2.1 Tamazight Berber

Rolf Noyer takes an interesting rule-based realization approach to Tamazight Berber verbal morphology, whose paradigm is shown as follows:

1. (1) Completive paradigm of Tamazight Berber dawa‘cure’ (Abdel-Massih Reference Abdel-Massih1971: 171; Noyer Reference Noyer1992: 132; Stump Reference Stump2001: 157)

   

Noyer's analysis of the Tamazight Berber paradigm in (1), as summarized by Stump (Reference Stump2001: 157), is given in (2).Footnote ³

1. (2) Noyer's analysis of the Tamazight Berber paradigm

   

Noyer's realization theory is based on feature discharge. Once a morphosyntactic feature value is discharged or spelled out by an exponent, it will no longer be available for further realization. Thus, the prefix n- {1, pl} blocks the suffix -γ {1} because the first person feature value that is realized by n- is no longer available for realization by -γ. This is a case of what Noyer calls discontinous bleeding in which the blocking and blocked affixes belong to distinct position classes. Similar analyses apply to cases in which n- {1, pl} blocks -n {pl}, -m {pl, masc} blocks -n {pl}, and t- {sg, fem} blocks -t {fem}. Noyer's theory follows precisely Pāṇini's Principle, which requires an affix with more specific morphosyntactic content to preempt others with less specific content. Tamazight Berber, however, has cases of extended exponence, in which a morphosyntactic feature value is realized by more than one form, thus disobeying Pāṇini's Principle. For example, the second person plural masculine exponent -m cooccurs with the second person exponent t- (t-dawa-m), showing extended exponence of the second person feature. Additionally, the second person singular exponent -d cooccurs with the second person exponent t- {2} (t-dawa-d). These cases of extended exponence pose a challenge for a theory based on feature discharge, because if the second person feature value is first realized by -m {2, pl, masc} or -d {2, sg}, it should no longer be available for realization by t- {2} and therefore we should not expect the cooccurrence of t- with -m/-d.

In order to allow for extended exponence, Noyer introduces extra machinery in the distinction between primary and secondary exponents.Footnote ⁴ An affix that realizes a morphosyntactic feature value as a secondary exponent depends on the presence of another affix that realizes the same morphosyntactic feature value as a primary exponent. Only an affix that realizes a morphosyntactic feature value as a primary exponent can block or be blocked by another affix that also expresses the same feature value as a primary exponent. An affix that realizes a morphosyntactic feature value as a secondary exponent cannot block or be blocked by another affix that expresses the same feature value as either a primary or secondary exponent. Extended exponence in Noyer's framework therefore demands the occurrence together of both a primary and secondary exponent. According to Noyer, in Tamazight Berber t- is a primary exponent of the second person feature value, which can be further realized by -m or -d, which must be secondary exponents of {2}, because {2} has been discharged by t-.

Stump (Reference Stump2001) argues against Noyer's (Reference Noyer1992) analysis of extended exponence. Stump shows that it is not always possible to determine whether a given exponent is primary or secondary, even for a single form. Thus, it is possible to treat the Tamazight Berber suffixes -m and -d as primary exponents instead of secondary exponents. See (3) (from Stump Reference Stump2001:165). Stump remarks (p. 168) that ‘Noyer's notion of feature discharge is not a satisfactory alternative to the postulation of rule blocks, since it depends on an empirically unmotivated and ultimately paradoxical distinction between primary and secondary exponents’.Footnote ⁵

1. (3) Stump's reanalysis of the Tamazight Berber paradigm

   

Stump (Reference Stump2001) presents an approach to Tamazight Berber verbal morphology within the framework of Paradigm Function Morphology, where realization rules that apply to the same affixal slot are placed in the same rule block. Within a rule block, Pāṇini's Principle is the only mechanism to determine which rule should apply (i.e. the Pāṇinian Determinism Hypothesis). Blocking is assumed to occur only within the same rule block, which corresponds to a single affixal slot. Extended exponence is allowed via multiple rule blocks: cooccurring exponents that would otherwise violate Pāṇini's Principle must fall in distinct rule blocks. Stump's analysis of blocking and extended exponence in Tamazight Berber follows (we simplify his notation). The output from one rule block becomes an input to the following one:

1. (4)

   

