Paradigm uniformity effects on French liaison

Abstract

French liaison is a type of external sandhi involving the use of a special consonant-final allomorph before vowel-initial words. Consonants occurring at the end of these allomorphs are challenging for phonological theory because of evidence that their prosodic and segmental realization is intermediate between the realizations of word-final and word-initial consonants. This puzzling behavior of French liaison has been used to motivate new phonological and lexical representations, including floating consonants, lexical constructions and gradient symbolic representations. This paper proposes an alternative analysis: the variable realization of liaison is derived as a paradigm uniformity effect, assuming traditional phonological and lexical representations. In a Word1-Word2 sequence, the liaison consonant at the boundary between the two words ends up acquiring properties of both word-final and word-initial consonants because of a pressure to make contextual variants of Word1 and Word2 similar to their citation forms. The proposal is implemented in a probabilistic constraint-based grammar including paradigm uniformity constraints and is shown to account for the intermediate behavior of liaison both in terms of prosodic attachment and segmental realization. The paper provides evidence for two key predictions of this analysis, using judgment data on the prosodic attachment of liaison consonants in European French and phonetic data on the interaction between liaison and affrication in Quebec French.

1 Introduction

French liaison is a type of external sandhi involving the use of a special consonant-final allomorph before vowel-initial words. The consonant at the end of this allomorph is called a liaison consonant. For instance, the adjective grand ‘great’ is generally realized as [], as shown in (1a) and (1b), but may appear under its liaison form [] before vowel-initial words, as shown in (1c).

• (1) French liaison

  

Liaison is a complex phenomenon that is influenced by a range of language-internal and -external variables beyond the basic phonological conditioning described in (1). Due to this complexity, liaison has featured prominently in many theoretical debates over the last decades, including debates on the syntax-phonology interface, the nature of phonological and lexical representations, and the role of lexical frequency in phonology (see Côté 2011 for an overview).

In recent years, there has been renewed interest in a particular challenge that French liaison raises for phonological theory. Liaison consonants vary in their pattern of realization. More specifically, their prosodic and segmental realization is intermediate between the realization of word-final and word-initial consonants. For instance, in the presence of a prosodic break between a liaison word and the following word, liaison consonants can be attached either at the end of the liaison allomorph, like word-final consonants (=liaison non-enchaînée), or at the beginning of the following word, like word-initial consonants (=liaison enchaînée; Encrevé 1988; Durand and Lyche 2008). This variability in prosodic attachment is illustrated in (2). Prosodic domains are indicated using parentheses.

• (2) Variable realization of French liaison across a prosodic break

  

This variability has led some researchers to propose specific underlying phonological representations for liaison consonants, including floating segments (Encrevé 1988; Tranel 1990) and gradient symbolic representations (Smolensky and Goldrick 2016; Smolensky et al. 2020; Tessier and Jesney 2021). It has also been used to argue against the traditional view according to which liaison consonants are lexically affiliated to Word1, either by positing that they belong to a lexical construction involving both Word1 and Word2 (Bybee 2001) or that they are independently affiliated to both Word1 and Word2 (Smolensky and Goldrick 2016).

This paper proposes an alternative account: the variable behavior of liaison consonants is not captured through an enriched phoneme inventory or lexicon. Instead it emerges from the structure of the lexicon as a paradigm uniformity effect, similarly to what has been proposed to account for incomplete devoicing in German (Roettger et al. 2014). More specifically, this paper builds on a hypothesis put forth by Steriade (1999) and according to which the liaison allomorph of a word (e.g. [] in (1c)) is attracted to the pronunciation of the corresponding citation form, i.e. the word as pronounced in isolation (e.g. [] in (1a)). Crucially, the liaison consonant is typically absent from the citation form. In a Word1-Word2 sequence, the requirement to be faithful to the citation form of Word1 will push the liaison consonant away from the end of this word onto the following word, therefore favoring a word-initial behavior.

The present paper extends Steriade’s original analysis by hypothesizing that the realization of Word2 is also subject to paradigm uniformity effects, as proposed by Zuraw and Hayes (2017) in their analysis of French h-aspiré. The requirement to be faithful to the citation form of Word2 will push the liaison consonant away from the beginning of Word2 in connected speech, therefore favoring a word-final behavior. These two opposite uniformity effects, represented with arrows going in opposite directions in (3), are proposed to underlie the variable realization of liaison consonants. The forms enclosed in boxes in (3) correspond to the citation forms of the two words involved in the sequence grand ami. The hypothesis that the citation form of Word2 also plays a role will be crucial to explain why liaison consonants do not behave just like word-initial consonants but also share properties with word-final consonants, both prosodically and segmentally.

• (3) The variable realization of liaison consonants as a paradigm uniformity effect

  

Section 2 summarizes the evidence for the variable prosodic and segmental realization of French liaison. Section 3 implements the paradigm uniformity analysis schematically represented in (3) in a probabilistic constraint-based grammar with paradigm uniformity constraints and shows how this analysis can derive the prosodic variability of liaison. Section 4 presents the results of an experimental study that both confirms the prosodic variability of liaison and provides evidence for the role of citation forms in this pattern. The evidence comes from a comparison of two types of liaison allomorphs differing in their similarity with the corresponding citation forms.

Section 5 shows how the analysis can be extended to account for the segmental variability of French liaison. This analysis builds on Steriade’s (2000) proposal that phonetic detail such as consonant-vowel coarticulation matters in paradigm uniformity effects. Section 6 reports on a phonetic study looking at the interaction of affrication and liaison in Quebec French, using data from the Phonologie du Français Contemporain (PFC) project. The results of this study provide evidence for the phonetic mechanism that is proposed to underlie the variable segmental realization of liaison in Quebec French.

Section 7 compares the paradigm uniformity analysis with previous analyses and highlights some of the strengths and weaknesses of these different approaches. In a nutshell, the paradigm uniformity analysis presented in this paper is shown to provide the most comprehensive account of the realization of liaison, as it is currently the only analysis that derives both prosodic and segmental variability. However it is insufficient to account for a range of effects on the rate of liaison. This section sketches how this problem can be remedied by indexing paradigm uniformity constraints to properties that are relevant to speech production (e.g. lexical frequency, contextual predictability), according to the production planning theory of sandhi phenomena (Kilbourn-Ceron 2017; Tanner et al. 2017).

2 Background on the realization of French liaison

The liaison allomorph of a word is used when the following word starts with a vowel, as illustrated in (1c). However the allomorph without liaison is still available in this context. Most of the work on French liaison has been dedicated to understanding which factors shape the distribution of the two allomorphs prevocalically (see Sect. 7 for more discussion on this topic).

This paper focuses on yet another important question in the literature on French liaison: how liaison consonants are realized when pronounced. As will be further reviewed in this section, liaison consonants pattern in a very puzzling way, as they share prosodic and segmental properties with stable word-final as well as word-initial consonants. Stable consonants differ from liaison consonants in being present regardless of the surrounding phonological context. For instance, word-initial [t] and word-final [t] in trente [] ‘thirty’ are stable because they are present regardless of the nature of adjacent segments in neighboring words. Section 2.1 focuses on the prosodic variability of liaison and Sect. 2.2 on its segmental variability.

2.1 Prosodic variability

This section assumes the prosodic characterization of French into three types of phrases proposed by Delais-Roussarie et al. (2015: 65–74): accentual phrase (AP), intermediate phrase (ip), and intonational phrase (IP). This proposal serves as a convenient descriptive framework to present the prosodic realization of liaison but is not key to the analysis.

The accentual phrase (AP) is the smallest prosodic constituent and includes minimally a content word along with all function words that depend on it syntactically, such as the AP il est devenu ‘he has become’ in (4). It can also include other content words that are construed as modifiers, such as the adjective grand ‘great’ in the AP mon grand ami ‘my great friend’ in (4). The intermediate phrase (ip) is a larger prosodic constituent that includes minimally one AP. Dislocations such as le voisin ‘the neighbour’ in (4) form their own ip. Finally, the intonational phrase (IP) is the largest prosodic constituent and is often followed by a pause. In (4), it corresponds to the whole sentence.

• (4) Il est devenu mon grand ami, le voisin.

  [{(Il est devenu)_AP (mon grand ami)_AP}_ip {(le voisin)_AP}_ip]_IP

  ‘He has become my great friend, the neighbour.’

The prosodic behavior of liaison depends on the position of liaison words in these prosodic domains. Within an AP, liaison consonants are syllabified with the following vowel, as are stable word-final and word-initial consonants (Gaskell et al. 2002; Spinelli et al. 2002; Durand and Lyche 2008: Sect. 3.3). For instance, in (un grand ami)_AP [] ‘a great friend,’ the liaison consonant is coarticulated with the vowel at the beginning of the following word. The same happens with stable word-final consonants, as in (mes trente amis)_AP [] ‘my thirty friends,’ and with stable word-initial consonants, as in (un grand tamis)_AP [] ‘a big sieve.’ For word-final consonants and liaison consonants, syllabification with the following vowel is described as resyllabification or as enchaînement in French linguistic terminology (Encrevé 1988).

When a prosodic boundary intervenes between Word1 and Word2, liaison consonants pattern differently from stable consonants: although lexically dependent on the identity of Word1,¹ the liaison consonant will typically behave like a word-initial consonant prosodically and attach to Word2. In this case, it is described as a liaison enchaînée. But it may also attach to Word1, in which case it is described as a liaison non-enchaînée. By contrast, stable final and initial consonants remain prosodically affiliated to their lexical hosts (Word1 and Word2, respectively) and do not show prosodic variability.

This puzzling prosodic behavior of French liaison can be illustrated with Word1-Word2 sequences in right dislocations (Tranel 1990; Côté 2005). Right dislocated elements belong to a distinct prosodic unit from their nucleus sentence: their prosody copies the prosody of the nucleus but is characterized by decreased intensity, lower pitch and a flat contour intensity (De Cat 2007: 34–43). In the prosodic analysis in Delais-Roussarie et al. (2015), right dislocation involves two distinct intermediate phrases (ip), as illustrated in (4). When Word2 is right dislocated, the liaison consonant is separated from the word it is lexically affiliated to (Word1) and attaches at the beginning of the following word (Word2) across the prosodic break. For instance, in (5a), liaison [t] is separated from its lexical host [] by a prosodic boundary between two intermediate phrases (ip) and attaches to []. By contrast, stable consonants remain prosodically attached to their lexical hosts, as shown in (5b) for word-final consonants (they attach to Word1) and in (5c) for word-initial consonants (they attach to Word2).

• (5) Liaison vs. stable consonants in right dislocations

  

Although Word2-attachment of liaison consonants is reported as the preferred option in the presence of a prosodic break, liaison consonants may still attach at the end of Word1. In other words, the prosodic realization of liaison is variable. When the liaison consonant is attached at the end of Word1, the liaison consonant is said to be non-enchaînée. The availability of liaison non-enchaînée has been famously described by Encrevé (1988), using a corpus of political speeches by prominent French politicians. Encrevé’s data are summarized in Table 1. The data show that the liaison allomorph is used in about half of the potential sites for liaison (49%). When pronounced, the liaison consonant behaves either as a word-initial segment at the beginning of Word2 (= liaison enchaînée; this is the most common pronunciation) or as a final segment at the end of Word1 (= liaison non-enchaînée).

