2.2 Phonological factors

The corpus results confirmed the generalisation that rising sonority clusters typically condition C forms of the prepositions. Most words beginning with steeply rising clusters such as [pr] showed CV rates of less than 1%, although there was considerable lexical variation in this group as well (see §2.3 below). We also confirmed the generalisation that CV forms of the prepositions [s] and [v] are used to avoid clusters of identical or similar consonants – [so] is used before sibilant-initial clusters (e.g. [sə stərikˈom] ‘with an old man’), and [vo] is used before the labial continuants [v] and [f] (e.g. [va frˈanʦii] ‘in France’). We did not find evidence that [ko] is used more than [k] before the dorsal segments [k], [g] and [x], in line with Matushansky (Reference Matushansky2002) and Steriopolo (Reference Steriopolo, Compton, Goledzinowska and Savchenko2007) (but contraTimberlake Reference Timberlake2004).

The proportion of the CV forms of [s] before sibilants was high, but not 100%. While all sibilants show a strong preference for the CV preposition [so], this preference is stronger when the word starts with [s] (mean proportion of the CV form: 94%) than when it starts with [ʂ] (86%) or [z] (88%). The difference between CV rate in [s] and in the other sibilants is significant (p<0·05 in both cases, Wilcoxon test). This suggests that the strength of the OCP effect depends on the degree of similarity between the preposition and the following consonant (see §3.2.1 below for similar results and discussion). The strong but non-categorical preference for the CV form before sibilants is also corroborated in our nonce-word experiment (§4). Thus the alternation is gradient even before sibilants: while there is a strong preference for [so] before [svinʦˈa], occasionally a speaker will produce [s svinʦˈa] ‘from lead’.

We also found that the OCP effect is more extensive than previously thought: it applies to more consonants than has been reported, and to non-adjacent consonants within the same cluster. Figure 1a shows that among the words that robustly occur with the CV form [so], this CV form is more strongly favoured when the second consonant of the word-initial cluster is a sibilant, as in the lemma [vzˈor] ‘gaze’: the median proportion of CV forms is 90% when the second consonant is a sibilant, compared to 58% when it is not. The preposition [v/vo] behaves in a similar way (Fig. 1b): when the second consonant of the following word is a labial continuant, there is a higher proportion of CV forms.Footnote ⁴

Figure 1

Effect of similarity between the preposition and the consonants in the word-initial cluster. Each row in the plot represents a lemma. A lemma can appear with each of the prepositions (a) [s/so] and (b) [v/vo] in four different forms (two cases, singular, plural); all relevant forms which met our inclusion criteria are shown in the plot. Error bars indicate 95% binomial confidence intervals. The category ‘both’ includes cases in which one of the consonants in the word-initial cluster has the same manner and place of articulation as the preposition; in ‘place’, only the place of articulation is shared; and in ‘none’ neither place nor manner are shared. The dashed line represents the median CV rate within each category. Note that for [v/vo] ‘both’ and ‘place’ both have a higher median than ‘none’, whereas for [s/so] ‘place’ patterns with ‘none’, and only ‘both’ words show a higher CV rate. Glosses for the forms in Figs 1–4 can be found in Appendix B.

Moreover, we found that the OCP holds not only between adjacent consonants that share place and manner, but also between homorganic consonants that differ in manner. Words with a labial consonant anywhere in their initial cluster, regardless of its manner of articulation, favour the CV form [vo] more than words that do not have a labial consonant (Fig. 1b). For example, a word like [mrˈak] ‘darkness’, which starts with the labial [m], will be more likely than a word like [nrˈaf] ‘character’ to appear with [vo], all other things being equal.

By contrast, when the preposition [s] is followed by a coronal consonant, it only dissimilates from it when that consonant is a sibilant: we did not find evidence that it dissimilates from [t], [d] or [n]. This sensitivity to manner of articulation in coronals but not in labials mirrors the situation in Arabic and Muna: co-occurrence constraints in these languages distinguish subclasses of coronals, but not labials or dorsals, possibly because coronals are perceived as more heterogeneous than consonants in other places of articulation (Coetzee & Pater Reference Coetzee and Pater2008). Since Russian does not have a non-fricative monoconsonantal coronal preposition (e.g. [t] or [n]), there is no way to determine whether the dissimilation pressure applies to coronals with identical manner of articulation, as in Arabic or Muna, or specifically to sibilants, as in Chol (Gallagher & Coon Reference Gallagher and Coon2009).

We did not find similarity-avoidance effects after the dorsal preposition [k], not even when the following word began with a [k]. Russian differs in this respect from languages with co-occurrence restrictions in roots, which tend to apply regardless of place of articulation (Frisch et al. Reference Frisch, Pierrehumbert and Broe2004, Coetzee & Pater Reference Coetzee and Pater2008). Thus dissimilation pressure is not a general property of monoconsonantal prepositions, but is specific to the prepositions [v] and [s]; whether this is for phonological reasons or due to lexical variation among the prepositions is hard to tell.

To ascertain that the differential OCP effects were statistically significant, we fitted mixed-effects logistic regression models to the set of words that robustly take the CV forms, using the R package lme4 (Bates et al. Reference Bates, Maechler and Bolker2012). We fitted two separate models, one for [v] and one for [s]. Both models had a predictor for the similarity between the preposition and the following cluster, with one of the following three levels: no features in common (baseline level), shared major place, or shared place and manner.Footnote ⁵ We included a by-lemma random intercept in the models. The standard errors of the estimates were calculated using bootstrapping as implemented in the R library boot (Davison & Hinkley Reference Davison and Hinkley1997, Canty & Ripley Reference Canty and Ripley2012). In each iteration of the bootstrap procedure, a random subset of the words was sampled with replacement (i.e. the same word was occasionally included more than once). The logistic regression model was then fitted to this subset of the words. This process was repeated 10,000 times, allowing us to estimate the distribution of the regression coefficients. Visual examination confirmed that the bootstrapped regression coefficients were normally distributed, justifying the use of the t distribution to calculate the significance levels of the regression coefficients. Statistical models confirm the graphical impression (Table II). In the case of [s], similarity in both manner and place of articulation increased the likelihood of the CV form, but similarity in place only did not. In the case of [v], similarity in place of articulation was enough to increase the likelihood of the CV form. Manner similarity did not give an additional boost to the CV form for [v].