There are at least three problems for Stump's model. First, blocking and extended exponence are analyzed under two separate mechanisms, i.e. blocking of exponents is derived via Pāṇini's Principle that applies within a rule block while extended exponence is derived via multiple rule blocks. Second, as Noyer notes, Stump's model cannot account for cases of discontinuous bleeding in which the blocking and blocked affixes belong to different rule blocks or position classes given that Pāṇini's Principle does not apply across rule blocks in Stump's model.Footnote ⁶ Third, Paradigm Function Morphology needs to use counterintuitive underspecification. For example, although the Tamazight Berber suffix -d is patently an exponent of {2, sg} because it only occurs in the slot of {2, sg} it is analyzed as {2} under PFM.

To briefly summarize, neither model provides a unified account of blocking and extended exponence. To allow for extended exponence, they each have to introduce additional mechanisms.

2.2 A Realization Optimality Theory approach to Tamazight Berber morphology

In this section, we present a Realization Optimality Theory account of the Tamazight Berber data. This is an inferential–realizational model of inflectional morphology (Matthews Reference Matthews1972; Zwicky Reference Zwicky, Niepokuj, Clay, Nikiforidou and Feder1985; Anderson Reference Anderson1992; Aronoff Reference Aronoff1994; Stump Reference Stump1993, Reference Stump2001) within the framework of Optimality Theory (Prince & Smolensky Reference Prince and Smolensky1993/2004). Any inferential–realizational model of morphology needs to posit grammatical functions that realize morphosyntactic feature values. Following Russell (Reference Russell1995), Kager (Reference Kager and Kleinheiz1996), Yip (Reference Yip, Lapointe, Brentari and Farrell1998), Hyman (Reference Hyman, Booij and Marle2003) and MacBride (Reference MacBride2004), we assume that the phonological realization of inflectional affixes is done through realization constraints. The basic format of a realization constraint is shown in (5), which states that a morphosyntactic feature is realized by a morphophonological form. The symbol ‘:’ is read as ‘realized by’.

1. (5) {Morphosyntactic feature}: {Morphophonological form}

Functional morphemes such as affixes are encoded in realization constraints, which are a cornerstone of Realization Optimality Theory. For example, the realization constraint {2}: t- for Tamazight Berber is read: ‘{2} should be realized by t-’.Footnote ⁷ Additionally, we follow Prince & Smolensky (Reference Prince and Smolensky1993/2004), which encodes Pāṇini's Principle in OT constraint rankings (6). As a consequence, a constraint realizing a feature set outranks another constraint realizing a non-null subset of the features realized by the higher-ranked constraint.

1. (6) Pāṇini's Theorem on Constraint Ranking (Prince & Smolensky 2004: 99)

   Let constraints S and G stand as specific to general in a Pāṇinian relation. Suppose these constraints are part of a constraint hierarchy CH, and that G is active in CH on some input i. Then if G>>S, S is not active on i.

Following previous works (e.g. Yip Reference Yip, Lapointe, Brentari and Farrell1998, Hyman Reference Hyman, Booij and Marle2003, MacBride Reference MacBride2004, Xu Reference Xu2007), we assume that morphosyntactic features are present in the input to realization and remain available throughout (i.e. are not deleted when ‘discharged’). The function Gen in Realization OT generates an infinite list of phonological forms to realize the features.Footnote ⁸ Since the outcomes of realizational morphology models are phonological forms, constraints of Realization OT specifically target morpho-phonological forms and no change of morphosyntactic features is assumed (see Grimshaw Reference Grimshaw1997).

In Realization OT, there is no methodological reason to underspecify the feature value set that an exponent realizes. The feature values associated with a given exponent are usually those shared on inspection by the forms in which the exponent occurs, no more and no less. Nor is there much reason to posit contentless default affixes. No morphosyntactic disjunctions are permitted either, leading to homophonous constraints in cases like the t- prefix for either {2} or {3, sg, fem} in Semitic languages. The key device within Realization OT that we introduce in this article is the markedness (more precisely economy) constraint *Feature Split, which bans the realization of a morphosyntactic feature value by more than one form.Footnote ⁹ This constraint favors simple exponence, which is assumed to be universally unmarked (Wurzel Reference Wurzel1989).Footnote ¹⁰ *Feature Split is a more general mechanism than Pāṇini's Principle, whose application further requires a subset relation among competing exponents. By varying the ranking of *Feature Split and constraints realizing the same morphosyntactic feature value(s), we can readily express both blocking and extended exponence. If *Feature Split is outranked by constraints realizing the same morphosyntactic feature value(s), we will expect extended exponence. Otherwise, we will observe blocking of inflectional affixes. From the learners' point of view, extended exponence is always a signal that *Feature Split, which by default outranks all realization constraints, must in this instance rank lower than the particular realizations that show extended exponence.