Table 1 Prosodic variability of French liaison in Encrevé’s corpus (Encrevé 1988: 56)

An example of liaison non-enchaînée by the late French president Jacques Chirac is provided in (6) (cited from Durand and Lyche 2008: 51). This example can be found on the YouTube channel of the Institut national de l’audiovisuel (INA) (https://youtu.be/t72zuDsSHAw?t=289; 4’49”). In this example, font ‘do.3pl’ and honneur ‘honor’ are not phrased together prosodically, as they normally would, but they belong to two distinct phrases. For concreteness, these two phrases are treated here as APs. The example in (6) provides a case of liaison non-enchaînée: liaison [t] in font is pronounced in the same prosodic phrase as Word1 and not at the beginning of Word2 in the following prosodic phrase. Liaison enchaînée would also be possible in that case, as reported by Encrevé (1988): the pronunciation would then be [].

• (6)

  

Although liaison non-enchaînée has sometimes been described as uniquely confined to high register and planned speech, Durand and Lyche (2008: 50–51) found examples occurring in natural daily interactions, in particular in the presence of prosodic breaks involving hesitations, as shown in (7a), or repetitions, as shown in (7b). Durand and Lyche (2008) write: “These examples seem to us extremely interesting: despite the clear predominance of liaison enchaînée in our corpus, they provide possible evidence against an analysis which simply treats a liaison consonant as an onset of Word2.” This behavior is not reported for stable word-initial consonants at the beginning of Word2: these are not allowed to be attached at the end of Word1 across a prosodic break occurring in the middle of a Word1-Word2 sequence (see Sect. 4 for experimental evidence).

• (7) Examples of liaison non-enchaînée in conversational speech (Durand and Lyche 2008: 50–51)

  

2.2 Segmental variability

The preceding section has provided evidence for the prosodic variability of liaison. This section shows that variability extends to the segmental realization of liaison. In the absence of prosodic break between Word1 and Word2, the distinction between liaison consonants, stable word-final consonants and stable word-initial consonants is not completely neutralized. There remain segmental cues that distinguish the three types of consonants, as will be reviewed in this section. In particular, liaison consonants have a segmental realization that is intermediate between that of stable word-final and word-initial consonants.

Fougeron (2007) showed that word-final consonants before a vowel (VC#V) do not have the same acoustic realization as word-initial consonants (V#CV), even in contexts that are traditionally treated as involving enchaînement/resyllabification of the final consonant. In particular, she found that word-final consonants tend to be shorter than word-initial consonants (Fougeron 2007: 13).

Liaison consonants are also reported to behave distinctly from both stable word-final and word-initial consonants phonetically in this context. For instance, an early study by Durand (1936: 238) found that stable word-final consonants (e.g. the final [t] of petite [pətit] ‘small.fem’ in une petite orange ‘a small orange’) differ from liaison consonants (e.g. liaison [t] at the end of petit [pətit] ‘small.masc’ in un petit orage ‘a small storm’) in retaining some cues of their implosive/non-prevocalic nature. Liaison consonants have also been found to differ from word-initial consonants and in particular to be characterized by a shorter duration on average (Gaskell et al. 2002; Spinelli et al. 2002, 2003). Taken together, these studies suggest that, on average, liaison consonants have a duration that is intermediate between that of stable word-final and word-initial consonants.

More targeted studies found that this effect actually depends on the nature of the consonant, as summarized in Table 2. For /t/, the duration is longer for word-initial consonants than for both word-final and liaison consonants, but without clear durational difference between the latter two types. For /z/, a study by Nguyen et al. (2007) found a shorter duration for word-final consonants. But this result was not replicated by Bagou et al. (2009). Neither study found a significant durational difference between word-initial and liaison /z/. For /n/, phonetic realization does not seem to be affected by the lexical status of the consonant, according to available studies: the duration of the consonant does not significantly differ whether the consonant is word-final, liaison or word-initial. Overall, taken together, the liaison consonant appears to pattern intermediately between word-final and word-initial consonants in phonetic realization, with some differences depending on the specific liaison consonant.

Table 2 Phonetic realization (duration) of consonants /t z n/ as a function of lexical type (stable word-final consonant, liaison consonant, stable word-initial consonant)

The clearest evidence for the intermediate segmental realization of liaison consonants comes from data on affrication in Quebec French (Côté 2014). Quebec French has a process of affrication that turns /t d/ into [ts dz] before /i y j ɥ/. But this process affects differently liaison consonants, stable word-final consonants, and stable word-initial consonants, as shown in Table 3. More specifically, liaison /t/ exhibits a rate of affrication that is intermediate between stable word-final /t/ and word-initial /t/: liaison /t/ is more prone to affrication than stable word-final /t/ but less so than stable word-initial /t/. This result was obtained using data from the PFC project (Côté 2016). The presence or absence of affrication was determined perceptually for each token by at least two judges (Côté 2014: 36-37).

Table 3 Affrication before /i y j ɥ/ in the PFC Trois-Rivières survey: count and frequency data (Côté 2014: 38)

It is important to note that only contexts involving resyllabification/enchaînement were included by Côté in the data reported in Table 3. For instance, among the 121 occurrences involving a stable word-final consonant before /i/ in the corpus, only 85 were included in the analysis (Côté 2014: 38). The remaining 36 occurrences did not involve resyllabification/enchaînement, i.e. there was a prosodic break (a pause or hesitation) between /t/ and the following /i/.² This means that the differences in affrication observed in Table 3 cannot be explained away as a by-product of prosodic variability: all contexts involve consonants that would be normally treated as onsets.

2.3 Summary

Liaison consonants have a very puzzling behavior in Word1-Word2 sequences. Prosodically, they pattern intermediately between stable word-final and word-initial consonants. In the presence of a prosodic break between Word1 and Word2, liaison consonants may attach at the end of Word1 (their lexical host), as expected for word-final consonants, but they may also be separated from their lexical host and attach at the beginning of Word2. In contexts that do not involve a prosodic break between the two words and are traditionally treated as onset contexts (i.e. the consonant and the following vowel are coarticulated together), the segmental realization of liaison consonants has also been found to be intermediate between the realization of stable word-final and word-initial consonants.

3 Prosodic variability of French liaison as a paradigm uniformity effect

This section proposes an analysis of the variable behavior of French liaison as a paradigm uniformity effect, focusing first on prosody. More specifically, this variability is proposed to result from a pressure to make contextual variants of Word1 and Word2 in Word1-Word2 sequences similar to the corresponding citation forms. The relevance of the citation form of Word1 for French liaison was originally proposed by Steriade (1999) in her work on lexical conservatism. This section shows that generalizing the uniformity requirement to both Word1 and Word2 predicts that liaison consonants should be variable in their prosodic attachment whereas stable consonants (word-final and word-initial) should only attach to their lexical host (Word1 and Word2, respectively).

Section 3.1 describes and motivates the general grammatical architecture that is assumed in the analysis. Section 3.2 shows how the analysis derives citation forms for words with liaison allomorphs and for words that lack such allomorphs. Section 3.3 shows how the prosodic variability of liaison consonants in Word1-Word2 sequences can be derived as a result of paradigm uniformity with the corresponding citation forms, using Encrevé’s (1988) corpus as case study. Section 3.4 further shows that the asymmetry between liaison and stable consonants is a necessary consequence (an implicational universal) of the proposed constraint set. The analysis can be found in Storme (2022) under the name prosodic-ambiguity-final-2.txt.

3.1 Grammatical architecture

The analysis is implemented in a probabilistic constraint-based grammar including input-output (IO) and output-output (OO) faithfulness constraints evaluated in parallel, according to the model in Fig. 1. The different components of this model are described and motivated below.

Fig. 1

Grammatical model assumed in the analysis (IO = input-output correspondence, OO = output-output correspondence)

The key ingredient in the analysis is the assumption that there is a family of output-output faithfulness constraints evaluating the similarity among contextual variants of a word (see Benua 1997; Kenstowicz 1996 on output-output faithfulness in general; see Kawahara 2002 for an application of output-output faithfulness to the similarity among contextual variants of a word). Specifically, it is assumed that there are constraints that penalize dissimilarities between connected-speech variants of a word and the corresponding citation form (Steriade 1997: 55-58). Citation forms correspond to the form of a word as pronounced in isolation, with the beginning and end of the word matching the beginning and end of the utterance. Evidence for the role of citation forms in paradigm uniformity comes from data showing that phonological alternations that are phonetically motivated at utterance edges are extended utterance-medially (Steriade 1997: 55-58; Myers and Padgett 2014). For instance, word-final devoicing is motivated phonetically utterance-finally (by the lack of robust cues to the voicing contrast), but not utterance-medially. Yet languages overapply word-final devoicing utterance-medially.

In the prosodic framework proposed by Delais-Roussarie et al. (2015: 65-74) for French (see Section 2.1), citation forms are intonational phrases that consist of a single word. Connected-speech variants are the forms of words as they occur in all other prosodic contexts, i.e. within accentual phrases, at the boundary between two accentual phrases or between two intermediate phrases.

What makes liaison consonants special vis-à-vis stable consonants is that they are (generally) absent from citation forms, as shown in Table 4. For instance, liaison [t] at the end of the liaison form [] does not appear at the end of the corresponding citation form []. However, stable [t] at the end of trente ‘thirty’ appears at the end of the corresponding citation form (i.e. []). Similarly, stable [t] at the beginning of tableau ‘table’ is also present at the beginning of the corresponding citation form. The requirement for connected-speech variants to be similar to the corresponding citation forms will be key to explain two properties of French liaison consonants: (i) why they do not always surface in connected speech and (ii) why they may be pushed away from both Word1 and Word2 in Word1-Word2 sequences.

Table 4 Liaison consonants are absent from citation forms whereas stable (final and initial) consonants are present in citation forms

The evaluation of output-ouput faithfulness constraints will assume base priority, following Benua (1997: 240): the phonology of the citation form is computed first and then the resulting output form is used in the evaluation of connected-speech variants, as shown by the unidirectional horizontal arrow in Figure 1. For French liaison, it means that the non-liaison allomorph that is used utterance-finally (e.g. []) will serve as a base in the evaluation of connected-speech variants, including in liaison contexts (i.e. before vowel-initial words).

The analysis further assumes that liaison words come with two underlyingly listed allomorphs: an allomorph without liaison and an allomorph with liaison (e.g. Gaatone 1978; Steriade 1999; Bonami and Boyé 2005). For instance, the masculine adjective grand ‘great’ has two suppletive allomorphs // and //. By contrast, non-liaison words have a single underlying representation, as shown in Table 5.

Table 5 Assumptions about underlying representations

The assumption that liaison involves suppletion is not key to the analysis. The classic generative analysis where liaison words correspond to a single underlying representation (for instance Dell 1985: 180–193) could also be adopted. In this analysis, grand ‘great’ corresponds to a unique underlying representation //. All surface realizations of the adjective, including the masculine non-liaison form [] and the masculine liaison form [], are derived from // by phonological rules (deletion and final devoicing, respectively). This approach is not adopted here because it requires fairly abstract underlying representations. For instance, this approach assumes that all stable word-final consonants are followed by schwa underlyingly (e.g. trente is analyzed as //), even though these schwas are virtually never pronounced, at least in non-meridional varieties (see Eychenne 2019 on final schwa). Moreover, the suppletion analysis adopted in this paper is further motivated by cases where it is not possible to derive liaison and non-liaison forms from a single underlying representation, as in the case of beau/bel []/[] ‘beautiful.masc’. These cases will be further discussed in Section 4.

