4.1 The whole set of data

The entire set of LAs extracted from the corpus comprises 2,503 words. The corpus data clearly show that the distribution of the intermorphs and suffixes is not governed by categorical rules. It is common to find variation in the choice of affixes. For some bases, three competing LAs with different affixes appear in usage (see section 6 for details). For example, the LAs of /alask-a/ ‘Alaska’ are /ala(-)sk-i/, /alask-aɲ-sk-i/ and /alask-ij-sk-i/. The token frequencies of the three adjectives are different: 656, 554 and 17. Similarly, /angɔl-a/ ‘Angola’ produces /angɔl-sk-i/ (805), /angɔl-aɲ-sk-i/ (202) and /angɔl-ij-sk-i/ (18). An investigation of the context of usage of the forms in the corpus reveals no evidence that any of the forms that appear in competition have acquired a different meaning from the others (but see footnote 11). Due to the observed variation in the data, we should expect to identify a gradient, rather than categorical, impact of a host of factors on the selection of an affix. The factors, which include base-final consonant(s), lexical strata and syllable structure, are subjected to statistical analyses in this section. The results are then translated into a constraint-based analysis that employs schemas as well as markedness and faithfulness constraints in section 5.

A multinomial logistic regression analysis was run on the data using multinom() function in the nnet package (Venables & Ripley 2002) in R (R Core Team 2021). The analysis uses suffix as the dependent variable and consonant, extrasyllabic, and foreign as predictors. Three interactions are also included: consonant and extrasyllabic, extrasyllabic and foreign, and consonant and foreign. The coding of the variables is given in (7). The possible affixes are coded in suffix. The category “V” stands for vowel insertion. The bare suffix /-∅-sk-/ (sk) is the reference category. For the variable consonant /s/ was chosen as the reference category because this consonant shows a fairly consistent behavior in that it usually chooses /-∅-sk-/ and deletes. In addition, it is relatively common in the data. For these reasons it provides a good baseline. The analysis yields p values, which were calculated on the basis of z scores. The results of the analysis are given in Appendix A (Analysis 1). Only statistically significant results are shown. A particular suffix is deemed preferred in a given context when its coefficient is positive and significantly different from the reference level. Conversely, a suffix is considered dispreferred when it has a negative coefficient that is significantly different from the reference level.

The stacked percentage bar plot in Figure 1 shows affix distribution and vowel insertion in LAs according to the base-final consonant. Note that vowel insertion (V), depicted as a separate category in Figure 1, in fact falls under the usage of the bare suffix /-∅-sk/, as none of the intermorphs is used. In other words, vowel insertion is a special case of root modification; it does not involve the usage of an intermorph. However, I use vowel insertion as a separate category, as it occurs alongside the intermorphs as a strategy to avoid extrasyllabic consonants. While there is a general preference for ∅-sk in the data in Figure 1, certain consonants stand out. For example, /ts/ predominately chooses -tsk- and almost half of the LAs with base-final /j/ exhibit the bare suffix and vowel insertion. /f/ mostly selects -ij-, while there is no clear preference for base-final /tʂ/. We return to the factor consonant in the next sections, where the consonant-related preferences are examined separately in the native and foreign stratum.

Figure 1: Observed affix and vowel insertion preferences depending on the base-final consonant.

A note about the behavior of /v/ is in order. Although /v/ is described as an obstruent in modern Polish, it shows certain traits of a sonorant in its phonological behavior, thus reflecting its historical provenance. It can be traced back to the bilabial glide /w/ (Bethin 1998: 203). Thus, in what follows /v/ is analyzed together with the sonorants in order to determine whether it functions as a sonorant or not. Evidence for the sonorant status of /v/ is given in section 5.1.

The graph in Figure 2 shows the distribution of the affixes depending on whether there is an extrasyllabic consonant in a potential LA formed with -∅-sk. The results of the multinomial analysis are consistent with the proportions shown in Figure 2. The presence of an extrasyllabic consonant in a potential LA in -∅-sk significantly increases the likelihood that vowel insertion (z = 2.13, p = .03) and the intermorphs /-aɲ-/ (z = 51.06, p < .001), /-ɛɲ-/ (z = 8.09, p < .001) and /-ij-/ (z = 3.71, p < .001) are used.

Figure 2: Observed affix and vowel insertion preferences depending on extrasyllabicity.

We turn to the factor foreign. The graph in Figure 3 shows the preferences in the two strata of the lexicon: native and foreign LAs. In the native stratum vowel insertion and the intermorphs /-aɲ-/, /-ɛɲ-/ and /-ij-/ are used in 125 of 1419 LAs, which constitutes 8.8%, while in the foreign stratum these strategies are used in 397 of 1084 LAs, which amounts to 36.6%. The intermorph /-ij-/ is practically not used in the native stratum (1 case). The multinomial analysis confirms the preference for the intermorphs in the foreign stratum, as compared with the native stratum: /-aɲ-/ (z = 35.75, p < .001), /-ɛɲ-/ (z = 28.71, p < .001) and /-ij-/ (z = 5.20, p < .001).