Let us reconsider the Tamazight Berber verbal paradigm in (1). Our proposed Realization OT grammar is presented in (7). Following Stump (Reference Stump2001), we assume that -m realizes {2, pl} and assimilates to [n] in the slot of {2, fem, pl}. Notice that the constraints {2, pl}: -m, {2, sg}: -d, and {2}: t- need to outrank *Feature Split because both -m {2, pl} and -d {2, sg} can co-occur with t- {2} (t-dawa-m, t-dawa-d) so that the second person feature value is realized by two exponents. The ranking of {2}: t- and {2, pl}: -m or {2, sg}: -d is indeterminate in that we cannot find any evidence to show that the former is outranked by the latter, but we assume that it still conforms to the specificity condition that requires a constraint with more specific morphosyntactic or semantic content to outrank a less specific realization constraint. For a clearer presentation, we rank *Feature Split higher than the remaining realization constraints simply to show that extended exponence is introduced by the constraints that outrank *Feature Split. But in fact, if, for example, {1, pl}: n- outranks *Feature Split, our results remain intact.Footnote ¹¹

1. (7) {2, pl}: -m, {2, sg}: -d, {fem, pl}: -t, {3, pl}: -n >>{2}: t- >>

   *Feature Split >>

   {1, pl}: n-, {1, sg}: -γ, {3, sg, masc}: i-, {3, sg, fem}: t-

Our Realization OT grammar captures every paradigmatic cell in (1). The tableau for t-dawa-d {2, masc, sg}, for example, is shown in (8) below. The illicit output candidates *dawa-d and *t-dawa are ruled out because both -d {2, sg} and t- {2} need to be spelled out despite the violation of *Feature Split. We leave to our readers the exercise of confirming that the grammar in (7) captures the other slots in the paradigm of (1). The careful reader will have noticed that on our analysis no case of blocking is observed in the paradigm in (1). But we do not claim that every paradigm of every language must contain examples of both blocking and extended exponence. Many languages show no examples of extended exponence. We doubt that there are no languages without any instances of blocking, though that remains to be seen.

1. (8) t-dawa-d {2, masc, sg}

   

Notice that in our approach there is no need to avoid the feature value set {2, masc, sg} in Tamazight Berber verbal morphology. The constraint {2}: t- is insensitive to gender distinction in the environment of second person subject agreement. By contrast, Noyer (Reference Noyer1992) rules out the input feature value set {2, masc, sg} under the analysis in (2) because otherwise *t-i-dawa (t- {2}, i- {sg, masc}) would be the correct outcome as pointed out in Stump (Reference Stump2001).Footnote ¹² Additionally, our Realization OT grammar does not resort to counterintuitive underspecification. For example, -d realizes {2, sg} in our framework while Stump (Reference Stump2001) analyzes it as an exponent of {2} even though it only occurs in the slots of {2, sg}.

The order of the suffixes -n (or -m assimilated into [n]) and -t can be determined by phonology.Footnote ¹³ The word-final cluster [nt] is more optimal than the final cluster [tn] because the former satisfies the Sonority Hierarchy Principle (Kenstowicz Reference Kenstowicz1994), which requires a coda to have a falling sonority contour, although various types of consonants can be underlyingly adjacent in Tamazight Berber (see Abdel-Massih Reference Abdel-Massih1971). The final cluster [nt] wins over [tən] with a ‘transitional vowel’ probably because of a constraint banning transitional vowels or empty morphs, though it is ranked low in Tamazight Berber because transitional vowels often break up complex consonant clusters.

