3.1 Backness alternation and flopping by default

We start with the most frequent nasal pattern, the [ɐ̃w̃ ~ õȷ̃s] alternation, which is also the most preferred in nonce words (see §4 below). In a constraint-based grammar, two main questions must be answered: what makes [õȷ̃s] preferred over [ɐ̃ȷ̃s], and what makes [õȷ̃s] preferred over [ɐ̃w̃s]?

Adopting the proposal in Schwindt & Wetzels (2016), the [round] feature of the singular [w̃] can receive one of two treatments: it can be deleted, resulting in plural [ɐ̃ȷ̃s], or it can be retained and flopped leftward from the coda to the nucleus in [õȷ̃s]. The proposed mappings are summarized in Figure 2, where dotted lines show deletion or fusion, and a solid arrow shows the flopping of the [round] feature from the [w̃] leftward. The plural suffix has an allomorph /-is/, found after all consonants (including glides), but the analysis can also work with the underlying representation /-s/; see discussion below. Only [ɐ̃w̃s] plurals involve deletion, in this case the deletion of the suffix vowel, and thus only these violate Max-V. Candidates that involve deleting anything from the root can be blocked by MaxRoot. The [ɐ̃ȷ̃s] and [õȷ̃s] plurals are both derived via fusion of the stem [w̃] with the suffix [i], violating Uniformity (McCarthy & Prince, 1995) which penalizes the fusion of two segments into one, but we omit this constraint from consideration because it does not distinguish [ɐ̃ȷ̃s] from [õȷ̃s]. In [ɐ̃ȷ̃s] plurals, the stem [w̃] loses its rounding, which violates Max(round). In [õȷ̃s] plurals, the round feature does not delete, but rather flops over to the preceding vowel, violating *Flop(round), which belongs to the *Flop family of faithfulness constraints (McCarthy 2003). The three patterns are thus derived by referring to three different faithfulness violations.

Figure 2

Proposed correspondence relations in [ɐ̃w̃s], [ɐ̃ȷ̃s], and [õȷ̃s] plurals.

The analysis can match the high frequency of [õȷ̃s] in the lexicon by making the weight of *Flop(round) substantially smaller than the weight of Max(round), as seen in Table 2, which shows the derivation of a plural for the nonce word [taˈɡɐ̃w̃]. The predicted acceptability is 98% for [õȷ̃s] and 2% for [ɐ̃ȷ̃s]. Candidates that have no deletion, e.g., [taˈɡɐ̃w̃is] or [taˈɡɐ̃w̃ȷ̃s], violate undominated markedness constraints against onset [w̃] or triphthongs and will not be included. We also omit many other logically possible candidates, e.g., ones with fortition of the glide to a less marked onset, blocked by faithfulness.

In MaxEnt, constraints are weighted, and each violation is multiplied by the weight of the constraint that assigns it. Summing the weighted violations of each candidate gives its harmony (ℋ). For example, in Table 2, the first candidate has a violation of Max-V, which is multiplied by 5.9, for a harmony of –5.9; violations are always negative. To convert harmonies into probabilities, each harmony is exponentiated, and the result is divided by the sum of the exponentiated harmonies in the tableau.

The weights in Table 2 were computed using the software provided in Hayes & Wilson (2008). The program is given the lexical statistics from §2, and it uses them to calculate constraint weights that match the lexicon as closely as possible.

To assign the highest probability to [õȷ̃s], the analysis must also penalize [ɐ̃w̃s], and therefore [ɐ̃w̃s] must violate some constraint more severely than [õȷ̃s]. As mentioned above, we propose that the plural suffix has an allomorph /-is/, and [ɐ̃w̃s] plurals delete the suffix vowel, violating Max-V. If, however, one assumes that the plural suffix is underlyingly /-s/, the plural [taˈɡɐ̃w̃s] is completely faithful to /taˈɡɐ̃w̃ + s/. If [ɐ̃w̃s] plurals are faithful, the only thing that can penalize them is markedness. One might propose a markedness constraint that targets the juncture between the back glide and the following [s], perhaps tying them to the tendency for an excrescent [j] before a tautomorphemic final [s], as discussed in Nevins (2015). The application of this proposal hits a snag in the São Paulo dialect(s) that we study here, since most speakers do not have an excrescent [j] in the plurals of vowel-final words, e.g. [soˈfa-s] ‘sofas’, *[soˈfaj-s] (Table 1a).