Figure 3: Observed affix and vowel insertion preferences in the two strata: native and foreign.

We now turn to the three interactions (see Appendix A for details). The results for the interaction of consonant and extrasyllabic show that a potential extrasyllabic consonant (/m n ɲ r l w v/) increases the probability of using (one or several of) the intermorphs and vowel insertion (only /j/ shows a preference for the bare suffix). The interaction of extrasyllabic and foreign has a significant effect for all the intermorphs (compared with the bare suffix): /-aɲ-/ (z = –14.22, p < .001), /-ɛɲ-/ (z = –6.33, p < .001) and /-ij-/ (z = 15.94, p < .001). This confirms that there are different preferences for the affixes used with potential extrasyllabic consonants in the native and foreign stratum. Finally, the results of the interaction of consonant and foreign indicate that for a majority of the consonants the intermorphs are used more often in the foreign than in the native stratum. Only the consonants /s ʂ ɲ w ʐ/ show a striking preference for the bare suffix in the foreign stratum. The results of the interactions suggest that the two strata: native and foreign, display different preferences for the intermorphs.

Based on these results, two multinomial analyses have been run on the data: the first one investigates the native stratum, while the second one examines the foreign stratum. In this way, we get more insight into the affix preferences in each of the two strata.

4.2 Native stratum

The multinomial analysis examines native LAs and uses the predictors in (8). In addition to the predictors consonant and extrasyllabic, the interaction of consonant and extrasyllabic is included in the model, as certain consonants can function as extrasyllabic or not. Specifically, the choice of an intermorph, vowel insertion or the bare suffix can depend on the syntagmatic context of a consonant.

Figure 4 shows affix and vowel insertion preferences according to the consonant.⁹ Table 3 provides the results of the multinomial analysis. It lists the statistically significant preferences and dispreferences for different strategies (based on positive vs. negative coefficients that are significantly different from the reference level). More detailed results are given in Appendix A (Analysis 2). While there is a general preference for -∅-sk across all the consonants, certain consonants show statistically significant preferences for the intermorphs and -∅-tsk. Voiceless non-labial stops and affricates predominantly choose the suffix -∅-tsk and less often the intermorph -aɲ-. Voiceless non-labial fricatives primarily select the bare suffix. The voiced velar stop /g/ chooses the bare suffix or the intermorph -aɲ-. Most sonorants and /v/ show a significant preference for the bare suffix. The only exception is /n/, which in addition shows a preference for the intermorphs. An explanation for this finding will be provided below, where the role of extrasyllabicity is elaborated. Labial stops and voiced coronal fricatives select either the bare suffix (more often) or the intermorph -aɲ- (less often).

Figure 4: Native stratum. Observed affix and vowel insertion preferences depending on the base-final consonant.

Included in the category of bases that end in /k/ in Figure 4 are bases that end in /sk/. Such bases are singled out here because the base final sequence /sk/ is formally identical to the bare suffix -∅-sk. In LAs derived from bases in /sk/ the bare suffix is invariably chosen (in all 63 of such cases). Crucially, the LAs contain a single /sk/ sequence, which means that the resulting string /sk/ is shared between the base and the suffix, as exemplified in (9).¹⁰ This will be analyzed as an instance of multiple correspondence in section 5.8.

Figure 5 displays the impact of the factor extrasyllabic. In order to avoid an extrasyllabic consonant in a potential LA with the bare suffix -∅-sk, three strategies are statistically significant: the usage of vowel insertion (z = 6.11, p < .001), and two of the intermorphs: -aɲ- (z = 148.84, p < .001) and -ɛɲ- (z = 42.92, p < .001).

Figure 5: Native stratum. Observed affix and vowel insertion preferences depending on extrasyllabicity.

The interaction of consonant and extrasyllabic shows which suffixes are chosen when a particular consonant (sonorant) is extrasyllabic as opposed to when the consonant is not extrasyllabic in a potential LA with the bare suffix -∅-sk. The role of this interaction is visible in the graphs in Figures 6 and 7. Figure 6 shows suffix distribution for the sonorants that do not appear as extrasyllabic in a potential LA with -∅-sk. These are usually sonorants that are preceded by a vowel in the base: VR. Such sonorants almost exclusively select the bare suffix -∅-sk, e.g. /tɔruɲ/ ‘Toruń’ > /tɔruɲ-sk-i/. We conclude that the sonorants that are not potentially extrasyllabic overwhelmingly select the bare suffix -∅-sk.

