So let’s look at a UG analysis in the spirit of Hyman (Reference Hyman1988).

5.4. A UG analysis of the A- prefix in Esimbi

What features must the A- prefix have to produce a vowel that is one step lower than the root vowel? There are theories which can do this very elegantly; for example, the Particle Phonology of Schane (Reference Schane1984) or versions of Element Theory (Kaye et al. Reference Kaye, Lowenstamm and Vergnaud1985; Backley Reference Backley2011). In such theories, we could say that the A- prefix literally consists of an A element; adding one A to the root vowel lowers it by one step. Maybe this approach is right! But here I will continue to follow the feature theory set out in (7).

Hyman (Reference Hyman1988) makes a number of proposals to account for the behaviour of the A- prefix. The one I find most compelling is that /a/ is characterised by [−ATR] (which, for purposes of this discussion, is equal to [+RTR]). The idea is that [−ATR] can interact with height features in particle phonology style, lowering each height by one step. While I agree with the spirit of Hyman’s analysis, I want to modify his specifications slightly. I assume the active feature is [+RTR]. Following Archangeli & Pulleyblank (Reference Archangeli and Pulleyblank2015) and for reasons of contrast, I consider /ɛ, ɔ/ to also be [+RTR]. Finally, I would like to include /ɨ/; though it is a derived vowel, it consists entirely of contrastive features, so is part of the contrastive inventory at some point. A possible contrastive feature hierarchy for this system is given in (41a); the feature specifications so generated are displayed in (41b).

Now that we have an explicit account of the vowel features of Esimbi, we can make the analysis outlined in (35) more precise, as in (42).

The specifications of the I- and U- prefixes (42a) are slightly revised: I- is [+front] rather than [−back], and U- is [−front] in addition to [+round], to conform to the feature hierarchy in (41a). Following Hyman (Reference Hyman1988), I assume that the A- prefix is specified only [+RTR]. The underlying root vowels in (42b) are as before.

In the current analysis, the height of a vowel is regulated by two features, [ $\pm $ high] and [ $\pm $ RTR]; therefore, both PHA in (42c) and RVR in (42d) must involve both those features. The output of RVR is a vowel that is [−RTR, +high]: underlying /i, u/ do not change; /e, o, ə/ change to [+high] and /ɛ, ɔ, a/ change to [−RTR] and add [+high].

According to PHA, prefixes unspecified for [RTR] and/or [high] assimilate to the root values of those features. In particular, the I- and U- prefixes receive: [−RTR, +high] from /i, u/, yielding [i, u]; [−RTR, −high] from /e, o, ə/, yielding [e, o] and [+RTR] from /ɛ, ɔ, a/, yielding [ɛ, ɔ].

The A- prefix is specified [+RTR]. The result of combining it with [−RTR, −high] from the root vowels /e, o, ə/ is a [+RTR] vowel with front/round features as specified in (44a) and (44b).Footnote ²⁸ When [+RTR] combines with root vowels /i, u/, the expected result is [+RTR, +high] (*[ʊ], looking ahead to (44b)). The actual result is [o]. As Hyman (Reference Hyman1988: 267) explains, the pronunciation of [ɪ, ʊ] can be very close to [e, o]; in several languages, these sounds have merged. Moreover, a constraint against [+RTR, +high] is cross-linguistically very common (Archangeli & Pulleyblank Reference Archangeli and Pulleyblank1994). Thus, we have the principle in (43), a kind of structure preservation (Kiparsky Reference Kiparsky1985) whereby vowels specified [+RTR, +high] are interpreted as [−RTR, −high].

The front/round features of the A- prefix are derived following the principles in (44).

To illustrate the above analysis, for roots with underlying [ $\pm $ high] vowels, we have the outcomes in (45) for the A- prefix.Footnote ²⁹

When the A- prefix occurs with the [+RTR] root vowels /ɛ, a, ɔ/, it simply remains [+RTR]; in this case, it receives the default features [−front] and [−round] (44c), resulting in [a]. A sample derivation is shown in (46).

As we saw for the I- and U- prefixes, when the A- prefix combines with a root, learners receive conflicting signals; in this case, the conflict is compounded:

• • in a root like /tu/ ‘ear’, the root vowel signals that it is [+high];

• • the U- prefix in [o-tu] signals that the root vowel is [−RTR, −high];

• • the A- prefix in [ɔ-tu] signals yet a different vowel height, [+RTR].

The simplest solution, and the one most consistent with the UG assumed here, is a version of the one adopted by Hyman (Reference Hyman1988): the I- and U- prefixes show the underlying height of the root, and the A- prefix lowers it. Three sets of features are in play:

• • the surface features on the root vowels after raising;

• • the underlying height/RTR features assigned to the root that show up in the I- and U- prefixes;

• • and the [+RTR] feature in the representation of the A- prefix.

5.5. Other analyses of Esimbi

Other writers have discussed the Esimbi prefix alternations from various points of view: Clements (Reference Clements1991b), Odden (Reference Odden1991) and Halle (Reference Halle1995) adopt the basic analysis of Hyman (Reference Hyman1988), with different theories of features and feature geometry; Walker (Reference Walker1999) and Kalinowski (Reference Kalinowski2009) employ an OT framework and van der Hulst (Reference van der Hulst2018: 261–263) uses Radical CV Phonology. Though the details of these analyses differ, they all, as do Archangeli & Pulleyblank (Reference Archangeli and Pulleyblank2015), attribute the height (and tongue root features, for some) of the prefixes to features associated with the roots.Footnote ³⁰ Halle (Reference Halle1995: 40) concludes his discussion with the following observation about the learnability of an abstract analysis of Esimbi:

6.1. The Polish problem in its classical form

The Polish opaque interaction became well known due to its inclusion in a problem set by Kenstowicz & Kisseberth (Reference Kenstowicz and Kisseberth1979: 72–73). Some of the essential forms, as presented there, are shown in (47).