Given the difficulty of the markedness based approach, we maintain the position that [ɐ̃w̃s] is in fact unfaithful. In this we follow Becker et al. (2018), who proposed that the plural suffix has two allomorphs: /-s/ selected for vowel-final stems and /-is/ selected for consonant-final stems. Final glides, like all consonants, select the allomorph /-is/, and the suffixal vowel deletes in [ɐ̃w̃s] plurals, violating Max-V, as seen in Table 2. The selection of /-is/ for consonant-final stems is transparent for stems that end in [ɾ, s] (Table 1b), and opaque for stems that end in a glide. With the front glides, the junctures *[ji] and *[ȷ̃i] are regularly simplified to [j] and [ȷ̃], e.g., /eˈɾɔj + is/→ [eˈɾɔjs] ‘hero(s)’ (Table 1a; also see Kawasaki 1982). With the back glides, the ill-formed junctures [wi] and [w̃i] are repaired either via deletion of the suffixal [i], allowing the stem to surface faithfully, or via fusion of the glide with the following vowel, resulting in a front glide [j] or [ȷ̃] (Table 2).

The analysis of oral [w] is exactly parallel, except that flopping the [round] feature onto an oral vowel is blocked, as seen in Table 3 with the derivation of the nonce /pɾiˈzɛw/. The violations and harmonies (ℋ) in Table 3 are otherwise identical to those in Table 2. The absence of competition from the flopped candidate allows most of the probability to be assigned to the candidate that deletes rounding, in this case predicting an acceptability of 88% for the backness alternation.

The flopping of rounding onto a vowel is only possible with [ɐ̃] and no other vowel. There is a wide range of analyses that can prevent the flopping of rounding onto other vowels, and the details are not crucial to the current discussion. Any mechanism that blocks, e.g., *[pɾiˈzɛw ~ pɾiˈzɔjs] would work. Generally speaking, Brazilian Portuguese is rich in height and laxness alternations, but very limited in backness and rounding alternations, suggesting a central role for Ident(back) in the language.

To summarize, the default/most frequent plural patterns are [ɐ̃w̃ ~ õȷ̃s] and [w ~ j]; we derive both from the interaction of three faithfulness constraints. For the oral [w], Max-V penalizes the deletion of the underlying /i/ from the plural suffix, while Max(round) penalizes the deletion of rounding from the stem. The heavier weight of Max-V predicts an acceptability of 88% for the [w ~ j] alternation in the default case (=polysyllabic stem with a final lax vowel). For the nasal [w̃], the same constraints and the same weights, with the addition of a candidate that flops rounding leftward, predicts an acceptability of 98% for the [ɐ̃w̃ ~ õȷ̃s] alternation in the default case (=polysyllabic stem with final stress). *Flop(round) has a weight of zero, and therefore the penalty it assigns to [õȷ̃s] plurals has no effect.

3.2 Deriving existing lexical items

In addition to predicting the acceptability of novel plural forms, the grammar should also be tasked with deriving the plurals of existing lexical items. For example, the noun [sidaˈdɐ̃w̃] ‘citizen’ is observed in the corpus we examined only with the plural [sidaˈdɐ̃w̃s], and not [sidaˈdõȷ̃s] as expected for a polysyllable – although the form [sidaˈdõȷ̃s] is indeed found in other corpora (Huback, 2010). What prevents the grammar from generating [sidaˈdõȷ̃s] as the plural?

One possibility is to use the UseListed framework (Zuraw, 2000). In this theory, the speaker memorizes the derived forms they encounter, e.g., [sidaˈdɐ̃w̃s], and these memorized forms are also used to train a productive grammar. The constraint UseListed penalizes productively formed plurals, ensuring that memorized plurals are used when they are known to the speaker. Further, UseListed penalizes frequent forms more than rare forms, ensuring that frequently used words are produced correctly more often, as documented by Huback (2010).