Table II

Similarity avoidance in words from the Russian National Corpus that are compatible with CV prepositions: logistic regression results. We used treatment coding of the categorical predictor, with the reference level being the absence of any shared feature between the preposition and the word-initial cluster.

2.3 Lexical factors

Although a number of phonological properties can be used to predict the form of the preposition, the alternation cannot be reduced to phonological factors alone. For example, (8) shows two words that start with the same cluster. The two CV rates are unlikely to be derived from the same underlying distribution for [mn]-initial words: the difference between the rows is highly significant (p<10−¹⁵, Fisher's exact test).

1. (8)

   

We discuss four properties of the lexical variation in this section. First, we identify what appears to be a systematic register effect (§2.3.1). §2.3.2 discusses lexical variation of a more arbitrary character, including cases in which the exact same phonological form behaves differently depending on its meaning (homonyms). In §2.3.3, we discuss the role of morphological structure: some morphemes show different CV rates depending on morphosyntactic context and morphological structure. Finally, §2.3.4 describes cases of idiosyncratic CV preference which are limited to the context of a specific idiom.

2.4 Sonority and lexical idiosyncrasy in monosyllabic yer stems

Vowel–zero alternations in Russian prepositions are sometimes analysed as a special case of a more general rule known as yer deletion (Lightner Reference Lightner1965, Reference Lightner1972, Halle Reference Halle1973, Pesetsky Reference Pesetsky1979, Melvold Reference Melvold1989, Farina Reference Farina1991, Yearley Reference Yearley1995, and many others). In §2.4.1 we review the aspects of the rule that are relevant to the prepositional alternations, and the predictions of the yer-deletion account for monosyllabic words containing a yer vowel. We contrast the yer-deletion account with an alternative account, which attributes the behaviour of monosyllabic yer words to phonotactic constraints and lexical variation. We then present corpus data supporting the phonotactics-plus-lexical-variation account (§2.4.2).

3.3 Statistical analysis

We analysed the behaviour of the [s]/[so] alternation before [v]-initial clusters (n=420), using a logistic regression model. The outcome variable was the proportion of the CV form. Based on our exploratory investigation, we included two phonological variables of interest: stress position (word-initial or elsewhere) and the type of consonant following [v] ([vR], [vS] or [vK]). We included two phonological control variables: the number of vowels in the word (which is identical to the number of syllables), and the number of consonants in the word-initial cluster (e.g. [fsV] compared to [fstV]).Footnote ¹¹ In addition, we included three non-phonological variables: case (instrumental or genitive), number (singular or plural) and log-transformed lemma frequency (based on the Russian National Corpus).

The results of the regression are shown in Table III. Factors that increased the likelihood of the CV form appear with a positive regression coefficient. We found that both of the main phonological predictors of interest had a significant effect on the alternation. Compared to the [vK] base level, [vS] clusters conditioned the CV form more often. This non-adjacent OCP effect was extremely robust (t=6·25, p<0·001), confirming the qualitative pattern shown in Fig. 8 above. The CV form was also less common before [vR] than [vK] clusters (t=−2·17, p=0·03), consistent with a sonority-slope effect, whereby the C form is discouraged before falling sonority clusters.

Table III

Logistic regression results for the [s]/[so] alternation before [v]-initial clusters in the Yandex corpus. The baseline level is [vK]; predictors with positive regression coe.cients increase the likelihood of the CV form [so].

Non-initial stress decreased the likelihood of the CV form. This effect was again highly significant (t=−2·94, p=0·003). We also found that longer words were less likely to condition the CV form (t=−3·44, p<0·001). This effect is partially correlated with the effect of stress, since short words are naturally more likely to have stress on their first syllable than long words; however, follow-up stepwise regression analyses suggest that the two effects are independent. Stress position was also correlated with cluster size in our sample: words beginning with longer clusters were more likely to be stress-initial (in line with Ryan to appear). Again, we verified that the effect of stress persisted after controlling for cluster size. Log lemma frequency, case, number and cluster size did not reach significance.

In a follow-up analysis, we divided the class of sonorants into nasals ([m n]) and liquids ([l r]). This analysis did not reveal any difference between the two types of sonorants (t=0·1, n.s.). The absence of a difference between the two types of sonorants may be due to the small overall effect of sonority slope: even collapsing across the two classes of sonorants it was only barely significant. Alternatively, the lack of significant difference may indicate that speakers only distinguish obstruents from sonorants and do not make finer distinctions within the class of sonorants, as has been suggested for Slavic (Bethin Reference Bethin1992 and others).

In conclusion, the Yandex corpus study provides more quantitatively robust evidence for the phonological factors that contribute to the Russian prepositional alternation; see Table I for an overview of the results of the two corpus studies.

4.3 Summary

The experiment confirmed that the CV preposition [so] was more acceptable when the stress was on the initial syllable, when the sonority slope in the initial cluster was decreasing, and when there was a sibilant anywhere in the initial cluster (OCP). The OCP effect was stronger when the sibilant was the first consonant in the cluster than when it was the second one. For the most part, the constraints interact in a cumulative way: while the CV form is favoured in sibilant-initial clusters across the board, this tendency is even stronger when the OCP constraint is reinforced by initial stress and falling sonority.