The order of the suffixes -n (or -m assimilated into [n]) and -t could also be described by a template that requires -t to follow -n (cf. Hyman Reference Hyman, Booij and Marle2003; Paster Reference Paster, Booij and Marle2005, Reference Paster2006, Reference Paster2009, to appear).Footnote ¹⁴ Since affix ordering is not a theme of this paper, we will not discuss this issue in detail. But see Xu (Reference Xu2007) and Aronoff & Xu (Reference Aronoff and Xu2010) for detailed discussion of affix ordering under Realization OT; they remark that a templatic approach should be the last resort, given that a template, by definition, is stipulative in nature.Footnote ¹⁵

Two remarks deserve emphasis at this point. First, in conventional OT, constraints are assumed to have universal status; but realization constraints are necessarily language-specific in that they realize arbitrary Saussurean signs. It is important to emphasize that the target of conventional OT is phonology while our model deals mainly with morphology, which, since at least Ferdinand de Saussure, has emphasized arbitrary associations of meaning and form. In other words, morphological realization is necessarily language-particular and arbitrary, in any framework. We are concerned with morphological realization, not with phonology, and language-particular realization constraints are crucial in dealing with morphological phenomena, by definition. Whether language-particular constraints are necessary for purely phonological aspects of language is, thus, completely outside the scope of our work. In Section 3, we will compare Realization OT to conventional OT models that persist in maintaining the universality of constraints. We will show that realization constraints are indispensable in the morphological component of the whole grammatical architecture and that conventional OT models are incapable of handling morpheme realization and morphology in general.

Second, constraint rankings are sometimes indeterminate: for example, the ranking of {2, sg}: -d and {fem, pl}: -t. Flexibility of rule orderings also arises in Noyer (Reference Noyer1992, Reference Noyer1997) and Stump (Reference Stump2001). For example, on Noyer's analysis the order of the affixes i- {sg, masc} and t- {sg, fem} is flexible, as pointed out in Stump (Reference Stump2001). Stump (Reference Stump2001) proposes three rule blocks, those in (4) above, to analyze Tamazight Berber verbal morphology. The third block has only one realization rule. Each of the first two contains four realization rules whose order is indeterminate.

To briefly summarize, our Realization OT approach to the Tamazight Berber verbal morphology avoids both rule blocks and the distinction between primary and secondary exponents.

2.3 Classical Arabic

Realization OT also applies to Classical Arabic, which exhibits both blocking and extended exponence. We compare our approach to the Classical Arabic prefixal conjugation with Noyer (Reference Noyer1992, Reference Noyer1997), and Stump (Reference Stump2001), and continue to argue for its advantages. Consider the following paradigms:

1. (9) Classical Arabic prefixal conjugation (from Noyer Reference Noyer1997: 4–5)

   

There are at least two interesting issues in the above paradigms. First, the second person exponent t- co-occurs with the second person feminine singular marker -ii in the environment of {2, fem, sg} (e.g. t-aktub-ii), which is a case of extended exponence: {2} is realized by both t- and -ii. Second, in the environment of {3, fem, pl} we observe y-aktub-na instead of *t-aktub-na.

Noyer's (Reference Noyer1997: 54) analysis of the affixes in (9) is as follows:

1. (10) Noyer's analysis of the Classical Arabic prefixal conjugation

   

To explain cases like y-aktub-na {3, fem, pl} in which -na {fem, pl} blocks t- {fem} (*t-aktub-na), Noyer assumes that {fem} is first discharged or realized by -na and is no longer available for realization by t-. This is a case of discontinuous bleeding in which a suffix blocks a prefix. To allow for cases of extended exponence such as t-aktub-iina, Noyer distinguishes primary from secondary exponents, that is, t- is a primary exponent of {2} while -iina is a secondary exponent of {2}. The suffix -iina therefore does not block or get blocked by t-.

By modifying Noyer's analysis of the Classical Arabic affixes under Realization OT, we can account for the paradigm in (9) and readily capture both blocking and extended exponence without either the contentless elsewhere exponents in his analysis or a distinction between primary and secondary exponents. Also, Noyer analyzes n- as an exponent of {1, pl} although n- is also an exponent of {1, dual}.Footnote ¹⁶ He analyzes n- as an exponent of {1, pl} so that n- can block -uuna, which is analyzed as an exponent of {pl} (n-aktub-u vs. *n-aktub-uuna). By doing that, he gets another case of discontinuous bleeding, which he advocates in his framework. In order to account for the syncretism of {1, dual} and {1, pl} forms that share the same prefix n-, Noyer must then use a feature-changing mechanism to convert the feature value set {1, dual} into {1, pl}, while admitting that such feature-changing rules should be avoided.Footnote ¹⁷

Our analysis of the affixes in (9) is presented in (11). Where the analyses differ (compare (11) and (10) above), we use boldface type.