Moore-Cantwell (2017), Moore-Cantwell & Pater (2016) propose a more nuanced framework in which lexical items are associated with lexically-specific constraint weights. The general grammar and the lexically-specific weights are both learned simultaneously from the environment (a corpus). Lexically specific weights are under pressure to minimize, moving the maximal amount of explanatory power to the regular grammar, leaving lexically specific constraints with the minimal weight that is needed to resist the regular grammar. For [õȷ̃s] plurals such as [boˈtɐ̃w̃ ~ boˈtõȷ̃s] ‘buttons’, the regular grammar already assigns 98% of the probability to the correct [boˈtõȷ̃s]; the lexically specific constraints have the modest task of bringing this probability up closer to 100% (but not exactly 100%; MaxEnt grammars can get arbitrary close but not reach 100%). This is shown in Table 4, where the three general faithfulness constraints seen in §3.1 above are augmented with three lexically specific versions of them: Max-V-botɐ̃w̃, Max(round)-botɐ̃w̃, and *Flop(round)-botɐ̃w̃. The first two penalize the unattested forms *[boˈtɐ̃w̃s] and *[boˈtɐ̃ȷ̃s]; the third one is assigned a weight of zero, since [boˈtõȷ̃s] should not be penalized. The weights of the lexically-specific constraints were calculated with the same software as above, providing the attested plural [boˈtõȷ̃s] at 100%. We omitted the zero-weighted *Flop(round)-botɐ̃w̃ from Table 4, but it was included in the analysis.

Polysyllables with a plural in [ɐ̃w̃s] or [ɐ̃ȷ̃s], such as [sidaˈdɐ̃w̃ ~ sidaˈdɐ̃w̃s] ‘citizen(s)’, diverge more strongly from the regular grammar, which hardly assigns any probability at all to the attested plural. The lexically-specific constraints must counter the grammar with larger weights, as seen in Table 5. Here, the two lexically-specific constraints Max(round)-sidadɐ̃w̃ and *Flop(round)-sidadɐ̃w̃ have weights that are at least twice as large as those in Table 4. Depending on one’s theory of learning, larger weights may take longer to acquire, and/or may require more exposure (greater token frequency). It is thus predicted that plurals such as [sidaˈdɐ̃w̃s] would require more time and/or more exposure to learn correctly.

Huback (2011) studied the effect of token frequency in the diphthongal plurals, and found that frequent items are produced with their normative plural more reliably than low frequency items. For example, comparing two words whose plural is normatively [ɐ̃w̃s], Huback observes that medium frequency [kɾisˈtɐ̃w̃] ‘Christian’ is produced with its normative plural more reliably than low frequency [vuwˈkɐ̃w̃] ‘vulcano’. Such effects can be incorporated into a future version of the model we use here, for example by reducing the plasticity of lexically specific constraints.

Finally, we show in Table 6 the treatment of an item that has multiple plurals, such as [ɡwaɾʤiˈɐ̃w̃ ~ ɡwaɾʤiˈɐ̃ȷ̃s, ɡwaɾʤiˈõȷ̃s] ‘guardian(s)’, where the learning software was provided with two plurals that are equally frequent. The given distribution was learned by adjusting the weights of the lexically-specific constraints appropriately; the learner is equipped to learn any combination of plurals for a given lexical item, while at the same time learning a general grammar that applies productively to novel items. The observed distribution that the learner encounters in its environment is learned and encoded in the grammar with only one mechanism: adjusting constraint weights. The underlying representation for any given lexical item remains unchanged.

Items with multiple plurals pose an insurmountable problem for lexical-only analyses, since a word like [ɡwaɾʤiˈɐ̃w̃] would require two separate underlying representations, without any mechanism that can represent native speaker knowledge of their statistical distribution or deployment choice in real-time.

An intermediate approach to learning alternations is offered in Pater et al. (2012), where surface forms are used to construct “UR constraints”; for example, the paradigms such as [boˈtɐ̃w̃ ∼ boˈtõȷ̃s] would generate two underlying representations for the stem, /boˈtɐ̃w̃/ and /boˈtõȷ̃/, with the first underlying representation selected in the singular and the second underlying representation selected in the plural. This approach is similar to the lexically-specific constraints we propose here, and crucially, it does not attempt to create abstract underlying representations that reproduce the etymology.