Figure 7 shows affix distribution for potentially extrasyllabic sonorants, that is, those which are preceded by an obstruent: VOR, e.g. /krɔsn-ɔ/ ‘Krosno’ > /krɔɕɲ-ɛɲ-sk-i/. When a LA with the bare suffix -∅-sk is formed, such sonorants are extrasyllabic. Compared with Figure 6, Figure 7 shows no consistent preference for the bare suffix. While /j/ and /l/ exhibit a preference for the bare -∅-sk (more than 50% of cases), the remaining sonorants show a preference for various intermorphs or vowel insertion. The fricative /v/ is not shown, as it does not appear in “an extrasyllabic position” in native LAs.

Figure 6: Native stratum. Observed affix and vowel insertion preferences depending on the base-final consonant when not extrasyllabic.

Figure 7: Native stratum. Observed affix and vowel insertion preferences depending on the base-final consonant when extrasyllabic.

Table 4 looks in more detail at which preferences and dispreferences are statistically significant for each sonorant when extrasyllabic, based on the results of the multinomial analysis. Extrasyllabic /n/ and /ɲ/ are avoided using the intermorphs -aɲ- and -ɛɲ- and vowel insertion. Extrasyllabic /r/ and /l/ are avoided using the intermorph -aɲ-. Extrasyllabic /w/ is avoided using the intermorph -aɲ- and vowel insertion. Finally, extrasyllabic /j/ is usually deleted and the bare suffix -∅-sk is used. These results suggest that when the sonorants /n/, /ɲ/, /r/, /l/ and /w/ are extrasyllabic in a potential LA with -∅-sk, specific strategies such as an intermorph or vowel insertion are recruited to preserve them. On the other hand, extrasyllabic /j/ tends to be deleted and the bare suffix is selected.

4.3 Foreign stratum

The multinomial analysis of the foreign LAs is designed in a similar way to the analysis of the native stratum. Appendix A (Analysis 3) offers more detailed results of the analysis. The graph in Figure 8 presents the usage of vowel insertion and various affixes depending on the base-final consonant. A cursory inspection of the graph suggests that the intermorphs are used more frequently than in the native stratum, which accords with the results of the analysis of the whole set of LAs presented in section 4.1.

Figure 8: Foreign stratum. Observed affix and vowel insertion preferences depending on the base-final consonant.

The affix preferences depend on the base-final consonant, as shown in Table 5, where the results of the multinomial analysis are provided. Dispreference for the bare suffix -∅-sk is diagnosed when -∅-sk and vowel insertion are chosen in 40% or less of cases. Voiceless non-labial stops show a preference for -tsk, but the intermorphs are also used. This class shows a dispreference for -∅-sk and vowel insertion. Voiceless non-labial fricatives predominately select -∅-sk. The voiced velar stop /g/ shows a preference for -∅-sk, but the intermorph -ij- is also commonly recruited. Sonorants predominately choose -∅-sk, but the intermorphs and vowel insertion are also used. The two labiodental fricatives behave differently from each other. While /f/ selects mostly -ij-, /v/ chooses the bare suffix -∅-sk, the intermorphs -ɛɲ-, -ij-, or vowel insertion. We return to the usage of vowel insertion in the context of /v/ below. Labial stops tend to select the intermorphs -ij- and -aɲ-. The voiced coronal stop and affricate select various intermorphs. The voiced coronal fricatives behave differently. While both /z/ and /ʐ/ show a preference for -∅-sk, /z/ in addition is likely to select various intermorphs.

Similarly to the native stratum, in the foreign stratum when the base ends in /sk/, the bare suffix -∅-sk is almost always selected (27 out of 28 such cases). As shown in (10), the /sk/ string in such LAs corresponds both to the root-final sequence and to the suffix.

Just like in native LAs, in foreign LAs the factor extrasyllabic plays an important role. As evident in Figure 9, one strategy is particularly commonly used to avoid extrasyllabic consonants in LAs with -∅-sk: vowel insertion (z = 103.82, p < .001). The intermorphs -aɲ- (z = 70.75, p < .001) -ɛɲ- (z = 25.27, p < .001) and -ij- (z = 73.43, p < .001) are also used but less often.

Figure 9: Foreign stratum. Observed affix and vowel insertion preferences depending on extrasyllabicity.

The graphs in Figures 10 and 11 illustrate the interaction of consonant and extrasyllabic. Figure 10 shows sonorants that do not appear in the extrasyllabic context. While there is a general preference for the bare suffix, certain sonorants show a significant tendency to use the intermorphs or vowel insertion, e.g. /r/, /l/ and /j/. The results in Figure 10 can be directly compared with the results in Figure 6, where the trends in the native stratum were depicted. Unlike in the native stratum, in the foreign stratum the usage of the intermorphs after the non-extrasyllabic sonorants is clearly detectable (except for /ɲ/ and /w/).