1. (11) Our analysis of the Classical Arabic prefixal conjugation

   

Several issues arise concerning our analysis. Noyer uses the feature value {+ind} while we use {ind} because generally we do not assume underspecification and {−ind} is therefore an illicit category in our framework. Additionally, according to Matthews (Reference Matthews1991) only marked features such as plural can form binary features, i.e. {+pl}, {–pl}. Indicative is an unmarked feature, so it should not be used for binary features. It is possible to analyze -na as a default exponent of {–perf, ind} since it occurs in the environment of both {2, fem, sg} and {masc, pl} which do not form a natural class. But what then of the suffix -u? The distribution of the suffix -u that realizes {–perf, ind} is also irregular. It basically occurs in the contexts of both {1} and {sg}, which do not form a natural class either. If we treat both -na and -u as default exponents of {–perf, ind}, it will be hard to explain why, for example, the exponent of {3, fem, sg, –perf, ind} is t-aktub-u instead of *t-aktub-na.Footnote ¹⁸

We analyze the three na-suffixes as homophones. It is common for languages to have homophonous affixes. In English, for example, the suffix -s can be a marker of either plural, or possessive, or third person singular agreement. The three na-suffixes are not reducible to one another except by illicit underspecification and we therefore list them separately.

It is possible to analyze, for example, -aani as a unitary suffix of {dual, –perf, ind} (see McCarthy Reference McCarthy, Downing, Hall and Raffelsiefen2005). As Noyer (Reference Noyer1997: 46) observes, ‘[w]herever the imperfect has a disyllabic suffix (-uuna, -iina, -aani), the subjunctive and jussive moods have only the first syllable of this suffix’. By positing a realization constraint like {dual, –perf, ind}: -aani, ‘we are forced to assert (in effect) that it is a mere accident that the [–indicative] affixes are in all cases the first syllables of the [+indicative] affixes’ (Noyer Reference Noyer1997: 47). To capture this generalization, Noyer proposes a morphologically conditioned rule of truncation under which the second syllable of a disyllabic suffix (-uuna, -iina, -aani) realizing {–perf, ind} is truncated in the context of {subjunctive} or {jussive}. By contrast, we analyze these disyllables as sequences of two separate suffixes, which captures Noyer's observation and avoids a rule of truncation, a relatively rare and marked type of process.

Noyer (Reference Noyer1997) analyzes the prefix y- as an elsewhere marker, which is expected to appear in any prefixal position that is not already occupied. We analyze it as an exponent of {3} since it only occurs in the context of {3}. We analyze t- as an exponent of {3, fem} so that based on *Feature Split it blocks y- in the environment of {3, fem} except where -na {fem, pl} occurs.Footnote ¹⁹

The jussive mood does not have an overt exponent. One way to express the jussive mood is to posit a zero suffix (see Noyer Reference Noyer1997) so that we can maintain the generalization that in the so-called Classical Arabic prefixal conjugation ‘every verb has at least and at most one suffix and at least and at most one prefix’ (Noyer Reference Noyer1997: 31). We can also assume that there is simply no exponent of the jussive mood. Under this assumption, a word has at most one suffix rather than exactly one suffix.

Finally, we use a templatic constraint to account for the distribution of -u, which realizes {–perf, ind}, and -a, which realizes {subjunctive}.Footnote ²⁰ Our generalization is that -u and -a show up in the positions that no other suffix can fill in. Without a templatic constraint that requires a word to have at most one suffix, it will be hard to explain why t-aktub-na {2, fem, pl, –perf, ind} is grammatical while *t-aktub-u-na in which t- realizes {2}, -u realizes {–perf, ind}, and -na realizes {fem, pl} is ungrammatical. This templatic constraint is defined as follows:

1. (12) Verb Stem – Suffix (≦1): An inflected verb can have at most one suffix.