The evaluation of words with several underlyingly listed allomorphs is based on the model proposed by Mascaró (2007) for phonologically optimizing allomorph selection (e.g. h/u-selection in Moroccan Arabic and exceptional post-nasal voicing in Basque; Mascaró 2007: 711, 718–723). In this model, both allomorphs are used as inputs in the evaluation, without any lexical ordering among them.³ The allomorph that best satisfies the phonotactic constraints of the language is selected. For French, the distribution of the two allomorphs will be analyzed as a case of phonologically optimizing suppletive allomorphy (see Inkelas 2014: 282–284 for crosslinguistic evidence for this kind of patterns). The non-liaison allomorph (e.g. //) is preferred in general because it does not have a final consonant but the liaison allomorph (e.g. //) may be preferred before a vowel as a strategy to avoid a vowel hiatus. Phonologically optimizing suppletive allomorphy is independently motivated in French. For instance, some verbal stems have two alternating allomorphs in [] and [] that cannot be derived from a single underlying form and yet have a phonotactically optimizing distribution in the present tense, with the []-allomorph occurring under stress (e.g. jette [] ‘throw.3sg’) and the []-allomorph in unstressed syllables (e.g. jetez [] ‘throw.2pl’; Storme 2020a).

The final important ingredient in the analysis is the use of a probabilistic grammar. Input-output mappings must be probabilistic in order to account for the variation observed in the realization of French liaison. The analysis will be implemented in a Maximum Entropy grammar (MaxEnt; Goldwater and Johnson 2003; Hayes and Wilson 2008). In this framework, probabilities of input-output mappings are derived from their harmony using the exponential function. And the harmony of an input-output mapping is equal to the weighted sum of its constraint violations, as in Harmonic Grammar (Smolensky and Legendre 2006). The choice of MaxEnt as a framework for probabilistic grammars is motivated by earlier research showing that this framework is well adapted to deal with variable phonological patterns (Zuraw and Hayes 2017; Flemming 2021).

3.2 Deriving citation forms

According to the model described in Fig. 1, the phonology of citation forms is derived first. At that stage, only input-output faithfulness and phonotactic markedness play a role.

For liaison words, the preference for the allomorph without liaison (e.g. [] ‘great’) can be attributed to the effect of a markedness constraint penalizing utterance-final consonants (*C_U]). *C_U] is a specific version of the constraint No-Coda (Kager 1999: 94) that penalizes coda consonants for their lack of good perceptual cues (Ohala 1990; Wright 2004). In the case study at hand, this constraint penalizes the liaison allomorph with a final consonant (e.g. [] ‘great’), as shown in Table 6(a). In this table, indices are used to indicate correspondence relations between input allomorphs and output allomorphs in the candidate set, following Mascaró (2007: 721). Row (a) shows the (faithful) mapping from input // to output [] and row (b) the (faithful) mapping from input // to output [].⁴ As for faithfulness, the two allomorphs tie because they are both listed underlyingly. For instance, the vowel-final candidate does not violate the faithfulness constraint penalizing consonant deletion (Max-IO) because the consonant is absent from the corresponding input allomorph.⁵

Table 6 Citation forms (UR = underlying representation)

There is a categorical preference for the vowel-final allomorph in citation forms in French. In MaxEnt, this can be captured by setting a high weight to *C_U]. The specific weight shown in Table 6(a) for this constraint (w = 5.51) was inferred jointly with the weights of all the other constraints presented in Sect. 3, using OT-Soft (Hayes et al. 2013).⁶

In order to block consonant deletion for words with final consonants but no vowel-final listed allomorph (e.g. trente [] ‘thirty’), the constraint that penalizes consonant deletion (Max-IO) must take precedence over the constraint penalizing utterance-final consonants (*C_U]), as shown in Table 6(b). This condition ensures that a vowel-final allomorph is preferred in citation forms only in case it is listed underlyingly, as for liaison words in Table 6(a). To put it differently, the preference for the vowel-final allomorph in liaison words can be analyzed as a case of emergence of the unmarked (see Mascaró 2007). Table 6(b) shows a concrete choice of weight for Max-IO that derives the observed categorical preference for the candidate with a final consonant when there is no listed vowel-final allomorph (w = 50). The weight for *C_U] is of course the same as in Table 6(a) because the same single grammar must derive all attested forms. Table 6(c) shows how the same grammar also blocks consonant deletion at the beginning of words that begin with a consonant underlyingly (e.g. tableau [tablo] ‘table’). The reader can check that the analysis in Table 6 derives the correct citation forms for liaison words and non-liaison words, as listed in Table 5.

3.3 Deriving connected-speech variants

In connected speech, markedness constraints that do not play a role utterance-finally become relevant and drive alternations. The analysis here focuses specifically on the context where liaison consonants and stable word-final/word-initial consonants have different prosodic behaviors, namely in Word1-Word2 sequences with a prosodic boundary between the two words and where Word2 starts with a vowel (see Sect. 2.1). In particular, the analysis focuses on the prosodic boundary between two accentual phrases (AP), as this is the context where the prosodic variability of liaison is the clearest, in particular in natural conversations (see Sect. 2.1).

The crucial markedness constraint that motivates the use of the liaison allomorph in this context is the anti-hiatus constraint *VV (see Steriade 1999; Tranel 2000). It is assumed that this constraint remains relevant in the presence of a prosodic break between the two vowels, at least at the boundary between two accentual phrases or intermediate phrases (see Sect. 2.1).⁷ This assumption is crucial to explain why liaison might occur across a prosodic break. Also, in addition to input-output faithfulness, paradigm uniformity with citation forms derived in Sect. 3.2 will also play a role, in line with the grammatical architecture described in Fig. 1.

Table 7(a) shows the analysis of liaison words in this context. The prosodic boundary between the two APs is indicated by |. Candidate (a) corresponds to the allomorph without liaison. Whereas this candidate did not violate any constraint in citation forms, it now violates the anti-hiatus constraint *VV because it is followed by a vowel-initial word (ami ‘friend’ in this case). This violation will leave room for the liaison allomorph to surface. Note that the constraint weights reported in Table 7 were inferred jointly for the analysis of citation forms and connected-speech variants.

Table 7 Connected-speech variants (CF = citation form, UR = underlying representation). The vertical bar | between the two strings in each candidate represents a prosodic break

Candidates (b) and (c) both feature the liaison consonant [t], with a prosodic attachment to Word1 (liaison non-enchaînée) and to Word2 (liaison enchaînée), respectively. These candidates fare better than candidate (a) phonotactically because they do not violate *VV. Furthermore, contrary to candidates (d) and (e) (with liaison [l]), they do not violate the input-output faithfulness constraint penalizing consonant epenthesis (Dep-IO) because /t/ (but not /l/) is listed underlyingly in the liaison allomorph.

However these candidates are not completely optimal either because they are not identical to the citation form [], contrary to candidate (a): they feature a consonant that is epenthetic in the output-output dimension. In Table 7(a), this lack of paradigm uniformity is penalized by two output-output faithfulness constraints, based on Kager (1999: 251): Right-Anchor-OO (abbreviated as R-Anch-OO) and Left-Anchor-OO (abbreviated as L-Anch-OO). These constraints play a crucial role in accounting for both the availability of the vowel-final allomorph and the prosodic variability of the liaison consonant in the liaison allomorph. They are defined in (8) and (9) and further explained below.

• (8) Right-Anchor-OO

  Assign one violation mark if the segment at the right edge of an output form does not stand in correspondence with the segment at the right edge of the corresponding citation form.

• (9) Left-Anchor-OO

  Assign one violation mark if the segment at the left edge of an output form does not stand in correspondence with the segment at the left edge of the corresponding citation form.

Right-Anchor-OO has the same definition as the Lex A-Phrase constraint proposed by Steriade (1999: 267) to account for the word-initial attachment of liaison consonants in dislocations (see Sect. 2.1). This constraint requires that any element at the right edge of a citation form has a correspondent at the right edge of the corresponding contextual variant and vice versa. In a Word1-Word2 sequence, this constraint has the effect of penalizing the deletion/epenthesis of a segment at the end of Word1 (in the output-output dimension). It penalizes candidate (b) in Table 7(a) because this candidate features a consonant at the right edge of [] that is absent from the corresponding citation form []. This constraint does not penalize candidate (c) if one assumes that a segment has to be contiguous with the rest of an output form to qualify as its edge. In the presence of a prosodic break between [] and [t], [] and [t] are not contiguous and therefore [t] does not qualify as a right edge for the output of the adjective grand. With this assumption in place, Right-Anchor-OO favors a prosodic attachment of liaison [t] at the beginning of Word2 (candidate (c)).

The present proposal extends Steriade’s analysis by assuming that paradigm uniformity does not only apply to the right edge but also to the left edge of words in connected speech. In a Word1-Word2 sequence, these two requirements will conflict and drive the variable prosodic attachment of liaison consonants. It should be noted that the idea that connected-speech variants must be faithful to their citation forms along their left edge was actually proposed by Zuraw and Hayes (2017) in the context of a discussion of h-aspiré words in French. H-aspiré words block a range of sandhi phenomena, including liaison but also other processes such as elision. Zuraw and Hayes (2017) proposed that this is due to h-aspiré words being subject to a greater pressure to be uniform with their citation forms along their left edge than other vowel-initial words. They used lexical indexation of constraints to derive this effect. However, the formal implementation of their analysis does not use paradigm uniformity constraints, as in this paper, but alignment constraints. Alignment constraints require that syllable boundaries and morpheme boundaries match. Alignment constraints could be used to derive the prosodic ambiguity of liaison, however they would fail to derive the segmental ambiguity of liaison: as mentioned in Sect. 2.2, liaison consonants are segmentally variable even in contexts where they are traditionally treated as onsets. By contrast, as will be shown in Sect. 5, paradigm uniformity can explain the segmental variability of liaison.

The requirement to protect the left edge of a word is modeled using the paradigm uniformity constraint Left-Anchor-OO. Left-Anchor-OO requires that any element at the left edge of a citation form has a correspondent at the left edge of the corresponding contextual variant and vice versa. In a Word1-Word2 sequence, this constraint has the effect of penalizing segment deletion/epenthesis at the beginning of Word2 (candidate (c) in Table 7(a)) and therefore favors a prosodic attachment of liaison [t] at the end of Word1 (candidate (b)).⁸

Table 7(a) shows a concrete choice of constraint weights that can derive the frequencies attested in Encrevé’s (1988) corpus. Constraint weights were inferred jointly for the analysis of citation forms and connected-speech variants.⁹ Crucially, the analysis is not only able to model the variation between allomorphs with and without liaison (candidates (b)/(c) vs. candidate (a)) but also to capture the prosodic variability of liaison consonants: both attachments to Word1 and Word2 are derived (candidate (b) vs. candidate (c)). The analysis also does a very good job at matching the corpus frequencies of the different variants for liaison words.