Figure 10: Foreign stratum. Observed affix and vowel insertion preferences depending on the base-final consonant when not extrasyllabic.

Figure 11 shows affix distribution in the context of various extrasyllabic sonorants in potential LAs with -∅-sk. All the sonorants select various intermorphs or vowel insertion in the majority of cases. The usage of the bare suffix -∅-sk is found for /j/ only, but even in this case the usage of vowel insertion and one of the intermorphs (-aɲ-) predominates.

Figure 11: Foreign stratum. Observed affix and vowel insertion preferences depending on the base-final consonant when extrasyllabic.

Table 6 details which preferences and dispreferences in affix selection are statistically significant for each potentially extrasyllabic consonant. Extrasyllabic /m/, /n/, /ɲ/ and /r/ are avoided using various intermorphs and vowel insertion. Certain strategies exhibit specialization. The intermorph -ɛɲ- is used exclusively in the context of the coronal nasals /n/ and /ɲ/. The glide /j/ merits a closer analysis. Judging by the graph in Figure 11, vowel insertion occurs in the majority of cases. However, vowel insertion comes out as not statistically significant in the results shown in Table 6. This is caused by a considerable number of instances in which the potentially extrasyllabic /j/ selects the bare suffix -∅-sk and is deleted. Avoidance of “an extrasyllabic /v/” leads to the usage of vowel insertion. The observed productive use of vowel insertion as a strategy to avoid sequences where /v/ is flanked by two obstruents, resembling a trapped sonorant, may thus be a remnant of its past status as a sonorant, e.g. /padv-a/ ‘Padova’ > /padɛf-sk-i/, */patf-sk-i/. These results provide confirmation that intermorph and vowel insertion are strategies aimed at avoiding extrasyllabic sonorants and “trapped” /v/.

4.4 Summary

The analysis has identified important generalizations pertaining to the selection of affixes and vowel insertion in the two strata. They are given in Table 7.

5.1 Product-oriented schemas

The proposed analysis refers to schemas and subcategorization frames, both of which have been used in previous studies. Paster (2006) argues that generalizations are phonologically arbitrary and include morphological information. For example, in Kaititj the ergative suffix appears as /-ŋ/ after disyllabic stems and as /-l/ after trisyllabic stems. Paster (2006) and Embick (2010) use subcategorization frames which make reference to phonological and lexical information. The Kaititj pattern is represented in terms of the subcategorization frames in (12), which state that disyllabic bases correspond to ergatives formed using /-ŋ/, while trisyllabic bases correspond to ergatives with the suffix /-l/ (“σ” stands for syllable.). Although the formula that captures the generalization makes reference to phonological vocabulary, in this case the syllable, this instance of allomorph selection is phonologically arbitrary in the sense that it does not in any way improve phonological well-formedness (Paster 2006).

Product-oriented schemas (Bybee 2001; Booij 2010) are useful in capturing the distribution of allomorphs. Product-oriented schemas define the shape of the output without reference to the input. The observed preference for -∅-sk after sonorants (especially in the native stratum) can be explained once we notice that all the intermorphs show the structure V+R (V stands for a vowel and R for a sonorant). Based on the results of the quantitative analysis, it is proposed that the product-oriented schema R-sk regulates the shape of LAs. The two subcategorization frames in (13) capture the impact of the schema. When the base ends in a sonorant (R), the bare suffix is selected in a LA, as represented in (13a). On the other hand, when the base does not end in a R (the elsewhere condition), an intermorph is selected, (13b). As the three available intermorphs /-ij-/, /-aɲ-/ and /-ɛɲ-/ have the structure VR, the output of both subcategorization frames, complies with the R-sk schema.