The analysis we provide here builds on the insights in Abaurre-Gnerre (1983), who proposes that the regular grammar produces [õȷ̃s] plurals, while [ɐ̃w̃s] and [ɐ̃ȷ̃s] plurals are derived via lexical marking (diacritics); in her analysis, the two plurals of [ɡwaɾʤiˈɐ̃w̃] are derived via optionality of the lexical marking. Missing from Abaurre-Gnerre (1983), however, is a mechanism for the prosodic factors that guide pluralization. In the next section, we show how our analysis encodes prosodic generalizations in terms of competition between faithfulness constraints, formalized with a learning mechanism that captures the statistical trends that these constraints are able to capture.

3.3 Protection of monosyllables

In [ɐ̃w̃]-final monosyllables, stem changes such as deletion or flopping of the [round] feature occur in the more prominent initial syllable of the word, where they violate initial syllable faithfulness (Barnes, 2006; Becker, 2009, Becker et al., 2011, 2017; Beckman, 1997, 1998; Casali, 1998; Jesney, 2011; Steriade, 1994; Trubetzkoy, 1939). Here we follow Becker et al. (2018), who attribute the special patterning of monosyllables in Portuguese to the crosslinguistic protection of initial syllables more generally (Becker et al., 2012). Thus, in the nonce plural mapping /ˈfɐ̃w̃ + is/ → [ˈfɐ̃ȷ̃s], as in Table 7b, the deletion of [round] violates both general Max(round) and the specific Max(round)-σ1, since the nasal glide [ȷ̃] surfaces in the initial syllable. In the MaxEnt grammar, a violation of the general Max(round) incurs a penalty of 3.9, and a violation of the specific Max(round)-σ1 incurs an additional penalty of 2.7. Similarly, the mapping /ˈfɐ̃w̃ + is/ → [ˈfõȷ̃s], as in Table 7c, incurs violations of the general *Flop(round) and the specific *Flop(round)-σ1. Monosyllabic [ɐ̃w̃s] plurals, exactly like polysyllabic [ɐ̃w̃s] plurals, violate Max-V. The suffixal vowel is equally absent from these plurals, and thus never violates any positional versions of Max-V. With these constraints and weights, the grammar’s prediction for a monosyllable is an acceptability of 67% for the [ɐ̃w̃s] plural and 33% for the [ɐ̃ȷ̃s] plural.

Turning to monosyllables with a lax oral vowel [a, ɛ, ɔ] in their nucleus, these parallel the nasal monosyllables, just like polysyllables with a lax vowel parallel the nasal polysyllables. As seen in Table 8, no constraints distinguish nasal [ˈfɐ̃w̃s], [ˈfɐ̃ȷ̃s] from oral [ˈbɾɔws], [ˈbɾɔjs], and therefore the grammar predicts the same rate of backness alternations in both cases. In the corpora we use here, the backness alternation has a type frequency of 41% in monosyllables with a lax vowel, compared to a type frequency of 25% in monosyllables with [ɐ̃w̃]; our analysis averages these two together and predicts a backness alternation rate of 33% in both cases. Here, the analysis does not perfectly match the corpus type frequencies, because there is no constraint that distinguishes oral and nasal glides. We show in §4.5 that the predictions of the model are strongly correlated with speakers’ behavior.

The effect of monosyllabicity is documented in Huback (2010, 2011), who suggests that monosyllables are controlled by a local “schema” (Bybee & Slobin, 1982), and that they “represent a separate class in the mental lexicon”. In our analysis, monosyllables are not separate, but alternations in monosyllables are penalized by initial syllable faithfulness. The difference between the two proposals is that putting monosyllables in a separate class allows monosyllables to be derived differently, e.g., they may undergo a change that polysyllables are immune from. Initial syllable faithfulness makes a stronger prediction: monosyllables can only be protected from change, and cannot undergo a change that polysyllables are immune from. An additional advantage of initial syllable faithfulness constraints is that they apply to both nasal and oral diphthongs, protecting both types of monosyllables with the same mechanism.