The analysis predicts prosodic variability for liaison consonants but not for stable word-final and word-initial consonants. This is shown in Tables 7(b) and 7(c), respectively.

In Table 7(b), candidate (b) deletes word-final [t] in the citation form of trente and epenthesizes a [t] at the beginning of the citation form of ami, hence violating the two output-output faithfulness constraints Right-Anchor-OO and Left-Anchor-OO. By contrast, candidate (a) does not violate any constraint and therefore harmonically bounds candidate (b). The specific choice of weights that makes the prosodic attachment of liaison consonants variable between Word1 and Word2 (Table 7(a)) predicts a categorical attachment to Word1 for stable word-final consonants (Table 7(b)).¹⁰

In Table 7(c), candidate (a) epenthesizes a [t] at the end of the citation form of vrai and deletes word-initial [t] in the citation form of tableau, hence violating the two output-output faithfulness constraints Left-Anchor-OO and Right-Anchor-OO. By contrast, candidate (b) does not violate any constraint and therefore harmonically bounds candidate (a). The specific choice of weights that makes the prosodic attachment of liaison consonants variable between Word1 and Word2 (Table 7(a)) predicts a categorical attachment to Word2 for stable word-initial consonants (Table 7(c)).

3.4 Implicational generalizations

The preceding section has shown that the paradigm uniformity analysis can capture the variable prosodic patterning of liaison consonants as attested in Encrevé’s corpus. This section further establishes that the asymmetry between liaison and stable consonants in (10) follows as a necessary consequence of the proposed constraint set, and this regardless of the framework for probabilistic grammar: Stochastic Optimality Theory (OT; Boersma and Hayes 2001), Noisy Harmonic Grammar (HG; Hayes 2017), or Maximum Entropy grammars (MaxEnt; Goldwater and Johnson 2003; Hayes and Wilson 2008).

• (10) Statistical implicational generalizations derived by the analysis

  • a. P(Word1-attachment|Liaison C)≤P(Word1-attachment|Final C)

  • b. P(Word2-attachment|Liaison C)≤P(Word2-attachment|Initial C)

  In words: Liaison consonants are less likely to attach to Word1 than final consonants and less likely to attach to Word2 than initial consonants.

In Stochastic OT and Noisy HG, the demonstration makes use of harmonic bounding. For words that do not have liaison allomorphs (e.g. trente ‘thirty’ and tableau ‘table’), the candidates that involve displacing the consonant from its underlying position to the following or preceding word (candidate (b) in Table 7(b) and candidate (a) in Table 7(c), respectively) violate a strict superset of the constraints violated by the candidates that involve no displacement (candidate (a) in Table 7(b) and candidate (b) in Table 7(c), respectively). In other words, these candidates are harmonically bounded and there is no way they can win under any constraint ranking or weighting. Consequently, in the presence of a prosodic break, stable final consonants in Word1 are predicted to attach categorically to Word1 and stable initial consonants in Word2 to attach categorically to Word2.

However for liaison words, the candidates involving attachment of the liaison consonant to Word1 and to Word2 (candidates (b) and (c) in Table 7(a), respectively) violate different constraints (Right-Anchor-OO and Left-Anchor-OO, respectively). So it is not the case that one pronunciation is inherently better than the other. Varying rates of Word1-/Word2-attachment are expected to be observed depending on the ranking values (in Stochastic OT) or weights (in Noisy HG) of Right-Anchor-OO and Left-Anchor-OO. In other words, the analysis predicts that the rate of Word2-attachment for liaison consonants should always fall between the rates of Word2-attachment for final consonants (equal to 0) and initial consonants (equal to 1).

In MaxEnt, the situation is different because the fact that a candidate is harmonically bounded does not entail that it has a zero probability of occurring (e.g. Hayes 2017). The demonstration is more involved and the constraint-violation profiles of the different candidates must be carefully compared across the different types of consonants (final, liaison, and initial), as discussed in Anttila and Magri (2018). This demonstration is not provided here for reasons of space. In a nutshell, generalization (10a) holds because the candidate with a liaison consonant at the end of Word1 fares worse within the candidate set for the liaison word (Table 7(a)) than the candidate with a stable consonant at the end of Word1 does within the candidate set for the consonant-final word (Table 7(b)). And generalization (10b) holds because the candidate with a liaison consonant at the beginning of Word2 fares worse within the candidate set for the liaison word (Table 7(a)) than the candidate with a word-initial consonant at the beginning of Word2 does within the candidate set for the consonant-initial word (Table 7(c)). The reader is referred to the output of the CoGeTo analysis (Magri and Anttila 2019) in the supplementary files. CoGeTo is an online tool developed by Giorgio Magri and Arto Anttila to analyze the typological predictions of probabilistic constraint-based grammars. The CoGeTo analysis shows that indeed the implications hold in MaxEnt as well.

4 Study 1: Epenthetic and suppletive liaison in European French

In the paradigm uniformity analysis of French liaison proposed in Sect. 3, the variable prosodic patterning of liaison consonants ultimately follows from their being absent from the corresponding citation form. But no variability is predicted if the liaison consonant is present in the citation form. The goal of this section is to test this prediction experimentally by exploiting the distinction between two types of liaison consonants that differ in whether they are present in the corresponding citation form.

Section 4.1 introduces this distinction and explains how it provides a testing ground for the role of citation forms in the realization of liaison consonants. Section 4.2 presents the methods used to test this prediction. Section 4.3 presents the results. Section 4.4 concludes with a brief discussion. The data and code for Study 1 are available in Storme (2022) under the names study1b-data.csv and study1b-code.R, respectively.

4.1 Epenthetic and suppletive liaison

Epenthetic liaison describes cases where the liaison allomorph contains the morphologically corresponding citation form as a substring, with the liaison consonant being epenthesized after this substring (e.g. . Suppletive liaison describes cases where the liaison allomorph does not contain the morphologically corresponding citation form as a substring but is based on a morphologically distinct form in the paradigm. For instance, the adjective beau [bo] ‘beautiful.masc’ uses the form [bɛl] as a liaison variant (e.g. bel ami [bɛlami] ‘beautiful friend.masc’). This form cannot be analyzed as the masculine citation form plus an epenthetic consonant. Rather it corresponds to the feminine form of the adjective (belle [bɛl] ‘beautiful.fem’). The two types of liaisons are represented in Table 8. It is important to note that epenthesis is not used here in its usual sense to mean that the liaison consonant is epenthesized in the input-output dimension. Rather it is used to characterize the relationship between the liaison allomorph and the citation form in the output-output dimension. The liaison consonant is still assumed to be present underlyingly in the liaison allomorph for both types of liaison words, as shown in Table 8 (see Sect. 3.1).

Table 8 Epenthetic liaison and suppletive liaison

The distinction between the two types of liaison is well-known and has been discussed by Delattre (1947: 150) and Tranel (1990, 2000) among others. Its relevance for the hypothesis of paradigm uniformity effects has been first discussed by Steriade (1999). The paradigm uniformity analysis predicts that only epenthetic liaison should pattern variably between stable word-final and word-initial consonants. For suppletive liaison, the liaison consonant is present at the end of the corresponding citation form (e.g. the [l] in bel [bɛl] is present at the end of the feminine citation form belle [bɛl]) and this word-final attachment should be reinforced in contextual realizations by paradigm uniformity.

Table 9 shows that the same grammar that derived prosodic variability for epenthetic liaison in Table 7(a) predicts a non-variable word-final behavior for suppletive liaison: candidate (e) (with liaison [l] attaching to Word2 across a prosodic break) is harmonically bounded by candidate (d) (with liaison [l] attaching to Word1). Epenthetic liaison (candidates (b) and (c)) is also ruled out because /t/ is not present in any listed allomorph for the adjective beau. Note that no constraint penalizes the liaison allomorph [bɛl] in Table 9. In a comprehensive analysis, this candidate would violate a constraint banning mismatches between the morphosyntactic specification of an adjective (masculine singular here) and the corresponding morphological exponent (feminine singular here), as proposed by Steriade (1999: 256). Adding this constraint would not affect the prediction concerning the non-variable prosodic behavior of suppletive liaison: this constraint would be violated equally by the candidates involving Word1-attachment (candidate d) and Word2-attachment (candidate e).

Table 9 Suppletive liaison consonants are predicted to behave categorically like word-final consonants and attach to Word1 (bel ami ‘beautiful friend’). The vertical bar | between the two strings in each candidate represents a prosodic break

There is preliminary evidence for the prediction that epenthetic liaison and suppletive liaison differ in this way, as pointed out by Steriade (1999). In right-dislocation contexts, Tranel (1990) reports that epenthetic liaison consonants attach to Word2 whereas suppletive liaison consonants attach to Word1, as illustrated in (11).

• (11) Epenthetic liaison vs. suppletive liaison in right dislocations

  

However, right-dislocation contexts are probably not the most appropriate context to make a case for the variable patterning of epenthetic liaison, as they very strongly favor a prosodic attachment to Word2 (=liaison enchaînée). As noted by Durand and Lyche (2008: 50), the contexts where epenthetic liaison consonants are more readily found to attach to Word1 (= liaison non-enchaînée) involve a hesitation between Word1 and Word2 (see Sect. 2.1).¹¹ The goal of Study 1 is therefore to compare the behavior of liaison consonants (both epenthetic and suppletive) and stable consonants (both word-final and word-initial) across a prosodic break involving a hesitation.

4.2 Methods

Adjective-noun (Adj-N) sequences were chosen as Word1-Word2 sequences. This choice was motivated by the fact that both epenthetic liaison (e.g. grand) and suppletive liaison (e.g. beau/bel) can be found among adjectives. Each of the four experimental conditions (epenthetic liaison, suppletive liaison, stable word-final consonants, stable word-initial consonants) was represented by 12 Adj-N sequences, for a total of 48 Adj-N sequences. Six adjectives were used by condition, as shown in Table 10, and each adjective appeared in two Adj-N sequences varying by the strength of their collocation. For instance, petit appeared both in petit ami ‘boyfriend’ (more frequent) and in petit anneau ‘small ring’ (less frequent).¹² This manipulation was meant to control for potential effects of the following noun on the behavior of liaison consonants, as this variable has been shown to influence some aspects of French liaison in previous research (Fougeron et al. 2001; Kilbourn-Ceron 2017).