There is good reason to believe that the class of sonorants (R) in the R-sk schema should be extended to include /v/. First, the analysis of the data in the previous sections demonstrates that the voiced labial fricative /v/ functions as a sonorant for two purposes: preference for ∅-sk- and the resolution of extrasyllabic sequences (vowel insertion). Second, Polish /v/ originated from a sonorant in Common Slavic (Bethin 1998: 203). In several Slavic languages it retains its sonorant properties. In Russian, it is pronounced as an obstruent and undergoes voice assimilation. However, unlike obstruents, it does not trigger voice assimilation. Lightner (1965) posits that the Russian /v/ is underlyingly a sonorant, /w/. The same pattern occurs in Czech (Short 1993). In many dialects of Ukrainian, it is both pronounced as a sonorant, [ʋ] or [w], and patterns as one with respect to voice assimilation (Czaplicki 2003). Although in Polish [v] both triggers and undergoes voice assimilation, it is possible that at least for some patterns [v] functions together with sonorants, as it is often the case that morphology and phonology lag behind phonetic change. For example, modern Polish /ʂ ʐ tʂ dʐ/ are described in phonetic studies as retroflexes (Hamann 2002) but function together with palatal consonants for certain morphophonological patterns (Gussmann 2007), the latter fact reflecting their historical origin. In the revised formulation of the schema in (14) “R” stands for “consonantal sonorants + /v/”. The formulation is consistent with Mielke (2008), who provides evidence that classes of sounds that function together in phonology can be language specific, as opposed to universal. For example, in Evenki (Nedjalkov 1997: 320, 175) suffix-initial /v s ɡ/ change to nasals when they follow nasal consonants, but other consonants do not nasalize in this position. Notably, /g/ and /s/ undergo the change, but /d/ does not. Therefore, it is not possible to say that alveolars (or stops) undergo the change, but velars (or fricatives) do not, or vice versa. Such phonetically unnatural patterns cannot be insightfully described using the familiar set of distinctive features and must instead refer to some arbitrary groupings of segments. Further instances of phonetically arbitrary generalizations will be identified later in this paper.

LAs that comply with the schema in (14) emerge in three different ways. In adjectives like the one in (15a), the sequence R-sk results from the use of an intermorph, while in the adjectives instantiated in (15b), a sonorant appears at the end of the base. Therefore, the latter adjective does not require an intermorph to comply with the schema. R-sk strings in LAs like the ones in (15c–e) emerge through phonological operations such as insertion, deletion or mutation.

5.2 Avoidance of the intermorphs

In the formal analysis of affix selection in LAs a general constraint against intermorphs will be used. *Struct penalizes phonological structure (Kager 1999: 404). It is based on the idea that structures without a specific morphosyntactic meaning should be avoided. Intermorphs, which are often described as suffix extensions (Kreja 1989), fall into this category. Suffixes such as -sk- are shielded from *Struct by means of higher ranked constraints (omitted from the tableaux) that require realization of morphosyntactic features.¹¹ Evaluations of LAs derived from bases ending in a VO (vowel + obstruent) sequence and a VR (vowel + sonorant) sequence are given in (16) and (17). “IM” stands for an intermorph, ++ stands for a strong boundary and + signals a weak boundary (following the distinction defined in section 2). Max penalizes consonant deletion. In (16) the schema requiring R-sk in a LA enforces the selection of an intermorph. In (17) the final R is present in the base, which means that using an intermorph is not required to satisfy the schema.

5.3 Extrasyllabic consonants

The corpus data show three commonly attested strategies to avoid extrasyllabic sonorants in potential LAs with the suffix -∅-sk: vowel insertion, usage of an intermorph or sonorant deletion as illustrated in (18). This can be viewed as an instance of conspiracy.

Sonority Sequencing Principle (SSP) will be used to represent the dispreference for extrasyllabic sonorants. Vowel insertion is penalized by the constraint Dep. Max penalizes consonant deletion. The evaluation in (19) shows the ranking necessary to generate two of the three attested ways to avoid extrasyllabic sonorants: candidate (b) shows vowel insertion and candidate (d) uses an intermorph. The evaluation of the same input in (20) produces the third of the attested outputs: a candidate with sonorant deletion, candidate (c). SSP dominates all the other constraints in (19) and (20). To generate non-uniformity of the outputs the ranking of the constraints Max, R-sk, *Struct and Dep must be probabilistic rather than strict. This issue is addressed in section 5.10, where I use a model that allows for assigning probability distributions to outputs using weighted constraints.¹² None of the strategies are used in (21), where there is no potential extrasyllabic sonorant and SSP is moot.

How do we account for the fact that different consonants use different strategies to avoid violations of SSP? In addition to markedness constraints such as SSP, consonant-specific schemas specifying which strategy is used are necessary, as exemplified in (22). The schemas are supported by the results of the statistical analysis in section 4. The schemas in (a) and (b) define the possible resolutions of an extrasyllabic /n/ (marked as “Cn”). The schema in (c) refers to an extrasyllabic /r/ (marked as “Cr”). Their ranking (or weighting) is probabilistic, reflecting the attested variation in the outputs.¹³ The idea that schemas (subcategorization frames) are ranked (or weighted) just like OT constraints is not new.¹⁴

5.4 Voiceless non-labial fricatives

For the remaining factors, there is also variability in the selection of the output. However, a clear preference for one of them can be identified. In the analysis, unless indicated otherwise, we consider the dominant output, as reflected in the type frequency data in the native stratum (provided in section 4.2). The hypothesized preferences are verified in the next section, where I model the grammars of LAs using a probabilistic framework. First, I investigate base-final voiceless non-labial fricatives (/s ɕ ʂ x/), as this factor promotes the selection of /-∅-sk/. As exemplified in (23), such fricatives tend to fuse with the following /s/ of /-sk-/. It is important to observe that the conditioning context is absent from the output but present in the input. That is, affix distribution in the output cannot be predicted from the output. Information from the input is crucial. We return to this issue in section 7.