5.1 Deletion or epenthesis?

Vowel–zero alternations can be analysed as either deletion or epenthesis. There are several arguments for both analyses in the case of the alternating Russian prepositions. On the epenthesis side, it has been observed that all Russian prepositions have vowel-final variants ([bˈes∼bˈezə] ‘without’, [ʧˈeris∼ʧˈerizə] ‘through’, [pˈerit∼pˈeridə] ‘before’, etc. – see Matushansky Reference Matushansky2002, Gribanova Reference Gribanova, Zybatow, Junghanns, Lenertová and Biskup2009a ).Footnote ¹⁶ The alternating vowels are always [+back], unlike yer vowels in lexical morphemes, which can be either back or front (see §2.4.1 for a discussion of yer vowels). This predictable quality would follow from an epenthetic account. Moreover, Gribanova (Reference Gribanova2008: n. 5) notes that prepositions without alternations, such as [po] and [do], can appear phrase-finally, whereas C prepositions cannot. Yer words always surface with a vowel when no other vowel is available (Yearley Reference Yearley1995, Gouskova Reference Gouskova2012), so if prepositions are part of the same deletion pattern as yers, they ought to surface to satisfy the requirement that all phonological words must have a vowel in Russian. An epenthetic account captures the observation that vowels tend to appear in prepositions only when they are needed to break up illicit clusters. Indeed, Pająk & Baković (Reference Pająk and Baković2010) analyse analogous alternations in Polish prepositions as epenthesis. Hayes (Reference Hayes2009: 235ff) suggests that Polish vowel–zero alternations in other contexts are more compatible with an epenthesis analysis than with a deletion analysis, because only one vowel, [ε], alternates productively (Czaykowska-Higgins Reference Czaykowska-Higgins1988, Yearley Reference Yearley1995).

There are also arguments for deletion. In the Moscow dialect of Russian, the alternating vowel in the prepositions is [ə] or [a], and vowels of both qualities are typologically common epenthetic vowels (Kitto & de Lacy 1999, Hall Reference Hall2011). In dialects with other vowel-reduction patterns, however, the vowel may surface as [o], and this is a far less common epenthetic vowel, possibly unattested (Hall Reference Hall2011). Even in Moscow Russian, prepositions have [o] forms in fixed expressions with preposition stress, such as [sˈo svitu] ‘from the world’ and [vˈo pəli] ‘in a field’ (Zaliznjak Reference Zaliznjak1985, Ukiah Reference Ukiah1998).

Our study presents another argument for deletion: we found that the CV forms of the prepositions are more likely to show up as [a] than [ə] (both in the Yandex study and in the experiment). This is easy to analyse in a deletion account: assuming iambic footing (σ; Halle & Vergnaud Reference Halle and Vergnaud1987, Alderete Reference Alderete1999, Crosswhite Reference Crosswhite1999), the vowel is retained in a prominent footed position: e.g. /so vdˈoxa/→[(sa vdˈo)xə]. It is deleted to improve the alignment of the lexical word and the phonological word: e.g. /so vdoveʦa/→[(s vdafʦˈa)]. Alternatively, the more prominent vowel [a] is less likely to delete than schwa, a typologically common pattern (Steriade Reference Steriade2001, Gouskova Reference Gouskova2003, Howe & Pulleyblank Reference Howe and Pulleyblank2004). The epenthesis analysis could assume something like foot binarity as the driver of epenthesis, but then it would have to explain why this vowel shows up only in prepositions.

Another argument for deletion comes from the pattern of lexical variation in our corpus: conservative contexts, such as idioms and ecclesiastical words, tend to favour the CV form of the prepositions rather than the C form. In fact, we were unable to find words that take the C form less than would be predicted by their phonological forms (e.g. a sibilant-initial word which only appears with [s] and never with [so]). The register effect fits with the situation in other languages if the alternation involves deletion: in this analysis, conservative registers are more faithful to the historical forms, whereas informal registers tend towards more deletion (see Coetzee & Kawahara Reference Coetzee and Kawahara2013, inter alia).

In summary, while we do not have a serious quarrel with the epenthetic analysis, the deletion analysis is simpler and more plausible historically and typologically, and we adopt it in what follows.

5.2 The constraints

This section presents the constraints we used to analyse the alternation. The syntactic distribution of prepositions suggests that they are clitics – they can attach to nouns, adjectives and adverbs (see Gouskova Reference Gouskova2010 and Padgett Reference Padgett2012 for a discussion of the phonological properties of prepositions, and Sekerina Reference Sekerina1997 and Fanselow & Ćavar Reference Fanselow, Ćavar and Alexiadou2002 on the syntactic behaviour of prepositions in scrambling). In our analysis, clitichood is the reason why vowels delete in these prepositions: there is a requirement for the lexical word edge to coincide with the phonological word edge, discouraging word-internal syllabic prosodic clitics. We formalise this requirement as an alignment constraint, after Selkirk (Reference Selkirk1995), as in (19).

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Align conflicts with Max(V), the familiar correspondence-theoretic faithfulness constraint. Vowels do not delete in Russian prepositions such as [po] ‘along’, [za] ‘behind’ and [u] ‘by’, so Align must have an effect in the grammar only when the syllable causing the misalignment contains the exponent of the prepositions [so], [vo] and [ko] (following the locality convention for indexed constraints introduced in Pater Reference Pater, Bateman, O'Keefe, Reilly and Werle2007). We assume that for non-alternating prepositions, Max(V) outweighs Align (see §6.2).

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Deletion is blocked by several markedness constraints on the resulting consonant clusters. One of these constraints is the Sonority Sequencing Principle (SSP). We will assume a gradient SSP cast in Harmonic Grammar, which assigns a violation mark of 0 to the best sequence of a stop followed by a glide, a mark of 1 to fricative–glide and stop–rhotic sequences, a mark of 5 to clusters of stops with stops or nasals with nasals (e.g. [mn] or the fake geminate [nn]), and so on. The worst sequence gets a violation score of 10, as shown in (21c). The sonority scale from (7) is repeated in (21b).

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To capture the fact that only cluster-initial words condition the CV prepositions, we define the blanket constraint (22) against triconsonantal clusters, which is blind to the particular phonological properties of the cluster. As discussed in detail in §6.2, indexing this constraint to individual morphemes allows the best modelling of the lexical variation, which is to some extent independent of the phonology of the cluster.

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We now turn to similarity avoidance. Our constraints need to capture the two facts in (23).

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To account for fact (a), we posit a general OCP constraint on sibilants within the same cluster, regardless of whether they are adjacent or separated by a consonant.