Solving this problem set requires the two rules in (48), applying in the order given.

The two rules in (48) are not particularly complicated, though vowel raising before a final voiced consonant is very rare, perhaps unique.Footnote ³¹ Nevertheless, their opaque interaction makes the problem surprisingly difficult if one encounters it on a time-limited exam. The trick is to realise that an underlying o raises before an underlying word-final voiced consonant, as seen clearly in the case of a non-nasal sonorant, as in (47h). However, when the final voiced consonant is an obstruent, as in (47c), the raised vowel only appears when the consonant has been devoiced, as in the singular, and is not raised when the final obstruent is overtly voiced, as in the plural. The opaque interaction of these rules is shown in the derivations in (49).

6.2. A revised view of Polish vowel raising

The forms in (47) make for a great exam question, so difficult that it appears that Polish learners did not all pass the test. According to Buckley (Reference Buckley2001) and Sanders (Reference Sanders2003), there are exceptions in both directions to o-raising as formulated in (48a): some vowels followed by an underlying voiced consonant do not raise, as in (50a)–(50d), and some vowels followed by an underlying voiceless consonant do raise, as in (50e)–(50h).Footnote ³²

To the lexical exceptions, Sanders (Reference Sanders2003) adds experimental evidence showing that the o{\textasciitilde}u alternation is not productive, and he joins Buckley (Reference Buckley2001) in inferring that o-raising as formulated in (48a) is not a synchronic rule in the grammar of Modern Polish. Sanders (Reference Sanders2003: 57) concludes that ‘thus, there is no need to analyze this case of opacity with a synchronic grammar’. Sanders (Reference Sanders2003: 14) assumes a strong form of lexicon optimisation (Prince & Smolensky [1993] Reference Prince and Smolensky2004) without lexical minimisation; on this approach, even predictable information is stored in the lexicon in order to make underlying representations as close as possible to surface representations. Thus, he derives stems with alternating o\~{}u (actually ɔ\~{}u) from more than one underlying form; for example, ʒwup ‘crib’ would derive from underlying /ʒwup/ and ʒwɔbi ‘cribs’ would derive from underlying /ʒwɔb-/.

Strong lexicon optimisation directly contradicts the morphophonemic principle in (5d) and related assumptions, and treats many predictable phonological alternations as suppletion. In the theory assumed here, the o{\textasciitilde}u alternation has to get some representation in a synchronic grammar.

Buckley (Reference Buckley2001) proposes that Polish retains a rule raising a back vowel before a word-final consonant, but that the voicing of that consonant is no longer relevant. He proposes rather that the vowel that alternates between [o] and [u] cannot be either /o/ or /u/, neither of which alternate, but must be a third vowel different from both of them. He proposes that this vowel, which he designates /O/, is underspecified for [high]. We thus have the contrasts shown in (51).

The merit of this proposal is that it posits three different vowels to account for three different behaviours. It also reflects the historical developments that led to the current grammar. As recounted in the sources (see Sanders Reference Sanders2003: 57–85), there was no historic raising of o before a word-final voiced consonant. Rather, at an early stage, *o or *ɔ lengthened before a word-final voiced consonant, perhaps as a compensatory lengthening for the loss of a final jer. The lengthened oː and short o subsequently diverged in height, as [oː] vs. [ɔ]. Later, long o shortened and merged with *u to u. So at a relevant point, there were indeed three non-low back vowels: /ɔ, o, u/.

Buckley (Reference Buckley2001) cites some precedents for his analysis (Kiparsky Reference Kiparsky, Hargus and Kaisse1993; Buckley Reference Buckley1994; Inkelas et al. Reference Inkelas, Orhan Orgun and Zoll1994). However, assuming CHT, I do not see a way to derive an /O/ underspecified for height that would be in contrast with both [−high] /o/ and [+high] /u/. An /O/ unspecified for height can occur in archiphonemic fashion in contexts with a reduced number of contrasts, such as can arise, for example, in unstressed positions (Spahr Reference Spahr2014) or in desinences (Dyck Reference Dyck1995). But this is not such a case.

I would slightly revise Buckley’s (Reference Buckley2001) account. Following Sanders (Reference Sanders2003) and others, I represent the non-alternating non-high vowel as /ɔ/. What learners would know is that the alternating vowel surfaces as either [ɔ] or [u] but is underlyingly distinct from both of them, because the latter do not alternate. A contrasting vowel that surfaces as either [ɔ] or [u] would most economically have features close to both of these vowels (cf. the ‘intermediate’ segment of Wang & Hayes Reference Wang and Hayesin press). Such a vowel is /o/, which can be distinguished from /ɔ/ by [ $\pm $ ATR] and from /u/ by [ $\pm $ high].

A partial feature hierarchy for the Polish non-low back vowels is given in (52), and (53) shows sample derivations. When /o/ becomes [+high], the only destination is /u/. Elsewhere, unraised [−high] /o/ must become [−ATR].