The schema and the constraints responsible for this outcome are given in (24). The schema in (a) mandates that the bare suffix is selected after S, which stands for a voiceless non-labial fricative. It is proposed that such positive schemas are useful, as certain consonants or groups of consonants show an affinity for a particular way of forming LAs (see also the various consonant-specific resolutions of extrasyllabic consonants mentioned above).¹⁵ The constraints *Ss and Ident[+anter] enforce coalescence and are jointly labeled CoalS. *Ss penalizes a voiceless non-labial fricative followed by /s/. Ident[+anter] makes sure that the two fricatives fuse to /s/, as opposed to /ɕ/, /ʂ/ or /x/. Uniform penalizes coalescence (McCarthy & Prince 1995).

The tableau in (25) shows an evaluation of a LA like /pʂasnɨ-sk-i/ derived from /pʂasnɨʂ/ ‘Przasnysz’. Two non-identical indices on one segment mean that two segments have been fused. Candidate (a) selects the wrong affix and fatally violates the relevant schema. Candidates (b) and (c) fail to apply coalescence and violate *Ss. Candidate (d) shows deletion, which is penalized by Max. Candidates (e) and (f) show coalescence, but in candidate (f) the output of coalescence is /ʂ/, which violates Ident[+anter]. Candidate (e) wins. The evaluation shows that Uniform must be ranked below the other constraints.

5.5 Voiceless non-labial non-continuants

Base-final voiceless non-labial stops and affricates /t ts tʂ k/, represented as [-voice, -labial, -continuant], regularly choose the allomorph -tsk of the suffix -sk. The input sequence: a base-final stop or affricate plus the suffix initial /s/ yields the affricate /ts/, as schematized and illustrated in (26). This process will be conceptualized as an instance of coalescence. Recall from section 2 that /g/ does not participate in the coalescence, hence the restriction to [-voice]. Similarly, labial stops fail to coalesce with the following suffix, e.g. /wɛb-a/ ‘Łeba’ – /wɛp-sk-i/. Therefore, base-final voiceless non-labial non-continuants, /t ts tʂ tɕ k/, need to be considered as a context favoring the allomorph /-tsk-/ of the adjectivizing suffix. Following (Jakobson et al. 1952), I assume that affricates are represented as strident stops. The fused [ts] acquires the feature [-continuant] from the non-labial stop or affricate and the remaining features, i.e. [-voice, +coronal, +anterior, +strident], from the fricative /s/.

The schema in (27) compels the usage of the bare suffix -∅-sk after a /T/, which stands for [-voice, -labial, -continuant]. The two constraints *Ts and IdentT[-contin] coerce the coalescence /T/+/s/ → /ts/. IdentT[-contin] is restricted to voiceless stops and affricates, as /g/ does not participate in coalescence. Ident[+anter], defined in (24) above, makes sure that the fused affricate is /ts/, rather than /tʂ/.

In the evaluation of a LA with a base-final T in (28), candidate (a) is eliminated because it selects an intermorph. Candidate (b) fails, as it forgoes coalescence and as a consequence violates *Ts. Candidate (c) shows deletion, which brings about a violation of Max. The remaining candidates show coalescence, but candidates (e) and (f) choose suboptimal outputs of coalescence and violate the relevant Ident constraints. Candidate (d), which shows fusion to /ts/, comes out victorious.

5.6 Voiced non-labial obstruents

Voiced non-labial obstruents are less likely to fuse with the suffix -sk than their voiceless counterparts and instead are more likely than their voiceless counterparts to choose an intermorph. Another common strategy is to delete the voiced obstruent. Both strategies are exemplified in (29). However, the output is not uniform. For instance, /z/ selects all the intermorphs as well as the bare suffix in the foreign stratum (see section 4.3).

The constraint Ident[+voice] in (30) coerces the preservation of [+voice]. In the case at hand, it is violated when a fused voiceless segment in the output [s_1,2] corresponds to two input segments with differing specifications for voicing, e.g. /z/ and /s/. This dispreference can be observed in the data, e.g. /s/ most often fuses with /s/, but /z/ is more likely to appear with an intermorph in the foreign stratum, and /k/ fuses with /s/, but /g/ does not.¹⁶ Voice Assimilation (VA) makes sure that obstruent clusters agree in voicing.