Table 10 Adjectives used in Study 1

Two French native speakers (female and male) read each of the 48 Adj-N sequences twice, with a hesitation (euh [œ]) between the two words. The two pronunciations varied in the prosodic attachment of the consonant between the two words. In one pronunciation, the consonant was pronounced at the end of Word1 before the hesitation. This corresponds to a case of liaison non-enchaînée for liaison conditions. In the other pronunciation, the consonant was pronounced at the beginning of Word2 after the hesitation. This corresponds to a case of liaison enchaînée. Examples are shown in Table 11 for each of the four experimental conditions. The prosodic attachment of the consonant was clearly indicated to the speakers using bold characters (e.g. un gran-[t] euh hommage/un gran euh [t]-hommage). The speakers were unaware of the purpose of the study when they were recorded.¹³ In order to make the loudness of the sound files comparable, the root-mean-square amplitude was equalized across the set of sound files and scaled to a max peak value of 1 using a Praat script written by Gabriël J.L. Beckers.¹⁴

Table 11 Experimental items

Twenty-four French participants were recruited via the CNRS RISC platform (https://expesciences.risc.cnrs.fr/) to participate in a study run online. The 48 Adj-N sequences were presented to participants in random order and each participant heard each sequence only once (they heard either the sequence produced by the female speaker or the sequence produced by the male speaker, and the assignment was done randomly for each sequence). For each Adj-N sequence, the two pronunciations were presented one after the other, with the pronunciation involving prosodic attachment to Word1 always preceding the pronunciation involving prosodic attachment to Word2 (with a one-second interstimulus interval).

Participants were asked to indicate which of the two pronunciations sounded more natural to them. The target Adj-N sequence was not presented graphically to participants in order to avoid any explicit orthographic bias. Liaison consonants (both epenthetic and suppletive) appear at the end of Word1 in the spelling and this could directly bias participants towards a word-final attachment. Participants were invited to wear headphones while taking the study. The LimeSurvey platform (LimeSurvey 2012) was used to carry out the study. The participants provided their informed consent to participate in the research and agreed to make their data available online. No sensitive information about participants was collected.

A Bayesian hierarchical logistic regression was fit to the participants’ responses as a function of the dummy-coded factor Consonant (reference level ‘stable word-final consonant’). Consonant has four levels, corresponding to the four types of consonants (stable word-final consonant, suppletive liaison, epenthetic liaison, stable word-initial consonant). The random-effects structure included: (i) random intercepts for each speaker, each participant, and each Adj-N sequence and (ii) by-speaker and by-participant random slopes for the effect of Consonant. The logistic regression was fit using the brms package (Bürkner 2017) in R (R Core Team 2020). A Bayesian approach was chosen (rather than a frequentist approach) because it provides more intuitive and meaningful inferences and also virtually always converges to accurate values of the parameters (Kruschke and Liddell 2018).

For hypothesis testing, the difference Δ in the posterior log-odds ratios of attachment to Word2 was computed for the different experimental conditions. Compelling evidence for a difference between two conditions was considered to be provided only in case zero was outside of the posterior 95% Credible Interval (CI) for Δ. Credible Intervals were obtained using the ETI (Equal-tailed Interval) method and the package bayestestR (Makowski et al. 2019).

4.3 Results

Figure 2 shows the posterior probability that the consonant attaches prosodically to Word2 for each consonant type. As predicted by the paradigm uniformity analysis, suppletive liaison and epenthetic liaison were found to pattern differently, with suppletive liaison being less likely to attach to Word2 than epenthetic liaison ($\Delta _{\text{sup liaison - ep liaison}}=-4.23$, CI = [−8.67,−0.04]). Suppletive liaison was found to behave like stable word-final consonants ($\Delta _{\text{sup liaison - final}}=-0.19$, CI = [−3.45,2.66]), favoring an attachment to Word1 almost categorically. Epenthetic liaison was found to have a rate of attachment to Word2 that is intermediate between stable word-final consonants ($\Delta _{\text{ep liaison - final}}=4.03$, CI = [0.96,7.22]) and word-initial consonants ($\Delta _{\text{ep liaison - initial}}=-11.28$, CI = [−22.82,−4.41]).

Fig. 2

Posterior probability of attachment to Word2 as a function of consonant type (mean and 95% CI)

4.4 Discussion

An important prediction of the paradigm uniformity was corroborated by the results of Study 1: liaison behaves variably as a word-final or word-initial consonant if and only if the liaison consonant can be analyzed as epenthesized at the end of the citation form. When the liaison allomorph is identical to the feminine form and cannot be analyzed as a substring of the masculine form (= suppletive liaison), no prosodic variability arises. This study is to the author’s knowledge the first controlled study that establishes this difference between epenthetic liaison and suppletive liaison.

5 Segmental variability of French liaison as a paradigm uniformity effect

This section shows how the model proposed in Sect. 3 can be extended to deal with the segmental variability of French liaison by making paradigm uniformity constraints sensitive to phonetic detail, as proposed by Steriade (2000). This section focuses on the interaction of liaison and affrication in Quebec French as this case study provides the clearest case of variable realization for French liaison: liaison /t/ has a rate of affrication that is intermediate between that of word-final /t/ and word-initial /t/ (see Sect. 2.2).¹⁵ Also, this case study can be modeled with the type of symbolic phonological grammars used in Sect. 3 since affrication is usually described in a categorical manner (presence/absence of affrication) and therefore can be analyzed using discrete phonological representations. Modeling phonetic realization in a continuous space would require moving from symbolic to phonetic grammars (Flemming 2001). This task is left for further research.

The key ingredient in the analysis will be the observation that coarticulation is bidirectional, namely it affects both the realization of C and V in a CV sequence. Bidirectionality of coarticulation predicts that a change on C (e.g. affrication in the case of Quebec French) correlates with a change on the following V. In combination with paradigm uniformity, this correlation will be crucial to explain why liaison consonants might pattern intermediately between word-final and word-initial consonants phonetically. In a nutshell, CV-coarticulation at word boundaries will potentially result in violations of paradigm uniformity for both words in a Word1-Word2 sequence. However this coarticulation will have different effects for the three types of consonants. Coarticulated liaison consonants will incur fewer output-output faithfulness violations than coarticulated final consonants (due to the liaison consonant being absent from the corresponding citation form). But coarticulated liaison consonants will imply more output-output faithfulness violations for the following vowel than coarticulated initial consonants will (because initial consonants are already coarticulated with the following vowel in the corresponding citation form whereas liaison consonants are not).

Section 5.1 provides some background on the bidirectionality of coarticulation, and shows how it applies in the case of Quebec French affrication. Building on these results, Sect. 5.2 shows how the analysis derives citation forms for words with liaison allomorphs and for words that lack such allomorphs. Section 5.3 shows how the segmental variability of liaison consonants as documented in Côté’s (2014) corpus can be derived as a paradigm uniformity effect, assuming bidirectionality of coarticulation. Section 5.4 further shows that the asymmetry between liaison consonants and stable consonants is a necessary consequence (an implicational universal) of the proposed constraint set. The analysis can be found in Storme (2022) under the name phonetic-ambiguity-final-2.txt.

5.1 Bidirectionality of coarticulation in CV sequences

Probably the best studied case of coarticulation is the assimilation in second formant (F2) frequency between consonants and vowels (see Flemming 2001: 16–23). A large number of studies have shown that C assimilates to V in CV, in particular F2 at consonant release can be described as an increasing linear function of F2 in the middle of the vowel: as the F2 in the middle of the vowel increases, the F2 at consonant release also increases (Lindblom 1963; Sussman et al. 1991). In turn, V has also been found to assimilate to C in CV, with F2 in the middle in the vowel being higher when F2 at consonant release is higher (Lindblom 1963; Broad and Clermont 1987). These results suggest that coarticulation is bidirectional in CV sequences: both C and V are affected when the two sounds are combined in a CV sequence, and any change affecting one of the two sounds should also affect the other one.

Bidirectionality of coarticulation extends beyond this well studied case and applies in particular to Quebec French affrication. In Quebec French, affrication of /t d/ before high front vowels and glides applies almost categorically morpheme-internally (Côté 2014). Phonetically, affrication involves a change in consonant manner: the stop burst is followed by a frication noise (Stevens 1998: 412). But affrication before high vowels does not only affect the realization of the consonant. It also correlates with changes in the following vowel (Cedergren and Simoneau 1985; Dow 2019). In particular, Cedergren and Simoneau (1985: 72–80) report that high vowels tend to be reduced/deleted in the vicinity of fricatives, including after affricates. This effect is stronger with voiceless fricatives/affricates. Because /t/ maps to a voiceless affricate [ts] after affrication, high-vowel reduction is expected to be particularly common after this sound. In the remainder of this paper, [] will be used to note this reduced/deleted high vowel. In other words, an underlying sequence /ti/ tends to be realized as [] on the surface in Quebec French, with both affrication and high-vowel reduction.

This coarticulatory pattern involving fricatives/affricates and high vowels is found in other languages such as Japanese (Beckman and Shoji 1984; Whang 2018). For instance, Whang (2018: 1166) found a positive correlation between lengthening of [tʃ] (from an underlying /t/) and high-vowel devoicing in [tʃi] sequences in Japanese. This result suggests that, as /t/ gets more affricated (the frication noise gets longer), the following high vowel gets more reduced, in line with what has been found in Quebec French. Based on such parallels, Cedergren and Simoneau (1985: 189) propose that this interaction stems from a universal phonetic constraint, but without providing more details. One possible mechanism relating the two changes is compensatory lengthening/shortening: there is a trading relationship between the duration of C and V such that if the frication noise of C lengthens then V shortens and conversely (see Whang 2018: 1160 and literature therein).

The present paper will remain agnostic as to what the precise coarticulatory mechanism underlying this pattern is. In what follows, the constraint that drives the interaction between affrication and high-vowel reduction will be noted descriptively as *tsi. Assuming that affrication of /t/ to [ts] is independently motivated before [i] in a language (by a markedness constraint *ti), the constraint *tsi will favor a candidate [] involving a concomitant change in vowel quality over a candidate [tsi] involving affrication but no high-vowel reduction.

5.2 Deriving citation forms

The same grammatical architecture is assumed in the analysis of segmental variability as in the analysis of prosodic variability (see Fig. 1). According to this model, the phonology of citation forms is derived first. At that stage, only input-output faithfulness and phonotactic markedness play a role.

The preference for realizing underlying /ti/ as [] (candidate (c) in Table 12(a)) can be attributed to the effect of the two markedness constraints *ti and *tsi described in the previous section. If these constraints have higher weights than the input-output faithfulness constraints protecting against changes in consonant continuancy (Ident-IO(cont)) and in vowel voicing (Ident-IO(voi))), then candidate (c) is predicted to be favored over the faithful candidate (candidate (a)) and over the candidate that only changes consonant continuancy (candidate (b)). Table 12(a) shows a specific choice of constraint weights in MaxEnt that derives the near-categorical rate of affrication of morpheme-internal /ti/ documented by Côté (2014). The weights were inferred using OT-Soft, as in Sect. 3.¹⁶

Table 12 Citation forms

Tables 12(b) and 12(c) show that the same grammar predicts that affrication and high-vowel reduction should not apply in the citation forms of words with stable word-final /t/ and words with word-initial /i/, respectively. In these cases, the relevant markedness constraints are not violated and therefore nothing motivates any change in consonant continuancy or vowel quality on the surface.

The analysis above accounts for the affrication of morpheme-internal /ti/ in Quebec French. The citation forms for liaison words must also be derived. In Quebec French, the allomorph without liaison (e.g. grand []) is categorically favored in citation forms, as in the variety from France analyzed in Sect. 3. This preference is due to a phonotactic markedness constraint penalizing utterance-final consonants, as shown in Table 12(d) (see also Sect. 3.2).

5.3 Deriving connected-speech variants

At the boundary between two words, affrication will potentially result in changes in both Word1 and Word2, due to the bidirectional nature of coarticulation. But this will have different implications in terms of paradigm uniformity with the corresponding citation forms depending on the type of consonant.