3.4 Licensing of nasal diphthongs

In nouns with non-final stress that end in [ɐ̃w̃], the plural most commonly maintains the diphthong faithfully. This result follows straightforwardly from the language-wide distribution of nasal diphthongs, most of which are strictly required to be in the stressed syllable. In Table 9, the candidates with unstressed [ɐ̃ȷ̃s] and [õȷ̃s] are penalized by License-ɐ̃ȷ̃/ˈσ and License-õȷ̃/ˈσ, which assign violation marks to these diphthongs in unstressed syllables. The plural [ɐ̃w̃s] is selected not because it is faithful, but because it is the least marked in this context.

These licensing constraints, which are employed in Table 9, reflect more general trends in the language, and form part of a larger family of Positional Licensing constraints that crosslinguistically allow more segmental contrasts in stressed syllables than in corresponding unstressed ones. In word-final unstressed position, only two nasal diphthongs are allowed: [ɐ̃w̃] and [ẽȷ̃]; the only exception is the nasal diphthong in the one word [ˈbẽȷ̃sõȷ̃s] ‘blessings’. While [ɐ̃w̃] has a high type frequency both in stressed and unstressed syllables, most other nasal diphthongs of the language have low type frequencies, and are almost completely limited to stressed syllables. The diphthong [ɐ̃ȷ̃] appears in a handful of roots, e.g., [ˈmɐ̃ȷ̃] ‘mother’, [ˈkɐ̃ȷ̃bɾɐ] ‘cramp’, and their derivatives, and in plurals of [ɐ̃w̃]-final words, always in a stressed syllable. As for [õȷ̃], it appears in the single item [ˈpõȷ̃] ‘put.3sg’ and its derivatives, and in the plurals of [ɐ̃w̃]-final words, again limited to the stressed syllable, with the exception of the plural [ˈbẽȷ̃sõȷ̃s] ‘blessings’.

The derivation of unstressed [ɐ̃w̃] is shown in Table 9, where the [ɐ̃ȷ̃s] and [õȷ̃s] plurals are penalized by the markedness constraints that require nasal diphthongs to be licensed by stress. In this grammar, the word [ˈbẽȷ̃sõȷ̃s], which is the only word in the language with an unstressed [õȷ̃], causes the weight of Lic-õȷ̃/ˈσ to be lower than the weight of Lic-ɐ̃ȷ̃/ˈσ. Not all speakers have this unusual word; for speaker who do not, the two markedness constraints will have similar weights, ruling out unstressed [õȷ̃] and unstressed [ɐ̃ȷ̃] equally.

While [ɐ̃w̃] and [ẽȷ̃] are the only nasal diphthongs allowed in word-final unstressed position, even these two are optionally reduced and oralized to [ʊ, ɪ] respectively (Bopp da Silva, 2005; Medeiros et al., 2021; Schwindt & Bopp da Silva, 2009). For example, [ˈɔɾfɐ̃w̃] ‘orphan’ may be reduced to [ˈɔɾfʊ̃, ˈɔɾfʊ]. We thus see that nasal diphthongs in Brazilian Portuguese strongly require stress, and even the more broadly distributed [ɐ̃w̃] and [ẽȷ̃] are eliminated from final unstressed syllables in some cases.

To summarize the analysis so far, nasal diphthongs appear in three environments: stressed non-initial syllable (the default), stressed initial syllable (protected by positional faithfulness), and unstressed syllable (restricted by markedness).

3.5 Vertical dispersion in oral diphthongs

Turning back to the oral [w], the [w ∼ j] alternation is most acceptable at 88% (see Table 3 above) in polysyllables that have a lax vowel [a, ɛ, ɔ] in their final syllables, but the acceptability of the alternation is lowered to 76% when the preceding vowel is one of the tense oral vowels [e, i, o, u], as seen in Table 10 below. Following Becker et al. (2017, 2018), we assume that the alternation is disfavored after a tense vowel due to the illformedness of the morphologically derived diphthongs [ej, oj] (while underived /ej, oj/ are acceptable). The tense vowel offers poor vertical distinction from the glide [j] compared to the more acceptable difference in height between a lax vowel and a glide in [aj, ɛj, ɔj].