The evaluation of a LA with a base-final /D/ in (31) shows the importance of Ident[+voice]. Candidate (b) incurs a fatal violation of a phonotactic constraint, *Ts (it is applicable to voiceless and voiced non-continuants). Candidate (c) is eliminated because it shows fusion of /D/ and /s/ and the fused /ts/ lacks [+voice]. Candidate (d) preserves [+voice] in the fused segment but violates VA, as two adjacent obstruents differ in voicing. In accordance with the trends identified in the data, the second possible output is candidate (e), with deletion. For this candidate to win, *Struct must be promoted over Max (the tableau is not shown for reasons of space). This again justifies the need for a probabilistic ranking of the constraints. In sum, the usage of an intermorph (candidate a) and deletion (candidate e) are preferred over coalescence for voiced obstruents.

5.7 Labials

Labial stops /p b/ and the voiceless fricative /f/ (/f/ does not appear in the native stratum) are also likely to select an intermorph, though this preference is visible only in the foreign stratum, e.g. /tɛb-ɨ/ ‘Thebes’ > /tɛb-aɲ-sk-i/. Here coalescence is prevented by the constraint Ident[+labial], which forbids changes in the [+labial] specification. In the evaluation in (32), Ident[+labial] and Ident[+anterior] militate against coalescence with a labial. Note that Ident[+anterior] as formulated in (24) applies to coronals only. The change of a coronal to a labial in candidate (d) violates Ident[+anter], as the coronal articulator, of which [+anterior] is a dependent (Hume & Clements 1995), has been deleted. Candidates with deletion, (e) and (f), incur fatal violations of Max. The ranking of R-sk over *Struct compels the selection of the output with an intermorph (candidate a).

5.8 Multiple correspondence

Multiple correspondence occurs when a given output string corresponds to two distinct input strings. For example, the string /sk/ serves both as part of the root and as an adjectival suffix in (33). The preference for the multiple correspondence of /sk/ is almost categorical in the data: 90 of 91 LAs with base-final /sk/ select the bare suffix -∅-sk.¹⁷

The schema in (34) enforces the selection of -∅-sk after base-final /sk/. Multiple correspondence is often coerced by the avoidance of identical sounds or morphemes (Czaplicki 2022).¹⁸ In OT formalization, a constraint against repeated elements, OCP (Goldsmith 1976), is ranked above a constraint penalizing multiple correspondence, Uniform, defined above. In accordance with the evidence suggesting that similarity avoidance is stronger in morphologically derived environments than within single morphemes (Jurgec 2016; Czaplicki 2022), the OCP in (34) is morphologically restricted.

In the evaluation of an LA derived from a base ending in /-sk/ in (35), indices are attached to the relevant /sk/ sequences to indicate their non-identity. The schema ensuring the selection of the bare suffix in this context is responsible for eliminating the candidate with an intermorph, (a). The presence of two /sk/ sequences across a strong morphological boundary in candidates (a) and (b) incurs a violation of the OCP. Candidate (c) with multiple correspondence wins as long as the OCP is ranked over Uniform.

5.9 Lexical strata

How can we account for the more common usage of the intermorphs in the foreign than in the native stratum? In the analyzed data, the intermorphs and vowel insertion are used in 36.6% of LAs of foreign origin, compared with 8.8% of LAs of native origin. Moreover, the intermorph -ij- is used exclusively in the foreign stratum. The different preference for the intermorphs can be derived from different constraint ranking (or weighting) in the two grammars: foreign and native. Two possibilities are considered. According to the first hypothesis, there is a dedicated constraint that requires that a LA contains an intermorph, Intermorph. This constraint is based on the idea that the intermorphs have become a marker of the foreign status of LAs. The constraint is a cover-term for constraints that refer to the usage of specific intermorphs in the context of particular consonants, e.g. r → -ij-, t → -aɲ-. Intermorph dominates *Struct in the foreign grammar. The second possibility is that there is no dedicated constraint requiring intermorphs and the difference between the two grammars rests on the different ranking of *Struct with respect to the other constraints regulating allomorph selection.²⁰ The hypothesized rankings of the constraints (both options) in the two grammars are given in (36).

LAs derived from /saxar-a/ ‘Sahara’ (foreign) and /mazur-ɨ/ ‘Mazury’ (native) serve to illustrate the observed discrepancies in the preference for the intermorphs in foreign and native words. Indices show whether a word belongs to the foreign or native stratum. In the evaluation of the foreign word in (37), the candidate with an intermorph wins, as LAs with the intermorphs are preferred in G_Foreign, reflecting the ranking of *Struct below the other relevant constraints. In the evaluation of the native word in (38), the candidate without an intermorph comes out victorious, as the ranking in G_Native inhibits the selection of the intermorphs. Thus, different rankings in the two grammars result in different outputs. As demonstrated by the results of the statistical analysis, the preferences in the affix distribution in LAs are gradient, rather than categorical. In the next section, I attempt to assess the importance of each constraint for affix distribution using a probabilistic framework. G_Native and G_Foreign are considered separately.