1. (24)

   

We account for fact (b) by introducing a specific constraint against adjacent sibilants, defined in (25). The dispreference for adjacent sibilants followed by a consonant (e.g. [sst]) is extremely strong. Preliminary MaxEnt modelling revealed that this preference is not adequately captured by the additive effects of *#CCC and a general constraint against two adjacent sibilants: either the dispreference is underestimated, or the general constraint against two adjacent sibilants is weighted very high, resulting in the undesirable penalisation of CCV sequences such as [s+sa]. Since existing MaxEnt models do not learn multiplicative (superadditive) interaction terms, as would be necessary to obtain a dispreference for [sst] which is stronger than the combined dispreference for [ss] and [CCC], we manually combined the two conditions into a single constraint.

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Since the experiment did not include the labial fricative preposition [v], we have only defined sibilant OCP constraints. A full set of constraints would have to account for the somewhat different behaviour of labial OCP discussed in §2.2. Likewise, we do not introduce a gradient OCP constraint penalising [s]+sibilant sequences in proportion to the featural overlap between [s] and that sibilant (see §2.2 and §3.2.1), since we only had one type of sibilant in our experiment ([ʂ]).

Finally, we attribute the effect of stress to the constraint Parse-σ, which is violated by unfooted syllables. We explain the role of this constraint in the analysis in the following section.

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5.3 A MaxEnt analysis of the nonce-word ratings

A MaxEnt grammar works as follows. Constraints have positive numerical weights rather than rankings. Suppose there are m constraints and n candidates. The harmony H _j of the jth candidate is determined by summing its violations for each constraint times the weight of the respective constraint, as in Harmonic Grammar (Legendre et al. Reference Legendre, Miyata and Smolensky1990, Goldwater & Johnson Reference Goldwater, Johnson, Spenador, Eriksson and Dahl2003, Smolensky & Legendre Reference Smolensky and Legendre2006, Pater et al. Reference Pater, Potts and Bhatt2007, Hayes & Wilson Reference Hayes and Wilson2008). Formally, if w_i is the weight of the ith constraint and v_ji is the number of times that candidate j violates constraint i, then we have (27).

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The probability of candidate j is then calculated as the exponent of H _j , normalised by the sum of the exponents of all harmony scores.

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We fitted the constraint weights to the observed frequencies of outputs with the C and CV forms from our experiment, using the MaxEnt Grammar Tool.Footnote ¹⁷ The weights are shown in Table V, arranged from highest to lowest.

Table V

MaxEnt constraint weights for experiment results.

The rest of this section demonstrates how the resulting MaxEnt grammar derives the patterns we identified in the results of the experiment. We start with the simplest case, the near-categorical deletion in words that start with a single consonant. As shown in (29), Align favours deletion in all prepositions: [sa kˈibəm] violates Align once, so its harmony score is the weight of Align (6·24) times −1 for the violation. Max is weighted at 0 for /so/, so it cannot block deletion. The MaxEnt grammar in Table V predicts the input /so kˈib-om/ to map to [s kˈibəm] 99·8% of the time (calculated as p₁=e ⁰/(e ⁰+e−^6·24)=0·998), compared to the 99% we observed in the experiment.

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When deletion yields a cluster that violates several of the markedness constraints, the predicted outcome varies, depending on the severity of the violations of the cluster constraints. In /so ʂtˈib-om/ (see (30)), the resulting cluster violates *#CCC, the constraint against adjacent sibilants *SimC-C and *s(C)S, and it has a relatively poor sonority profile. The harmony of the deletion candidate [s ʂtˈibəm] is a summation of its performance on *#CCC, the constraints on sibilants and the SSP, which it violates six times. Thus, even though none of these constraints are weighted more than Align, their cumulative action makes deletion a lot less probable. Deletion is predicted to be blocked 87·2% of the time. In our experiment, people preferred the CV form 80% of the time.

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A slightly higher sonority rise makes deletion less likely: in /so ʂrˈib-om/, deletion is predicted only 72% of the time. This is shown in (31).

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A sufficiently bad sonority profile will make deletion less likely even in words that have no sibilants near the preposition. Deleting the preposition's vowel in /so rdˈib-om/ results in a #CCC cluster that violates the SSP nine times, which in tandem with the *#CCC violation is sufficient to override Align 58% of the time.

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We capture the stress effect through Parse-σ. Deletion is more likely when the vowel of the preposition is reduced to [ə], which we take to be due to its unfooted status (assuming iambic footing for Russian; see Halle & Vergnaud Reference Halle and Vergnaud1987, Alderete Reference Alderete1999, Crosswhite Reference Crosswhite1999, Gouskova Reference Gouskova2010, though cf. Revithiadou Reference Revithiadou1999, Bethin Reference Bethin2006). As shown in (33), the retained vowel cannot be footed in [sə (ʂribˈom)], so its deletion is more favoured in comparison with the footed vowel in [(sa ʂrˈi)bəm] in (31).

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In clusters that have non-adjacent sibilants in the potential #CCC cluster, deletion is only weakly encouraged, since the weight of *s(C)S is smaller than that of *SimC-C. The violation scores of the two candidates for the input /so xsib-ˈom/ are very close (see (34)), and the predicted frequencies (60% and 40%) match our experimental results.

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Finally, we did not include /so sV…/ wugs in our experiment, because they pattern virtually categorically: they surface with the C form of the preposition. The result in (35) is generated in the MaxEnt grammar.

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To sum up, this analysis allows us to capture the cumulative effects of the OCP, stress and sonority sequencing through constraint weighting. Even though the weight of Align exceeds that of any other constraint here, the lower-weighted constraints can override its preference for deletion. The cumulative effect of these constraints is captured directly through the summing of their weights, and the frequencies of the outputs we got in the experiment are matched fairly closely.