Dissimilarities with citation forms are penalized by two new output-output faithfulness constraints: Ident-OO(cont) and Ident-OO(voi). These constraints correspond to Ident-IO(cont) and Ident-IO(voi) used in the analysis of morpheme-internal affrication, but in the output-output dimension: they penalize dissimilarities between contextual variants and the corresponding citation forms in terms of consonant continuancy and vowel quality, respectively. Table 13 shows how affrication implies different patterns of violations of these constraints depending on whether the consonant is a stable word-initial consonant, a liaison consonant, or a stable word-final consonant.

Table 13 How affrication affects the similarity with citation forms depending on the type of consonant

For liaison consonants, affrication implies a number of feature changes that is intermediate between the number of feature changes for stable word-final and word-initial consonants. Only the feature change affecting vowel quality at the beginning of Word2 (i → ) is penalized by paradigm uniformity. The change in consonant continuancy at the end of Word1 (t → ts) is not penalized because the liaison consonant is missing from the corresponding citation form. For stable word-final consonants, affrication implies two feature changes relative to the corresponding citation form (one on the consonant at the end of Word1 and another one on the vowel at the beginning of Word2). For stable word-initial consonants, affrication does not imply any feature change relative to the corresponding citation form, since affrication already applies (almost) categorically in this form.

As shown in the last column of Table 13, the rate of affrication is inversely correlated with the number of feature changes implied by affrication across the three types of consonants. This can be understood as a paradigm uniformity effect: the grammar militates for uniformity between contextual and citation forms, resulting in less affrication for forms in which affrication would imply more feature changes.

Note that the paradigm uniformity constraints used in the analysis of prosodic variability (Right-Anchor-OO and Left-Anchor-OO) will not play a role here. The reason is that all output candidates that do not feature a prosodic break between Word1 and Word2 violate Anchor constraints equally regardless of how consonants are realized segmentally at the junction of the two words. Anchor constraints assess faithfulness for the segment as a whole regardless of its internal feature specifications. For instance, in the absence of a prosodic break between Word1 and Word2, a liaison consonant is in contact with both the right edge of Word1 and the left edge of Word2. As a consequence, it is penalized equally by the two Anchor constraints regardless of whether it is affricated or not. Similarly, candidates involving a word-final consonant followed by a vowel-initial word (as in trente innocents) incur the same violations of Right-Anchor-OO and Left-Anchor-OO, regardless of whether the consonant is affricated or not. And the same goes with candidates involving a vowel-final word followed by a consonant-initial word (as in vrai tyran).

Table 14 shows how an analysis including Ident-OO(cont) and Ident-OO(voi) can derive the rates of affrication attested in Côté’s (2014) study for the different types of consonants: liaison consonants (Table 14(a)), stable final consonants (Table 14(b)), and stable initial consonants (Table 14(c)).¹⁷ As in the analysis of prosodic variability, the use of the liaison allomorph is motivated by a markedness constraint penalizing vowel hiatuses (*VV). The choice of a specific realization for the consonants occurring at the boundary between Word1 and Word2 is driven by the interaction between phonotactic constraints (*ti, *tsi), input-output faithfulness constraints (Ident-IO(cont) and Ident-IO(voi)), and output-output faithfulness constraints (Ident-OO(cont) and Ident-OO(voi)). Ident is abbreviated as Id in Table 14.

Table 14 Connected-speech variants

The analysis derives all three realizations attested in Côté (2014) for liaison words, as shown in Table 14(a): absence of liaison consonant (candidate (a)), liaison without affrication (candidate (b)), and liaison with affrication (candidate (d)). It also derives the specific frequencies attested for each of these realizations.

The analysis also does a good job at matching the frequencies of affricated realizations and non-affricated realizations for stable word-final /t/ before /i/ (candidate (c) in Table 14(b) vs. candidate a in Table 14(b)). The fact that affrication is less likely for word-final /t/ than for liaison /t/ follows from differences in the way affrication is penalized by output-output faithfulness in these two cases: the candidate with affrication violates Ident-OO(cont) in the consonant-final word (candidate (c) in Table 14(b)) but not in the liaison word (candidate (d) in Table 14(a)), due to the liaison consonant being absent from the citation form.

The analysis also does a good job at deriving the quasi-categorical affricated realization of word-initial /t/ before /i/ (candidate (c) in Table 14(c)). The fact that affrication is more likely for word-initial consonants than for liaison consonants follows from differences in the way affrication is penalized by output-output faithfulness in these two cases. Affrication is not penalized at all in the consonant-initial word (candidate (c) in Table 14(c)) because it has already applied in the corresponding citation form. Affrication is penalized by Ident-OO(voi) in the liaison word (candidate (d) in Table 14(a)): affrication of liaison /t/ correlates with a reduction of the vowel at the beginning of Word2, in violation of paradigm uniformity ([i] is unreduced in the citation form).

5.4 Implicational generalizations

The preceding section has shown that the paradigm uniformity analysis can capture the intermediate rate of affrication of liaison consonants as attested in Côté’s (2014) corpus. But the analysis actually derives the intermediate realization of French liaison in (12) as a necessary consequence of the proposed constraint set, and this regardless of the framework for probabilistic grammars (Stochastic OT, Noisy HG, or MaxEnt).

• (12) Statistical implicational generalizations derived by the analysis

  • a. P(No affrication|Liaison C)≤P(No affrication|Final C)

  • b. P(Affrication|Liaison C)≤P(Affrication|Initial C)

  In words: Liaison consonants are less likely to resist affrication (/ti/ → []) than final consonants and less likely to undergo affrication than initial consonants.

The demonstration is more involved than in the case of prosodic variability (Sect. 3.4) because here no candidate is harmonically bounded. The constraint-violation profiles of the different candidates must be carefully compared across the different types of consonants (final, liaison, and initial). In a nutshell, generalization (12a) holds because the candidate with an unaffricated liaison consonant (candidate (b) in Table 14(a)) fares worse within the candidate set for liaison words than the candidate with an unaffricated final consonant (candidate (a) in Table 14(b)) does within its own candidate set. And, similarly, generalization (12b) holds because the candidate with an affricated liaison consonant (candidate (d) in Table 14(a)) fares worse within its candidate set than the candidate with an affricated initial consonant (candidate (c) Table 14(c)) does within its own candidate set. For more details, the reader is referred to the output of the CoGeTo analysis (Magri and Anttila 2019) in the supplementary materials. This analysis shows that indeed the implications in (12) hold in Stochastic OT, Noisy HG, and MaxEnt.

6 Study 2: Liaison and affrication in Quebec French

One key ingredient in the analysis of Quebec French liaison proposed in Sect. 5 is the idea that coarticulation affects both C and V in CV, and more specifically that affrication of /t/ correlates with a reduction of /i/ in /ti/ sequences. This hypothesis was crucial to explain why affrication is less likely for liaison consonants than for word-initial consonants.

The goal of this section is to test whether affrication does indeed correlate with vowel reduction across a word boundary, for both stable word-final consonants and liaison consonants. Section 6.1 presents the methods used to test the hypothesis. Section 6.2 presents the results. Section 6.3 concludes with a brief discussion. The data and code for Study 2 are available in Storme (2022) under the names study2-data.csv and study2-code.R, respectively.

6.1 Methods

Data from the Quebec PFC project (Côté 2016) were used to investigate this question. The analysis focuses on one minimal pair from the PFC word lists that feature an underlying sequence /ti/ at the boundary between two words: grand innocent ‘great innocent’ (with liaison /t/) and trente innocents ‘thirty innocent (people)’ (with stable word-final /t/). These data are particularly interesting because they make it possible to test both whether affrication and high-vowel reduction are correlated and how this correlation might differ for liaison consonants and stable word-final consonants. The analysis does not focus on word-initial /ti/ sequences as the PFC word lists do not include minimal pairs allowing for a controlled comparison with liaison and word-final consonants.

The data from all locations available in the corpus in 2021 were selected, corresponding to a total of 394 participants.¹⁸ Annotations were done manually in Praat (Boersma and Weenink 2021). /t/ duration was used as acoustic correlate for affrication: an underlying /t/ that is affricated on the surface should be longer than an underlying /t/ that is not affricated. The choice to use duration as a dependent variable was also motivated by the fact that earlier phonetic studies on French liaison also focused on duration (see Sect. 2.2). The duration of /t/ included the burst and/or frication noise, following Whang (2018: 1163). Vowel reduction was also annotated, using the presence of formant structure as a criterion. In the absence of clear formant structure, no vowel /i/ was included on the corresponding tier. This does not mean that the vowel is completely absent phonetically as phonetic reflexes of /i/ could be present in the burst or frication noise of /t/. Pauses and schwas that sometimes occurred between /t/ and /i/ were also annotated, as well as cases of non-conventional consonant realizations (for instance, some participants pronounced a [z] between trente and innocents) and cases where the liaison consonant was absent (in these cases, no consonant was annotated on the corresponding tier). Segment durations were extracted automatically using a Praat script.

Figure 3 shows the annotation for two occurrences of /ti/ in the corpus. Figure 3a shows an occurrence of liaison /t/ and Fig. 3b an occurrence of stable word-final /t/. In Fig. 3a, liaison /t/ appears to be characterized by a long frication noise and there is no visible vowel after it, as it is directly followed by [n]. This realization corresponds to the transcription of /ti/ as [] in Sect. 5. In Fig. 3b, the burst of stable word-final /t/ is much shorter and /i/ is clearly visible in the spectrogram after it. This realization corresponds to the transcription of /ti/ as [ti] in Sect. 5. These two occurrences thus illustrate the correlation that should be found in the corpus if affrication correlates with vowel reduction in /ti/ sequences.

Fig. 3

Annotation in Praat

Only sequences that involve a [t] on the surface (affricated or not) and no pause between the consonant and the vowel were included in the final analyses, corresponding to a total of 322 participants and 494 occurrences of consonants (243 liaison consonants and 251 stable word-final consonants).

To assess the reliability of the coding of consonant duration and vowel presence, a subset of the stimuli were annotated again by the author two years after the first annotation was carried out. 50 occurrences of the /ti/ sequences included in the final analysis were randomly sampled from the original set and reannotated in Praat. Reliability was assessed using the intraclass coefficient correlation (ICC) in the irr package in R. A good reliability was found for the coding of both consonant duration (ICC(A,1)=0.869, p<.001) and vowel presence (ICC(A,1)=0.842, p<.001). The datafile for the reliability study can be found in Storme (2022) under the name check-study2-data.csv and the corresponding R script is available under the name study2-reliability-study.R.

Two statistical analyses were conducted on the original dataset. A Bayesian logistic regression was fit to the data using the brms package in R, with Vowel (present, absent) as a dependent variable and Consonant (liaison, final), Consonant duration and their interaction as independent variables. The goal of this first analysis was to test whether vowel deletion correlates with lengthening of /t/, as expected under the hypothesis that affrication results in high-vowel deletion/reduction.