5.10 Grammar modeling

Classic OT models, which assume strict constraint ranking, are not sufficient to generate the attested variation in the selection of outputs of LAs. In an attempt to determine the gradient impact of various pressures I use a model that allows for assigning probability distributions to outputs, rather than predicting a single winner. Such probabilistic frameworks come in two flavors: they refer to either constraint ranking or constraint weighting. A Stochastic OT grammar (Boersma 1998) is a probability distribution over strict-ranking OT grammars. Each constraint is assigned a ranking value, which is used to determine the probability of a given constraint ranking after adding noise. When the ranking values of two constraints are far apart from each other, the ranking of the constraints is fixed. When the ranking values of two constraints are closer to each other, the ranking of the two constraints is more likely to be reversed and variation occurs. In contrast, Harmonic Grammar (Legendre et al. 1990) uses constraint weighting. Each constraint bears a real number that determines its importance in the selection of the winning candidates. In particular, the weighted sum of the constraint violations of each candidate, termed the harmony of the candidate, is used to select the winning candidates. Both frameworks can in principle be used to model the distribution of LAs. However, recent evidence indicates that Harmonic Grammar is more effective in modeling variation than Stochastic OT (Zuraw & Hayes 2017). For that reason, we use Harmonic Grammar, and more specifically, its implementation called Noisy Harmonic Grammar (NHG; Boersma & Pater 2016). What makes NHG probabilistic is that at each evaluation time, some Gaussian noise is added to each constraint’s weight, which might lead to a change of the winning candidate.

The tableaux used in the simulations of the Polish data are given in Appendix B. The key constraints formulated in the previous sections have been used. As regards the constraints coercing coalescence, CoalS is a shorthand for *Ss and Ident[+anter], and CoalT stands for *Ts and Ident[-cont]. The tableaux list the inputs, output candidates and all the constraint violations (marked by “1”). Frequency values reflect the type frequency of the specific pattern in the data (how often a winning candidate occurs for each pattern). OTSoft (Hayes et al. 2013) was used to run two simulations: one for the native grammar and one for the foreign grammar.²¹ The weighting of the constraints derived from the simulations is given in Table 8.²²

The SSP is the constraint with the highest weight in both grammars, which means that extrasyllabic sonorants are strongly avoided. The most striking difference between the two grammars is the relative weight of *Struct. In the native grammar, *Struct is weighted among the first four most important constraints. In contrast, in the foreign grammar it belongs to a group of constraints with a medium weight. This difference suggests that the intermorphs are less preferred (i.e. more dispreferred) in the native than in the foreign grammar. The constraint coercing the usage of an intermorph, IM, is not particularly active in the two grammars. The constraint R-sk exhibits a medium weight in both grammars (though it is slightly more important in the native grammar, as compared with the foreign grammar, where the constraint is counterbalanced by a general preference for the intermorphs). This result provides evidence for the importance of the R-sk schema for allomorph selection in LAs. Further evidence for the impact of R-sk is provided below.

As regards the source-oriented schemas requiring the selection of the bare suffix, they have a small impact, with the notable exception of S → sk in the foreign grammar and perhaps sk → sk in the native grammar. More specifically, in the foreign grammar voiceless non-labial fricatives show a preference for the bare suffix (with coalescence), in spite of the general affinity of the other consonants for the intermorphs. The affinity of base-final /sk/ for the bare suffix is weighted higher in the native than in the foreign grammar, where its impact is small. This means that certain classes of segments may show different preferences in affix choice than others. Phonotactic constraints regulating coalescence (CoalS and CoalT) and similarity avoidance (OCP) are weighted high in both grammars. The fact that Ident[+voice] and Ident[+labial] are weighted high suggests that coalescence tends to be blocked for voiced obstruents and labial obstruents.²³ The relative weighting of Dep over Max in the two grammars indicates that segment deletion is preferable over segment insertion when satisfaction of higher ranked constraints is at stake. In addition, Dep and Max are weighted higher in the native than foreign grammar, which indicates that segmental faithfulness is respected more in the native than foreign grammar.²⁴

The product-oriented schema R-sk turned out to be important in the simulations. Additional evidence for the relevance of the schema R-sk is based on the comparison of the relative frequency of final Rs in LAs (i.e. before the -sk suffix) and their base nouns. The latter frequency provides a baseline useful in determining whether final sonorants are overrepresented in LAs. The data in Table 9 show that final Rs are more common in LAs than in their base nouns. The proportions of final Rs are 0.83 for LAs and 0.697 for their base nouns, with the difference between them amounting to 0.133. A binomial test in R (binom.test(2078, 2503, p = 0.697)) yields p < .001 and a 95% confidence interval from 0.815 to 0.845. This provides additional support for the impact of the R-sk schema in LAs.²⁵