Finally, we address an alternative analysis that we rejected for Russian. In their analysis of a similar pattern in Polish, Pająk & Baković argue that the CV preposition surfaces whenever the alternative is to assimilate sibilants or labials, which would result in a violation of the constraint they call NoGem/NVA ‘no non-vowel-adjacent geminates’ (2010: 651). The evidence for this analysis is that the alternative to variable C∼CV alternation in Polish is voicing and coronal place assimilation, which applies in [z+sV] clusters but not in [z+sCV] clusters. Thus, either assimilation fails to apply or the vowel shows up to break up the clusters – a kind of conspiracy to avoid preconsonantal geminates. Russian also has variable coronal place assimilation, but this analysis would not work for the language.Footnote ¹⁸ The problem is that Russian vowels show up even in clusters that cannot assimilate completely to make a geminate: labial–labial–C clusters such as [vmn] and [fpr] are also avoided (recall Fig. 1). There is also an interaction between non-adjacent sibilants, which cannot form a geminate across an intervening consonant (even if they could be argued to be articulatorily local, as in Gafos Reference Gafos1999). Russian also has a preposition which Polish lacks, [k], which exhibits sonority effects but not antigemination (e.g. /ko grob-u/→[g grabˈu] ‘towards a coffin’). While the place difference between dorsal stops and other consonants is essentially stipulated in our analysis, it is simply not the case in Russian that geminates before consonants are avoided across the board, or that preposition vowels appear only to avoid preconsonantal geminates.

Pająk & Baković (Reference Pająk and Baković2010) and Baković (Reference Baković2005) do shed light on a feature of the Russian alternation that we do not analyse in detail, however: the gradient similarity effect among sibilants (see Fig. 6). The direction of the effect suggests that faithfulness is at play: assuming that there is at least some assimilation between the preposition consonant and the following sibilant, deletion is less likely when it implies having to make more changes to the preposition's consonant. It is additive in the way we predict: /so ʐriʦom/ is less likely to have deletion than /so ʂvedov/ because [z/ʐ ʐriʦˈom] requires more featural unfaithfulness than [s/ʂ ʂvˈedəf]. We do not analyse this directly, because our experiment tested only one sibilant, but the gradient similarity effect can be captured through the interaction of faithfulness to the features of the preposition's sibilant with the other markedness constraints violated by the resulting cluster.

5.4 Complex conditioning contexts for alternations as gang effects

The experimental results clearly show that the probability of the CV form is jointly determined by multiple constraints simultaneously, rather than by the highest-ranked one. Even the near-categorical OCP constraint against adjacent sibilants does not overshadow the weaker sonority-sequencing constraint: sibilant-initial clusters are more likely to occur with the CV preposition if they have a relatively bad sonority profile ([ʂt] occurs with CV more often than [ʂr] does). Similarly, stress on the following syllable makes a CV preposition slightly more likely across the board, on top of the phonotactic constraints related to the cluster.

Casting the analysis in a weighted-constraints theory allows us to capture these additive effects, while keeping the constraints themselves relatively simple compared to previous analyses in standard OT. For example, to explain why the OCP applies only to [ssC] clusters rather than [ssV], Steriopolo (Reference Steriopolo, Compton, Goledzinowska and Savchenko2007) assumes that preconsonantal sibilants are unsyllabified appendices rather than syllable onsets – a structure often posited for Slavic (Bethin Reference Bethin1992, Yearley Reference Yearley1995, among others). The constraint that blocks deletion in Steriopolo's analysis is the OCP locally conjoined with the constraint against unsyllabified consonants. This structural definition of the context for the OCP does not explain our findings, however. We found an OCP effect even with sibilant–liquid clusters such as [ʂr], and these are usually assumed to be tautosyllabic. The OCP applies across an intervening consonant (as in [sa msˈibəm]), where the second sibilant is syllabified with the following vowel. Our solution to this analytic problem is to keep the OCP constraint itself relatively simple, deriving the complex conditioning from its interaction with the constraint against three-consonant clusters. Neither three-consonant clusters nor OCP violations by themselves are sufficient to condition a high rate of CV prepositions; the effect arises through cumulative action. Such ‘gang’ effects have been observed in other gradient phenomena (Keller Reference Keller2000, Jäger & Rosenbach Reference Jäger and Rosenbach2006, Hayes & Wilson Reference Hayes and Wilson2008, Pater Reference Pater2009, Potts et al. Reference Potts, Pater, Jesney, Bhatt and Becker2010).

As Boersma & Hayes (Reference Boersma and Hayes2001) point out, much of the success in modelling variation in constraint-based theories depends on the choice of constraints. A detailed comparison of constraint-based theories of variation would require comparing analyses that use different constraint sets and definitions, which would take us too far afield. We want to make one point that bears on the issue of how to analyse the stress effect in particular. In principle, gang effects do not require constraint weighting: some limited gang effects are possible in Stochastic OT (Boersma Reference Boersma1997, Boersma & Hayes Reference Boersma and Hayes2001), and standard OT can capture certain types of gang effects through local conjunction (Smolensky Reference Smolensky1995). Local conjunction is a way to allow two low-ranked constraints to override a higher-ranked constraint when they are violated simultaneously: for example, in some languages, word-final consonants are allowed and voiced consonants are allowed, but word-final consonants cannot be voiced. Ito & Mester (Reference Ito, Mester, Féry and van de Vijver2003) capture this by conjoining NoCoda and *VoicedObstruent in the domain of a segment; the resulting constraint is violated by segments that violate both constraints, and the conjoined constraint can compel unfaithful mappings that neither of the individual markedness constraints can compel. To extend this approach to the stress effect we found, one could conjoin Align with Parse-σ: the resulting constraint would be violated only by a syllable that is unfooted and causes misalignment of lexical and prosodic word edges, as in [sə (ʂribˈom)]. But conjunction would not work with other possible accounts of the stress effect, such as a licensing-by-cue analysis (Steriade Reference Steriade2001). The idea behind such an analysis is that schwa is more likely to delete than [a] because its deletion is less noticeable.Footnote ¹⁹ Implementing this would require conjoining a constraint that specially protects [a] but not [ə] (Max[a]) with each of the markedness constraints that disfavour deletion (*#CCC, *s(C)S, and so on). Recall tableaux (31) and (33): the goal is to make deletion slightly worse when it involves [a] rather than [ə], which means that Max[a] would work in tandem with other constraints that disfavour deletion – all of them markedness constraints. The problem is that conjunction of Max with markedness is impossible: these constraints do not share a locus of violation (Moreton & Smolensky Reference Moreton and Smolensky2002). In a weighted-constraints theory, on the other hand, Max[a] can interact with markedness constraints through cumulativity, so this analysis can be implemented. In (36), we show the weights of the constraints and the harmony scores for two inputs that differ in stress position. The crucial interaction is in (36b), where the weight of Max[a] is combined with that of the rest of the markedness constraints to make deletion less likely in pretonic position than in a position with greater reduction.