A Bayesian linear regression was also fit to the data, with Consonant duration as dependent variable and Consonant (liaison, final) as independent variable. The goal of this second analysis was to test whether liaison /t/ is phonetically longer than stable word-final /t/. A greater duration for liaison /t/ is expected if liaison /t/ is more affricated than stable word-final /t/, as reported by Côté (2014) on a perceptive basis, and if liaison consonants are generally longer than stable word-final consonants (see Sect. 2.2). The analyses did not include random effects because there was at most one occurrence of each type of consonant (liaison, final) per speaker.

6.2 Results

The results of the logistic regression confirm the hypothesis that /t/-lengthening correlates with a higher likelihood of /i/-deletion, as shown in Fig. 4. An increase of 1 ms in /t/ duration corresponds to a decrease of 0.08 unit (CI = [0.06,0.11]) in the posterior log-odds ratio of /i/-presence. This result was found to hold for both liaison and stable word-final consonants, as the interaction term between duration and consonant type was not significantly different from zero (β = 0.02, CI = [−0.01,0.05]). Moreover, liaison /t/ was found to favor /i/-deletion more than than word-final /t/ (β = −2.25, CI = [−4.31,−0.27]), independently from the effect of duration.

Fig. 4

Posterior probability of /i/-deletion as a function of /t/-duration and consonant type (liaison, final)

The results of the linear regression show that liaison /t/ is longer on average than word-final /t/ (β = 11.79, CI = [7.66,16.01]), as shown in Fig. 5. This lengthening corresponds to an increase of 19% in duration. This is compatible with the observation in Côté (2014) that liaison /t/ is more affricated than stable word-final /t/ on average. This is also compatible with earlier observations about the relative duration of liaison consonants and stable word-final consonants more generally (see Sect. 2).

Fig. 5

Posterior distribution of consonant duration (ms) for stable word-final /t/ and liaison /t/ (mean and 95% CI)

6.3 Discussion

The results of Study 2 support a key hypothesis of the paradigm uniformity account of the segmental variability of Quebec French liaison: affrication at a word boundary results in reduction/deletion of the following vowel. This hypothesis was crucial to explain why the rate of affrication is smaller for liaison /t/ than for word-initial /t/. Reduction of the initial vowel of Word2 after affricated liaison /t/ makes the connected-speech variant of Word2 less similar to its citation form (where reduction does not apply) and therefore is undesirable for paradigm uniformity. By contrast, word-initial /ti/ sequences already undergo affrication in citation forms and therefore there is no reason to block affrication in the corresponding connected-speech variants.

Moreover, the results also support the hypothesis that liaison /t/ is more prone to affricate than stable word-final /t/. In the paradigm uniformity analysis, this follows from the effect of the corresponding citation form. Stable word-final /t/ is influenced by the corresponding unaffricated [t] in the citation form. Liaison /t/ does not correspond to any [t] in the citation form and therefore is less likely to resist affrication.

7 Comparison with other analyses

This section proposes to take a step back and look at how the paradigm uniformity analysis of liaison proposed in this paper compares with earlier analyses (see Côté 2011 for an overview). Before doing so, it is important to remind the reader that the analysis presented in this paper addresses only one of the two main research questions on French liaison, namely how liaison consonants are realized when pronounced (=Q1). The other main research question is about which factors affect whether the liaison consonant in a liaison word is pronounced or not (=Q2). This second research question is motivated by the observation that the rate of liaison in Word1-Word2 sequences depends not only on the initial segment of Word2 (vowel/consonant) but also on other phonological and non-phonological properties of Word1 and Word2 as well as language-external factors, as shown in Table 15.

Table 15 A non-exhaustive list of variables reported to condition the rate of liaison along with a non-exhaustive list of sources (PoS = part of speech, Freq = frequency)

Analyses of French liaison differ in their scope: some of them, like the present analysis, only focus on Q1, others only on Q2 and finally some theories deal with both Q1 and Q2. Table 16 presents a sample of analyses of French liaison, with the first column indicating which research question they focus on. Analyses may also differ in how they answer the research question. Analyses of French liaison can be conveniently divided into two broad categories, depending on whether the explanatory burden relies mainly on representations (a richer phoneme inventory and/or a richer lexicon) or on computation (a richer constraint set), as indicated in the three rightmost columns of Table 16. Although the production planning hypothesis proposed by Kilbourn-Ceron (2017) is not directly formulated in terms of constraints, it can be implemented this way, as will be shown in Sect. 7.4.

Table 16 Analyses of French liaison: a typology. Q1: How are liaison consonants realized when present? Q2: Which factors condition the rate of liaison before vowel-initial words?

Sections 7.1–7.3 review the first three analyses listed in Table 16 and highlight how they compare to the paradigm uniformity analysis in accounting for Q1. Section 7.4 concludes by sketching how insights from Kilbourn-Ceron’s production planning hypothesis can be combined with the paradigm uniformity analysis to get a more comprehensive model of French liaison accounting for both Q1 and Q2.

7.1 Floating consonants

Liaison consonants have been analyzed as floating segments by several researchers, including by Encrevé (1988: 169–173) and Tranel (1990: 183–184) in the framework of autosegmental phonology and by Tranel (2000: 49–52) in the framework of Optimality Theory. In these approaches, liaison consonants are lexically affiliated to the first word but differ from stable word-final consonants in not being attached to the word’s early prosodic structure. This property allows them to be associated at a later stage of prosodic-structure building to either Word1 or Word2 in a Word1-Word2 sequence (Encrevé 1988: 182).

The specific proposal advanced by Tranel (1990) is represented in (13). In this analysis, liaison /z/ does not project a skeletal slot and is therefore ‘floating’ at the end of Word1 in the early prosodic structure. When the two words are combined together, the liaison consonant has to be attached somewhere prosodically. Rightward syllabification attaches it at the beginning of Word2, making it a liaison enchaînée. Leftward syllabification attaches it at the end of Word1, making it a liaison non-enchaînée. Liaison words that use the feminine form as liaison variant (e.g. bel [bɛl] ‘beautiful’) are analyzed differently: in these words, the final consonant is attached to the word’s early prosodic structure (Tranel 1990: 183) and therefore behaves like other stable word-final consonants (see Sect. 4 on the distinction between epenthetic and suppletive liaisons).

• (13) Liaison consonants as floating segments: gros anneau ‘big ring’ (based on Tranel 1990: 184)

  

Analyses using floating segments are the closest in scope to the paradigm uniformity analysis: their focus is also on deriving the variable realization of liaison consonants before vowel-initial words. However they differ from the paradigm uniformity analysis because they build the variable behavior of liaison consonants directly into their phonological representations. These approaches indeed require to enrich the phoneme inventory of French with a new set of phonemes. For instance, Tranel (2000: 51–52) introduces a phonological feature to distinguish stable consonants (noted as C) from liaison consonants (noted as L).

By contrast, the paradigm uniformity analysis adopts the exact same phonological representation for liaison and non-liaison consonants. The difference between liaison consonants and other consonants ultimately emerges from differences in lexical representations: liaison words have several listed allomorphs varying by the presence/absence of a final consonant whereas other words don’t (see Sect. 3). And the fact that epenthetic liaison and suppletive liaison behave differently emerges from differences in the similarity between the liaison allomorph and the corresponding citation form (see Sect. 4).

One empirical advantage of the paradigm uniformity analysis is that it accounts for both types of variability (prosodic and segmental). By contrast, the approach using floating segments currently only accounts for prosodic variability. If liaison consonants become identical to onset consonants after rightward resyllabification, then it is unclear why they should pattern differently from stable word-initial consonants segmentally in this context, as documented in Sect. 2.2. The same problem would arise for approaches using alignment constraints (e.g. Zuraw and Hayes 2017; see the discussion in Sect. 3.3).

As pointed out by a reviewer, one possibility would be to exploit the fact that there remains a difference in the underlying representations of liaison and non-liaison consonants in Tranel’s analysis: one projects a skeletal slot whereas the other does not, as shown in (13). For Quebec French, a rule of affrication that is sensitive to this underlying difference could then be conceived. However it is unclear why this affrication rule would necessarily have a probability of application that is intermediate between the rules applying to stable word-final consonants and to stable word-initial consonants. In the paradigm uniformity analysis, this asymmetry follows as an implicational generalization from independently motivated principles of coarticulation and paradigm uniformity with citation forms (see Sect. 5).

7.2 Lexical constructions

In the approach using lexical constructions, the liaison consonant belongs neither to Word1 nor to Word2 but to a construction involving the two words (Bybee 2001). For instance, there is a lexical construction of the form // ‘great N,’ where X_V-initial is a vowel-initial noun and /t/ a consonant occurring between the Adj and the N. Nouns that are more frequently associated with the adjective grand ‘great’ are more likely to be stored under this frame, explaining for instance why the likelihood of the liaison consonant increases with the frequency of the Word1-Word2 sequence (see Fougeron et al. 2001; Kilbourn-Ceron 2017).

Although lexical constructions are primarily motivated by the type of frequency effects reported in Table 15 (e.g. the rate of liaison is higher for liaison words with higher lexical frequency), Bybee mentioned in passing that they can also account for the prosodic variability of French liaison. She argues that a prosodic break may intervene in the middle of a lexical construction in the same way as it may intervene in the middle of a word. For instance, it it possible to say un élé phant [] ‘an ele (prosodic break) fant’ with a prosodic break in the middle of the word éléphant. Liaison non-enchaînée and liaison enchaînée would then correspond to situations where the prosodic break within a lexical construction intervenes after and before the liaison consonant, respectively.

This approach suffers from the same limit as the approach using floating consonants in that it does not account for segmental variability. Moreover, it potentially presents another problem. Stable word-final consonants and word-initial consonants do not seem to be separable from their lexical host prosodically, even in high-frequency two-word sequences. For instance, a prosodic break seems much more natural after the stable final consonant of Word1 than before it in the compound porte-avion ‘aircraft carrier’ (porte euh avion ).

Bybee (2001) sketches an explanation for why it does not happen: “Since the words of a construction are usually associated with other instances of the same word, their identity as words is known, and the point between two words is a possible place to pause.” In other words, a pause is more likely to occur between words than within words inside a multiple-word construction because the word forms inside this construction stand in correspondence with their base forms (which are independently stored outside of any construction). In other words, stable word-final [t] in porte-avion cannot be resyllabified across a prosodic break because there is a pressure from the base form porte to maintain the [t] at the end of Word1. Liaison consonants are not subject to the same pressure because they are absent from the base forms of Word1 and Word2. When fleshed out, this explanation actually clearly refers to principles of paradigm uniformity among morphologically related forms. This means that an analysis using lexical constructions alone is not sufficient to derive the variable realization of liaison and must be supplemented with a mechanism allowing for paradigm uniformity.

However the lexical-construction approach has an advantage over the paradigm uniformity analysis presented in this paper in that it can account for lexical effects on the rate of liaison. This difference derives from the fact that multiple-word constructions are stored in the lexical-construction analysis whereas they are not in the paradigm uniformity analysis presented in Sects. 3 and 5. Altough paradigm uniformity could in principle be combined with lexical constructions to get a more comprehensive model of French liaison, it is not immediately clear how to reconcile the differences in lexical representations between the two analyses. Liaison consonants do belong to Word1 underlyingly in the paradigm uniformity analysis (see Table 5 in Sect. 3) whereas they do not in Bybee’s analysis. Section 7.4 will show that the production planning hypothesis proposed by Kilbourn-Ceron (2017) is more directly compatible with the assumption that liaison consonants belong to Word1 and therefore provides a better fit to the paradigm uniformity analysis proposed in this paper.