Table 10 shows the derivation of a nonce word such as [ˈɦosew] with a tense oral vowel before a final [w]. The constraint *ShallowDiphthong reduces the probability of the [w ∼ j] alternation after a tense vowel in all contexts, regardless of stress or monosyllabicity. Formally, *ShallowDiphthong is a markedness constraint that assigns one violation each to [ej], [oj], and [uj] but not to [ɛj], [ɔj] or [aj]; compare to the similar constraint *HearClear (Minkova & Stockwell, 2003). The analysis predicts an acceptability of 76% for the [w ∼ j] alternation in a polysyllable regardless of stress; the prediction for a stressed syllable in, e.g., [muˈzew] ‘museum’ would be identical. In monosyllables, *ShallowDiphthong works in tandem with Max(round)-σ1 to reduce the acceptability of the [w ∼ j] alternation from 33% (see Table 8) to 17%.

The markedness of the shallow diphthongs [ej, oj] relative to the better dispersed [aj, ɛj, ɔj] finds support from work on the typological distribution of diphthongs by Kubozono (2001), who observes that diphthongs with greater height dispersion are more common in the world’s languages, with [aj] being the most common. For further exploration of diphthong dispersion in Brazilian Portuguese, see Nevins (2012), and more recently, Eberle (2022).

The sensitivity of the [w ~ j] alternation to the laxness of the preceding vowel is also seen in innovative or nonstandard plurals, which are only observed following a lax vowel, e.g., with [a] in [deˈɡɾaw ∼ deˈɡɾajs] ‘step(s)’ alongside the standard plural [deˈɡɾaws], and with [ɛ] in [tɾoˈfɛw ∼ tɾoˈfɛjs] ‘trophy(s)’ alongside the standard plural [tɾoˈfɛws]. There are no parallel examples of innovative plurals following a tense vowel.

3.6 Summary of the analysis

We presented a probabilistic grammar that partially matches the frequencies of plurals in the lexicon using a set of phonological constraints. By default, nouns that end in a back glide [w, w̃] undergo a backness alternation to the corresponding front glide [j, ȷ̃] due to fusion with the vowel [i] of the plural suffix. The rounding of the stem glide flops leftward if the preceding nucleus is [ɐ̃], and the rounding is deleted otherwise. The acceptability of this default alternation is reduced by three phonological factors: the protection of monosyllables by initial syllable faithfulness, the licensing of the nasal diphthongs [ɐ̃ȷ̃, õȷ̃] by stress, and a dispreference for the poorly dispersed diphthongs [ej, oj]. The tableaux that were used to train this grammar are provided in Appendix A. In addition to the general constraints in these tableaux, which apply productively to any word, existing or novel, we also used lexically-specific constraints to correctly derive established plurals of existing lexical items.

The analysis matches lexical statistics based on grammatical principles, unlike general-purpose statistical models that are not similarly constrained. For example, the backness alternation is predicted to be equally acceptable in monosyllables with [ɐ̃] and monosyllables with a lax nucleus [a, ɛ, ɔ], despite the frequency differences in the corpora, since both kinds of plurals are derived using the same set of constraints. Similarly, the alternation is predicted to have the same acceptability in polysyllables that have a tense nucleus in their final syllable regardless of stress. The proposed analysis is built on general grammatical principles that are well-founded typologically and have broad application in Brazilian Portuguese and beyond.

4.1 Participants

The participants were recruited online via social networks and word of mouth.

The participants volunteered their time and effort. We analyzed data from the 70 participants who completed the task and self-identified as being at least 18 years old and living in Brazil; the rest of the data was discarded. Of these 70, 60 participants said they were living in the state of São Paulo. Regarding their dialect, 56 people said they speak with a São Paulo accent, either urban or rural. Gender: 37 identified as female, 31 as male, and 2 did not say. The average self-reported age was 33 (range 19–74, median 31).