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Analysed in this way, the Russian stress effect represents a possible gang effect between markedness and faithfulness, in addition to markedness-markedness (Pater Reference Pater2009, Potts et al. Reference Potts, Pater, Jesney, Bhatt and Becker2010) and faithfulness-faithfulness gang effects (Farris-Trimble Reference Farris-Trimble2008).

While the additive approach generally allows us to obtain a good fit to the experimental results, it does not suffice in the case of the near-categorical OCP constraint against adjacent sibilants in clusters. As mentioned in §5.2, modelling this phenomenon as an additive effect of *#CCC and a general OCP constraint against adjacent sibilants (*SS) would require assigning a very large weight to *SS, thereby incorrectly predicting dissimilation in simple onsets (e.g. [s+sa]). To get around this problem, we posited the constraint *SimC-C, which is essentially a conjoined version of *SS and *#CCC. A potential alternative to hand-crafting conjoined constraints such as this one is expanding the expressive power of the MaxEnt model by allowing it to learn multiplicative interactions between constraints, so that the joint effect of two constraints is allowed to be larger than the sum of their individual effects.

6.1 Introducing scaled constraints

There are several approaches to lexical variation in Optimality Theory and related frameworks. In cophonology theory (Inkelas et al. Reference Inkelas, Orgun and Zoll1996, Orgun Reference Orgun1996, Anttila Reference Anttila2002, Inkelas & Zoll Reference Inkelas and Zoll2007), lexical variation is analysed by assigning different constraint rankings to different morphemes. By contrast, the indexed-constraints approach (Benua Reference Benua1997, Itô & Mester Reference Itô, Mester and Tsujimura1999, Pater 2006) assumes a single constraint ranking for the entire language, and captures lexical variation by positing two or more instantiations of the same constraint, each indexed to a different set of morphemes. When applied to Harmonic Grammar or a maximum entropy grammar, this approach translates into morpheme-specific constraint weights. Finally, Coetzee & Pater (Reference Coetzee, Pater, Goldsmith, Riggle and Yu2011) and Coetzee & Kawahara (Reference Coetzee and Kawahara2013) implement morpheme-specific weights in Harmonic Grammar using scaling factors. When a faithfulness constraint is evaluated on a given word, the weight of the constraint is adjusted by an additive scaling factor, which is determined by extragrammatical properties of the word (e.g. its frequency). In the scaling factors approach, the constraint is not multiply instantiated in the grammar; instead, its weight varies, depending on the word being evaluated.

We adopt the scaling factors approach, but extend it in three ways. First, Coetzee & Kawahara (Reference Coetzee and Kawahara2013) assume that all faithfulness constraints are scaled to the same degree by a morpheme's scaling factor; we depart from this assumption, and instead allow the scaling factors to vary by constraint. Second, we assume that scaling factors can apply both to markedness and faithfulness constraints (Flack Reference Flack2007, Gouskova Reference Gouskova2007, Pater Reference Pater, Bateman, O'Keefe, Reilly and Werle2007). Finally, we introduce scaling factors that are lexically listed and vary idiosyncratically from morpheme to morpheme, in addition to scaling factors that reflect properties such as frequency and register. Using the notation introduced in §5.3, if s_ji is the sum of all scaling factors relevant to evaluating constraint i with respect to candidate j, including frequency, register and lexically specific factors, then the harmony of candidate j is given by (37).

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While our modified constraint-scaling approach is in some respects a notational variant of constraint indexing, we prefer it for two reasons. First, a constraint-scaling mechanism is independently needed to capture the register effect we have observed. Second, as we show elsewhere, constraint weights are determined not only by the individual morpheme immediately following the preposition, but also by the morphological structure of the derived word that the morpheme is part of, which is not necessarily listed in the lexicon. It is not obvious how this would be handled using lexical indexing. A flexible constraint-scaling factor approach can straightforwardly predict the CV rate of the derived word from the stem and its suffixes (Gouskova & Linzen in preparation).

6.2 A scaled-constraints analysis

The three prepositions [k/ko], [s/so] and [v/vo] are exceptional in that other prepositions which end in a vowel, such as [na] and [po], never alternate with monoconsonantal forms (*[n] or *[p]). In our analysis, the constraint that needs to be weighted differently for these three prepositions is Max(V), which blocks the deletion of the vowel. By default, the weight of Max(V) exceeds that of Align enough to never allow vowel–zero alternations, which achieves the categorical resistance to deletion in most prepositions. Under the scaling factors approach, the alternating prepositions need to be assigned a negative scaling factor, which would bring the weight of Max(V) down enough to enable Align to significant impact the form of the preposition. Indeed, in the MaxEnt model fit shown in §5.3, Max(V) is the lowest-weighted constraint. Assuming that the language-wide weight of Max(V) is very high, say 25, the scaling factor for the prepositions should be s _k/s/v =−25. Of course, each of the prepositions may have a different scaling factor, indicating a lower overall tendency for deletion in e.g. [s] than in [k].Footnote ²⁰

Moving on to the variation among the morphemes following the three prepositions, recall that words that can condition the CV form of the prepositions are overwhelmingly cluster-initial. At the same time, the specific word-initial cluster is not restricted to any phonologically defined subset of clusters (e.g. falling sonority clusters only). This suggests that the constraint that should be assigned morpheme-specific weights is *#CCC, which encourages the retention of the vowel in the preposition when it is followed by a cluster-initial morpheme. We assume that the nonce-word experiment reflects speakers' phonological knowledge about regular lexical items; the basic weight of *#CCC should therefore be the weight obtained from our MaxEnt model, namely 4·26. Lexical items that show a higher CV preference than would be expected from their phonological properties are assigned positive scaling factors, such that the weight of *#CCC is higher than the default for these words. For instance, the contrast between the near-categorical deletion of the vowel in [s dvˈigətilʲə] ‘from the engine’ and the tendency to retain the vowel in [sə dvarˈa] ‘from the yard’ will be captured by assigning [dvˈor] a positive scaling factor for *#CCC.