7.3 Gradient symbolic representations

In the approach using gradient symbolic representations, phonological representations of phonemes are enriched with an activity degree ranging from zero to one (Smolensky and Goldrick 2016; Smolensky et al. 2020). In the evaluation of input-output mappings, faithfulness violations are multiplied by the activity degree of segments in the input. This approach predicts that phonemes with a lower activity degree will be less protected by faithfulness and therefore more likely to undergo a phonological process. This approach derives the higher likelihood of deletion for liaison consonants as compared to stable consonants by assuming a lower activity degree for liaison segments underlyingly: liaison consonants have an activity degree strictly smaller than 1 whereas stable consonants have an activity degree equal to 1.

Two further assumptions are made in order to derive the prosodic variability of liaison consonants (Q1) and lexical effects on the rate of liaison (Q2). Liaison consonants are assumed to be stored both at the end of liaison words and at the beginning of all vowel-initial words. This explains why they might be realized both at the end of Word1 (liaison non-enchaînée) and at the beginning of Word2 (liaison enchaînée). Furthermore, liaison consonants are assumed to have word-specific activity degrees. Together with the assumption that liaison consonants are present both in Word1 and Word2 underlyingly, this allows for the rate of liaison to depend on the identity of Word1 and Word2.¹⁹

The representational assumptions of this analysis are illustrated in (14), using the sequence grand innocent as an example. The degree of activity of liaison consonants is indicated as a subscript. For stable consonants, the degree of activity is always equal to 1 and therefore not explicitly indicated. A word like innocent [] ‘innocent’ is stored with all the possible liaison consonants that can be attached to it as first segment. When the words grand and innocent are combined, the activity level of liaison /t/ increases, allowing it to surface with some probability. Because the /t/ is underlyingly present in both words, it can surface either at the end of Word1 or at the beginning of Word2.

• (14) Liaison consonants as gradient phonemes affiliated to both Word1 and Word2 (Smolensky and Goldrick 2016)

  

This approach derives some lexical effects on the rate of liaison (but not all; see footnote 19) and accounts for the prosodic variability of liaison. However, as articulated to this point in time, it fails to derive the intermediate behavior of liaison in terms of segmental realization. The reason is that it incorrectly predicts that liaison consonants should always be more likely to undergo a sound process than stable consonants. This prediction happens to be correct regarding deletion (liaison consonants are more likely to delete than stable consonants) but not regarding affrication (liaison /t/ is less likely to affricate than stable initial /t/). This problematic prediction is made because, due to its lower activity degree, a liaison /t/ that is affricated on the surface incurs strictly fewer faithfulness violations than a stable initial /t/ that is also affricated on the surface. For instance, affricating liaison /t/ in grand innocent in (14) would violate Ident-IO(cont) 0.48 + 0.09 = 0.57 time whereas affricating initial /t/ in timide would violate it one time (the degree of activity of a stable consonant is equal to one). As a consequence, liaison /t/ should be more likely to affricate than initial /t/. But this is not the case (see Côté 2014 and Sect. 2.2). The mechanism proposed to account for the rate of liaison therefore turns out to be problematic to account for its intermediate segmental realization.

7.4 Towards a comprehensive model of French liaison

The paradigm uniformity analysis provides the most comprehensive account of the realization of liaison consonants (Q1). Among the four approaches reviewed in this paper, it is the only one that can derive the variability of liaison in both prosodic and segmental terms. The approach using lexical constructions does not account for the variability of liaison unless supplemented with a mechanism allowing for paradigm uniformity. The approach using floating segments accounts for the prosodic variability of liaison but not for its segmental variability. The approach using gradient symbolic representations accounts for prosodic variability but makes incorrect predictions about the segmental realization of liaison consonants and stable consonants.

However the paradigm uniformity analysis presented in this paper does not account for the factors that affect the rate of liaison (Q2), contrary to the lexical-construction approach and the approach using gradient symbolic representations. One could attempt to combine these different approaches to get a more comprehensive model of French liaison. However they are based on very different assumptions about underlying phonological/lexical representations, making it difficult to find a common ground.

The analysis most compatible with the representational assumptions of the paradigm uniformity analysis is the production planning hypothesis (Wagner 2012; Tanner et al. 2017) as applied to French liaison by Kilbourn-Ceron (2017). Like the paradigm uniformity analysis, this analysis does not need to depart from traditional phonological/lexical representations. Moreover, it shares the same constraint-based orientation: the rate of liaison is determined by linguistic and cognitive constraints on speech-production planning.

According to the production planning hypothesis, an external sandhi process such as French liaison arises at the junction between two words when those two words are planned in the same planning window. And two words are more likely to be planned together if they are easy to retrieve from memory. The fact that the rate of liaison is higher in Word1-Word2 sequences in which Word1 and Word2 are frequent, contextually predictable, and short is compatible with the production planning hypothesis because these properties all facilitate word form retrieval (Kilbourn-Ceron 2017: Chap. 4).

Insights from the production-planning hypothesis can be incorporated into the paradigm uniformity analysis by indexing output-output faithfulness constraints to properties that are relevant for production planning (see Pater 2007 on constraint indexation). A word that is harder to retrieve from memory will tend to be planned in its own planning window, and therefore to be less connected to adjacent words. In other words, it will tend be more similar to the corresponding citation form. In the constraint-based model proposed in this paper, the parameters that regulate the similarity with citation forms are the weights of output-output faithfulness constraints. The effects that influence production planning can thus be captured by weighting output-output faithfulness constraints higher for words that are harder to retrieve. For instance, words with low lexical frequency would be evaluated by a set of output-output faithfulness constraints that have higher weights than the output-output faithfulness constraints evaluating words with high lexical frequency. As mentioned in Sect. 3.3, lexical indexation of paradigm uniformity constraints has already been proposed by Zuraw and Hayes (2017) to account for the greater resistance of French h-aspiré words to external sandhi processes. Generalizing this approach to other types of properties, and in particular to properties that are relevant to speech production, looks like a promising avenue to model the rate of French liaison.

Table 17 illustrates this approach using a toy example based on the analysis of prosodic variability from Sect. 3.3. The analysis focuses on one lexical property that has been shown to affect the rate of liaison, namely the conditional probability (or predictability) of Word2 given Word1. The production planning hypothesis predicts that, in Word1-Word2 sequences, the liaison allomorph of Word1 should become more likely as the contextual probability of Word2 given Word1 increases. This prediction is made because Word2 should be easier to retrieve and therefore more likely to be planned together with Word1 if Word2 is more predictable contextually. In line with this prediction, Kilbourn-Ceron (2017: 146) found that a higher conditional probability of Word2 given Word1 correlates with a higher rate of liaison.

Table 17 How an analysis including indexed output-output faithfulness constraints accounts jointly for the rate and realization of liaison. The vertical bar | between the two strings in each candidate represents a prosodic break

The analysis in Table 17 compares the pronunciation of grand anneau ‘large ring’ and grand ami ‘great friend.’ The two sequences differ by the conditional probability of Word2 given Word1: after grand, anneau is less frequent than ami and therefore more likely to be planned in a separate planning window from the preceding word, according to the production-planning hypothesis. In the constraint-based model of paradigm uniformity, this translates into the following conditions. The contextual pronunciation of anneau is evaluated by a constraint that penalizes dissimilarities between connected-speech variants and the corresponding citation forms for words with low contextual predictability (Left-Anchor-OO_{low predictability}). Furthermore, this constraint has a higher weight than the constraint that evaluates the pronunciation of words with high contextual predictability such as ami (Left-Anchor-OO_{high predictability}). Table 17 shows that this approach correctly predicts that the rate of liaison should be smaller before the less predictable word (27% before anneau vs. 49% before ami)²⁰ while still accounting for the prosodic variability of French liaison (the liaison consonant can attach at the end of Word1 or at the beginning of Word2 in both grand ami and grand anneau). All other constraints and constraint weights are the same as in the analysis presented in Sect. 3.3.

The toy analysis in Table 17 also shows that speech-production planning is predicted to affect not only the rate of liaison but also its prosodic realization: Word1-attachment of liaison consonants should be proportionally more likely when Word2 is contextually less probable (because, in this case, the output-output faithfulness constraint evaluating Word2 has a high weight and will therefore strongly push the liaison consonant away from it). And the same is expected to hold for the segmental realization of liaison: for instance, liaison /t/ should have a lower rate of affrication when Word2 is contextually less probable. These predictions should be tested in future work.

8 Conclusion

Liaison consonants have been shown in previous research to pattern in an intermediate way between stable word-final and word-initial consonants. The present paper has shown that it is not necessary to attribute this behavior to differences in the phonological underlying status of liaison consonants. Rather it can be derived from the observation that liaison words come under two variants (with and without liaison) and from independently motivated principles of uniformity among paradigmatically related forms (contextual variants of a word and the corresponding citation form). Also, the variable behavior of liaison consonants can be derived without positing lexical constructions or massive allomorphy in the lexicon. It is sufficient to assume that only liaison words have two listed allomorphs. An explicit implementation of the analysis in a probabilistic constraint-based grammar was proposed and shown to be able to derive the variable behavior of French liaison in terms of both prosodic and segmental properties. Crucially, the analysis assumed standard lexical and phonological representations as inputs. In the end, liaison is only one among the many types of phonologically optimizing suppletion found across languages (Inkelas 2014: 282–284). Its puzzling behavior comes from the way suppletion interacts with paradigm uniformity at word edges.

Quantitative evidence was provided for two important hypotheses of the paradigm uniformity analysis. Study 1 showed that liaison consonants are variable in their prosodic attachment only if they are absent from the corresponding citation form, thus making a clear argument for the role of paradigm uniformity with citation forms. Study 2 provided evidence for the phonetic mechanism that underlies the paradigm uniformity analysis of the segmental variability of liaison in Quebec French. Affrication of /t/ was found to correlate with a higher likelihood of high-vowel reduction in Quebec French, for both liaison and stable word-final consonants. This result is in line with the hypothesis that affrication at word boundaries has consequences for uniformity with the citation forms of both Word1 (through a change affecting word-final /t/) and Word2 (through a change affecting word-initial /i/). This hypothesis was key to explain why liaison /t/ is less likely to affricate than word-initial /t/ before /i/.

There are two ways in which the paradigm uniformity analysis of French liaison could be further developed and evaluated. First, it should be extended to account for patterns of segmental realization that involve continuous phonetic representations. This will require moving away from symbolic constraint-based grammars and adopting phonetic constraint-based grammars instead (see Flemming 2001). Second, the analysis presented in this paper mainly focused on deriving the variable realization of French liaison. But a comprehensive model of French liaison should also include the factors that have been reported to affect the rate of liaison. Section 7.4 has sketched how some of these effects could be captured by indexing output-output faithfulness constraints to properties that are relevant in speech production, according to the production planning hypothesis of external sandhi (Kilbourn-Ceron 2017). Future work should test further the predictions of this approach.