4.2 Materials

The materials for this experiment were originally created for Rizzato (2017), and had the following structure: a total of 57 nonce nominal paradigms were used, including 13 fillers, 15 iambs, 15 trochees, and 14 monosyllables (one monosyllable was discarded before the experiment was run because it sounded like a brand name). The target items are listed in Appendix B. The example item [ˈpovʊ] ‘people’ was added as well.

The target items all ended in [ɐ̃w̃], e.g., [ˈbɾɐ̃w̃], and for each, three plurals were created: one with final [ɐ̃w̃s], one with final [ɐ̃ȷ̃s], and one with final [õȷ̃s], e.g., [ˈbɾɐ̃w̃s], [ˈbɾɐ̃ȷ̃s], [ˈbɾõȷ̃s].

The fillers and the example item were all disyllables with [o] in the first syllable and [ʊ] in the second, e.g., [ˈsodʊ]. Their three plurals had the stressed vowels [o], [ɔ], [u], e.g., [ˈsodʊs], [ˈsɔdʊs], [ˈsudʊs].

To present the items as masculine singular-plural paradigms, six frames were created. Each frame was made of two sentences. The first sentence ended with a masculine singular determiner (e.g., [ˈesɪ], ‘this.masc’) followed by the nonce singular. The second sentence ended with a plural determiner (e.g., [ˈoitʊ] ‘eight’) followed by the nonce plural. The sentences were randomly paired with the items.

A female native speaker of urban São Paulo Portuguese, a 20 year old college student, read the sentences three times in a quiet room. The best token of the three was converted to mp3 format. The recordings were not manipulated in any way and were reported to sound very natural.

4.3 Procedure

The experiment was run online using Experigen (Becker & Levine, 2015), with participants using the device and browser of their choice. The server executed a random selection of 24 items for each participant: six each of monosyllables, iambs, trochees, and disyllabic fillers. The experiment was conducted after ethical approval for research with human participants was granted by the Unicamp ProReitoria Ethics Committee, approved for project number 40681820.0.0000.8142.

Participants were informed that the experiment was related to the Portuguese language, involved invented words, that there were no ‘right or wrong answers’. They were told that their participation would be voluntary and anonymous, and that their personal information would be maintained confidential.

In each trial, the frame was shown in Portuguese spelling at the top of the screen, with the singular written, and a blank left for the plural (see Figure 3). A first sound button was shown; when it was pressed, the frame was played with one randomly chosen plural. When the audio file was done playing, two buttons appeared, “bom” and “ruim” (“good” and “bad”). Once one of these two was pressed, both buttons were disabled, and participants were led through the same combination of one sound button and two judgment buttons for the second randomly chosen plural, followed by the third plural. A sample trial is shown in Figure 3. The sound buttons were not disabled, so participants were free to hear the sounds again, but not change any previous responses. Once the third plural was judged, the experiment moved to the next trial.

Figure 3

A sample item, presenting the nonce word ⟨funhão⟩ [fũˈɲɐ̃w̃]. Translation of the frame “Your mother saw my_M.SG new_M.SG funhão, and now she says that she will buy herself a few_M.PL__________”. Translation of the buttons: “good”, “bad”.

The first trial was always the example item [ˈpovʊ], after which the 24 randomly chosen items were presented. At the end of the experiment, participants were asked to provide demographic information as described above.

Rizzato (2017) conducted an experiment that uses the same materials that are used here, but with a different procedure: all three plurals were presented first, and then participants were asked to choose the best of the three. In contrast, the procedure we use here allows each plural to be judged individually as soon as it is heard.

4.4 Results

Participants mostly accepted only one of the three plurals for a given item (53%), but sometimes accepted two plurals (35%), bringing the informative trials to 88% of the total. In the uninformative trials, participants accepted all three plurals for a given item (10% overall, 14% for monosyllables, 7% for iambs, 9% for trochees) or rejected all three (2% overall, 2% for monosyllables, <1% for iambs, 4% for trochees). The raw results are available at https://becker.phonologist.org/projects/bpnasal/, and the results by item are listed in Appendix B.

No outliers were found among the items or the participants. Shapiro-Wilk tests confirmed that the distribution of the responses was not significantly different from normal either by item or by participant.