As mentioned above, the gradient variation in CV rates between lexical items does not lend itself to a dichotomous distinction between regular items and exceptions: in principle, each lexical item may require a different scaling factor for *#CCC, although there may well be some subregularities (Zuraw Reference Zuraw2000, Albright & Hayes Reference Albright and Hayes2003). Table VI gives a rough estimate of the range of scaling factors required to derive the range of CV rates in the corpus (abstracting away from the words' phonological shape, for purposes of illustration).

Table VI

A scaling factors approach to gradient exceptionality.

The effect of scaling factors is illustrated in (38) for [dvˈor], under the assumption that s _dvor =2·98.

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Even when a morpheme conditions idiosyncratic CV rates, the distribution of each of the specific prepositions is affected by the phonological constraints we have identified. For instance, [dvˈor] shows a non-adjacent OCP effect: the mean CV rate for [s] and [k] is 62%, whereas for the preposition [v], which is identical to one of the consonants in the word-initial cluster, the CV rate is an almost categorical 96%. The interaction with language-wide phonological constraints suggests that learners do not simply store the deletion rate for each morpheme in their lexicon (as proposed, for example, by Guy Reference Guy2007), but rather consider both language-wide and lexically specific constraint weights in the same additive weighting. The greater preference of [dvˈor] for the CV form of [v], compared to [s] and [k], falls out naturally from the combination of the scaled weight of *#CCC and the labial dissimilation constraint *v(C)Lab. There is no need to index any other constraint to [dvˈor] to derive this behaviour, as shown in (39).

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Tying the lexical variation to *#CCC makes a potential prediction for other contexts: if another phonological rule involves the prohibition on #CCC clusters, then morphemes indexed to the constraint should exhibit variation proportional to their scaling factor.Footnote ²¹ Word-initial CCC clusters can be created in several ways: through morpheme concatenation (/C+CC …/), deletion in the preposition (/CV+CC/→#CCC) or deletion of a vowel morpheme-internally between three consonants (/CVCC/→CCC … or /CCVC/→CCC …). The latter kind of deletion is not found in Russian nouns – Gouskova & Becker (2012) show that CVCC words never display yer deletion in Russian, and CCVC words resist it as well. Since only #CCV … words condition the prepositional alternation variably, the lack of such words in the yer sublexicon makes the prediction impossible to test.

6.3 Register effects

Many of the morphemes we found that showed a CV preference were ecclesiastical words (see §2.3.1). An overall register bias of this sort is straightforwardly analysed using the scaling factors mechanism: a register-wide scaling factor increases the weight of faithfulness to the underlying vowel of the preposition (Max(V)), joining the existing preposition-specific scaling factor (Boersma & Hayes Reference Boersma and Hayes2001, Coetzee & Kawahara Reference Coetzee and Kawahara2013). For illustration purposes, consider the word [krˈest] ‘cross’, which has a CV rate of 68%. Non-ecclesiastical words that start with the same cluster, such as [kravˈatʲ] ‘bed’, tend to have a very low CV rate. Recall that we stipulated that the global weight of Max(V) is 25, such that s _k/s/v =−25. Tableaux (40a) and (b) show how the difference between [krˈest] and the non-ecclesiastical [kravˈatʲ] can be accounted for by assuming that the register-wide scaling factor is s _ecc =3.

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Alternatively, it may be that the ecclesiastical words we found constitute an isolated set of lexical items that emerged through a diachronic process and are therefore not qualitatively different from other high-CV words like [dvˈor]. If that is the case, the higher CV rate should be handled by morpheme-specific scaling of *#CCC, as in (38), rather than by register-wide scaling of Max(V), as in (40a). This alternative explanation predicts that a putative religion-related nonce word should not exhibit register effects in an experiment such as the one described in §4.

6.4 Morphological context

The problem of CV rates varying by morphological context has two sides: variation within the inflectional paradigm and conditioning by derivational suffixes (see §2.3.3). We will focus on the inflectional cases; for a full treatment of derivational effects, see Gouskova & Linzen (in preparation). The most prominent example of CV rates varying within the inflectional paradigm is [dnʲ-] ‘day’, which conditions different CV rates for the two homophones of [s], ‘with’ and ‘from’: [z dnʲˈom] ‘with the day (birthday)’ but [sa dnʲˈa] ‘from the day’ (cf. Fig. 3). Similarly, the root /mnog-/ ‘much’ in [mnˈoʐəstvə] conditions slightly more CV prepositions when used to mean ‘a large amount’ and more C prepositions when used to mean ‘a set’. This pattern was specific to these roots – we did not find an overall difference in CV rates between the two homophones of the preposition [s] in the Yandex corpus (§3.2.5). The explanation we suggested for these cases is that a root, e.g. ‘day’, has two homophonous allomorphs, which differ slightly in their contextual meaning and in how they condition prepositional phonology. The allomorph selected in the ‘holiday’ context, [z dnʲˈom], behaves like most other [dn]-initial words. The allomorph selected in other contexts has a higher scaling factor for *#CCC, favouring CV prepositions. The context for allomorph selection is semantic/morphosyntactic (Bobaljik Reference Bobaljik, Bachrach and Nevins2008), but it has consequences for the phonology. The analysis is otherwise no different, using a scaling factor for allomorphs just as for other exponents of morphemes, as shown in (41).