The results are presented in Figure 4. Overall, the participants’ preferences reflected the lexicon, especially for the iambs and trochees. The preferences are strongest with iambs, where [õȷ̃s] plurals were the most acceptable at 95% vs. 24% for the other two plurals. For trochees, [ɐ̃w̃s] plurals were most acceptable at 79% vs. 34% for the other two plurals.

Figure 4

Two-way forced judgements of each of the three plurals (n = 70); bars represent 95% confidence intervals, or 1.96 standard errors.

As for the monosyllables, the unattested [õȷ̃s] was least acceptable at 47%, as expected. But the [ɐ̃w̃s] and [ɐ̃ȷ̃s] plurals did not follow the lexicon exactly: the highest type frequency [ɐ̃w̃s] was accepted at 58%, but the lower type frequency [ɐ̃ȷ̃s] was accepted slightly more often at 62%. As for the statistical significance of̃ the these results, one must proceed with caution: when a participant provides three judgments for a given item, these three judgments are not completely independent, and thus the number of degrees of freedom is hard to determine. According to t-tests fitted to the monosyllables, [õȷ̃s] plurals are significantly less acceptable than [ɐ̃w̃s] and [ɐ̃ȷ̃s] plurals, but [ɐ̃w̃s] and [ɐ̃ȷ̃s] plurals are not significantly different from each other; these results need to be considered with caution given the aforementioned question about assessing the degrees of freedom.

The results we present here are very similar to the ones in Rizzato (2017). Recall that Rizzato used the same items we used here, but required participants to choose one of three plurals as best. In contrast, we allowed participants to endorse or dismiss each of the three plurals separately. There was no difference to speak of in the treatment of polysyllables between the two experiments. As for the monosyllables, in both experiments, [ɐ̃ȷ̃s] was preferred over [õȷ̃s], but there was a difference in the treatment of [ɐ̃w̃s]: in our experiment, [ɐ̃w̃s] was chosen almost as often as [ɐ̃ȷ̃s], while in Rizzato’s experiment, [ɐ̃w̃s] was chosen rarely, even more rarely than [õȷ̃s] (the exact numbers are given in Appendix B). Our results are closer to the observed trend in the lexicon, suggesting perhaps that our methodology allowed speakers to use their grammars more accurately.

4.5 Discussion

The plural forms of [ɐ̃w̃]-final nouns depend on prosodic context, as predicted by the analysis: the default [õȷ̃s] is strongly preferred with iambs. The [õȷ̃s] plural is blocked in trochees due to the limitation of [ɐ̃ȷ̃s] and [õȷ̃s] to the stressed syllable, leaving [ɐ̃w̃s] as the best option. In monosyllables, initial syllable faithfulness disfavors [õȷ̃s] and prefers [ɐ̃w̃s], but the acceptability of [ɐ̃ȷ̃s] turned out to be greater than predicted by the analysis.

The results are squarely in favor of a grammar that learns the plurals of existing items using phonological factors, as predicted by the proposed analysis, and confirming the intuitions of Abaurre-Gnerre (1983). The empirical observations show the insufficiency of lexicon-only approaches that encode individual lexical items without prosodic generalizations, and thus fail to derive the observed productive effect of monosyllabicity and stress.

To quantify the predictive power of the analysis, we measured the correlation between the numerical predictions of the analysis with the participants’ choices. For the nasal glide, we use our own experimental results, and for the oral glide, we use the results from Becker et al. (2017). The result is shown in Figure 5, where the overall correlation between the predictions and the observations is strong and highly significant (Spearman’s rank correlation ρ = .82, p < .001) overall. The correlation is strong and significant for the nasal glide (ρ = .87, p < .005) and the oral glide (ρ = .72, p < .05) individually. The acceptability rates and model predictions that were employed in these calculations are given in Appendix A. It is likely that the predictions could be improved by further adjustment of the model; we hope that this paper serves as an invitation for more accurate future quantitative analyses.

Figure 5

Strong correlation (ρ = .82) between the lexicon-trained analytical predictions and the participant choices, by condition. For the oral vowels, [a] represents lax vowels and [o] represents tense vowels.