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6.5 Variation and frequency

We now turn to the role of word frequency in alternation. High-token frequency is generally known to encourage deletion: when faced with the choice between a longer and a shorter form of a word, people are often more likely to use the shorter form when the word is frequent or predictable. For example, the schwa in the frequent word memory is more likely to delete than the schwa in the infrequent word mammary (Hooper Reference Hooper and Christie1976, Dalby Reference Dalby1984, Patterson et al. Reference Patterson, LoCasto and Connine2003). Similar results have been demonstrated for English t/d-deletion (Bybee Reference Bybee, Barlow and Kemmer2000, Coetzee & Kawahara Reference Coetzee and Kawahara2013), Dutch schwa epenthesis (Tily & Kuperman Reference Tily and Kuperman2012) and other phenomena. In contrast with these studies, we did not find evidence that speakers were less likely to use the longer CV form of the preposition before high-frequency words. This may be because only phonetically gradient reductions increase in likelihood when the frequency of the word increases; the Russian vowel–zero alternation appears to be a case of a categorical deletion rule rather than a gradient phonetic process of the sort described in the studies mentioned above. However, in the absence of phonetic data on the realisation of the vowel in CV prepositions, we cannot draw definite conclusions from this fact.

Our study also differs from previous studies in that the deleted material is part of the preposition rather than the content word. The CV rate should therefore be modulated by the frequency of the preposition, rather than the frequency of the content word. There is evidence that frequency does not affect the pronunciation of function words, at least not to the same extent as content words (Bell et al. Reference Bell, Brenier, Gregory, Girand and Jurafsky2009). In addition, our sample of prepositions is very small, and inherently confounded with phonological factors, making it difficult to detect effects of the frequency of the preposition on the CV rate. On the other hand, Bell et al. (Reference Bell, Brenier, Gregory, Girand and Jurafsky2009) show that most function words are more likely to be reduced in duration when they are predictable from the following context word. This predicts that the vowel in a given preposition, say [s/so], should be less likely to be realised before a word that always occurs with that particular preposition (for example, in the context of a frequent collocation). We leave the testing of this prediction for future research.

The lemma-frequency effects we did find went in the opposite direction: in monosyllabic yer words, higher-frequency words were more likely to appear with CV prepositions, retaining a residue of the historical yer rule (see §2.4). These monosyllabic roots pattern with high-frequency function words, which always appear with CV prepositions ([sa mnˈoj] ‘with me’ and [sa fsˈem] ‘with all’). Frequency thus has a conserving rather than reducing effect in our data (Bybee Reference Bybee2006): after systematic yer alternations were lost, the CV rate of each monosyllabic root had to be learned on a morpheme-by-morpheme basis. Morpheme-specific rates for low-frequency morphemes did not have enough evidence in their favour; as a consequence, they were not learned by the next generation of speakers, and disappeared from the language. Our data join previous examples of sound changes that affect infrequent words first, such as glide deletion in southern American English (Phillips Reference Phillips1981, Reference Phillips2006).

We found an interaction between lemma frequency and the degree of sonority sequencing principle violation, such that frequent words showed a slightly larger effect of sonority sequencing. This is the opposite of what would be expected from a conserving effect of frequency: frequent words should be less affected by phonological pressure, and should therefore be more likely to retain the older pattern (i.e. preference for CV).Footnote ²² It is possible that sonority slope has two kinds of effects: both the synchronic effect on phonologically ‘regular’ words that we built into our MaxEnt model, and a diachronic filter on exceptions, which makes it more likely for words with SSP violations to become exceptions in the first place. The diachronic effect may be much larger than the synchronic one, which could explain the surprising direction of the interaction.

6.6 The syntax–phonology interface

We now return to the architecture of the syntax–phonology interface. In lexicalist theories of the syntax–phonology interface, such as Lexical Phonology (Kiparsky Reference Kiparsky1982, Reference Kiparsky1985, Mohanan Reference Mohanan1982, Kaisse & Shaw Reference Kaisse and Shaw1985), only lexical rules are allowed to have lexical exceptions, and only postlexical (e.g. phrasal) rules can be variable. Coetzee & Pater (Reference Coetzee, Pater, Goldsmith, Riggle and Yu2011) offer an extensive and convincing critique of this division, but their examples focus on lexical rules that are variable. The case of Russian shows that so-called postlexical rules can indeed have lexical exceptions. Through the corpus study, we identified a number of morphemes that systematically appear with CV prepositions, even though the productive phonological pattern that is extended to nonce words calls for a C preposition in similar phonological environments.

There has been some disagreement as to whether Russian prepositions are really phonologised postlexically. According to Kiparsky (Reference Kiparsky1985), Russian prepositions attach in the lexicon; his arguments are based on rule ordering in voicing assimilation (see also Hayes Reference Hayes, Aronoff and Oehrle1984). But, as we noted earlier, Russian prepositions are not affixes – they can cliticise phonologically onto nouns, adjectives, quantifiers or adverbs. It seems doubtful that all of these combinations are derived in the lexicon. There are alternative analyses of voicing assimilation that do not assume either opaque rule ordering or this architecture, relying on the prosodic structure of prepositions instead (Padgett Reference Padgett2002, Gouskova Reference Gouskova2010).

Russian is not an isolated example; many syntactically conditioned mutation rules have lexical exceptions (e.g. in Mende (Hayes Reference Hayes, Inkelas and Zec1990) and in Celtic languages (Green Reference Green2006)). Our corpus studies and experiment supply another case of a variable phonological rule that is part of phrasal/sentence phonologyFootnote ²³ and that shows lexical variability. This has consequences for the organisation of the grammar and the syntax–phonology interface. Phonological theory must allow for lexical exceptions in phrasal phonology, not just in the treatment of word phonology. The distinction between phrasal and word syntax is difficult to motivate on syntactic grounds alone (Marantz Reference Marantz1997, Reference Marantz2008; though cf. Bermúdez-Otero Reference Bermúdez-Otero2011, Reference Bermúdez-Otero and Trommer2012), so the elimination of the analogous distinction in phonology is independently motivated. Phrasal and word phonology are not different: both can show lexical variation.