We encode our analyses of the Classical Arabic affixes into realization constraints. The grammar that consists of realization constraints, *Feature Split, and Verb Stem – Suffix (≦1) is presented as follows.Footnote ²¹ For a clearer presentation, we rank *Feature Split lower than the realization constraints that introduce extended exponence. The grammar in (13) captures every cell of the paradigms in (9).Footnote ²² It is by no means the only possible ranking, given that the ranking of constraints like {1, sg}: - and {3}: y- is indeterminate.

1. (13) {2, fem, sg, –perf, ind}: -na, {masc, pl, –perf, ind}: -na, {dual, –perf, ind}: -ni >> {2, fem, sg}: -ii, {masc, pl}: -uu, {dual}: -aa>>{2}: t- >>

   *Feature Split, Verb Stem – Suffix (≦1)>>{fem, pl}: -na >>

   {3, fem}: t-, {1, sg}: ->>{1}: n-, {3}: y-, {–perf, ind}: -u, {subjunctive}: -a

Cases of extended exponence like t-aktub-ii {2, fem, sg, subjunctive} in which {2} is realized by both t- and -ii are accounted for by ranking the realization constraints {2, fem, sg}: -ii and {2}: t- higher than *Feature Split. The case of discontinuous bleeding in which -na {fem, pl} blocks t- {3, fem} in the context of {3, fem, pl} (y-aktub-na vs. *t-aktub-na) can only be ascribed to *Feature Split and the ranking *Feature Split>>{fem, pl}: -na>>{3, fem}: t->>{3}: y-. Thus *Feature Split crucially ranks between the two realizations for {2} that violate it and the realizations for {fem} and {pl} that obey it. See the tableau in (14).

1. (14) y-aktub-na {3, fem, pl}

   

Realization OT provides a unified account of blocking and extended exponence in Arabic without recourse to a distinction between primary and secondary exponents. Curiously, in Biblical Hebrew, we find t-aktub-na not only for {2, fem, pl, –perf} but also for {3, fem, pl, –perf}, rather than y-aktub-na, as in Arabic. The Hebrew form can be derived by ranking *Feature Split lower than both realization constraints, thus allowing both t- {3, fem} and -na {fem, pl} to realize {fem} simultaneously in the {3, fem, pl, –perf} form, rather than blocking the extended exponence (as in Arabic).Footnote ²³

We can imagine that Stump (Reference Stump2001) would assume that, for example, blocking of n- {1} by - {1, sg} in Arabic takes place within a single rule block while the occurrence of both t- {2} and -ii {2, fem, sg} is accounted for by placing t- and -ii in two rule blocks. This analysis is subject to the same criticism as above: the lack of a unified explanation for blocking and extended exponence and the inability to handle discontinuous bleeding.

The languages we have discussed so far by no means exhaust the list of those in which blocking and/or extended exponence occurs, but they suffice to illustrate our model, which can easily apply to many others with blocking and/or extended exponence. A few more languages show extended exponence.Footnote ²⁴ In Ancient Greek, ‘Perfective has extended exponents in e-le-lí-k-e-te (le-, y not y:, -k-); likewise Past (e-, -e-); likewise Active (-k-, -e-, -te)’ (Matthews Reference Matthews1991: 180). In Icelandic, the verb hafðir ‘have’ {2, sg, pret, ind} shows extended exponence, i.e. {sg} is doubly realized by the suffixes -i and -r and {pret} is realized by the suffixes -ð, -i as well as the stem vowel a (Anderson Reference Anderson1992: 55). In Welsh Romany, the preterite is realized by both the suffix -d and the suffixes that realize person and number as well (e.g. kam-d-án ‘love’+pret+2.sg.pret) (Stump Reference Stump1993: 450, citing Sampson Reference Sampson1926). In Archi, class markers representing the class of the head, which is not in the example (15), show up several times in a word. As seen in (15), ‘the root is as:á “of myself”, ej and u are suffixes, as is t:u, which forms adjectives’ (Corbett Reference Corbett1991: 108, citing Kibrik Reference Kibrik1977). In this example, d and r are markers of class II.

1. (15) d-as:á- r-ej- r-u-t:u- rII-of.myself-II-suffix-II-suffix-suffix-II‘my own’ [female]

These examples of extended exponence are fully compatible with Realization OT, which relies on violable markedness constraints such as *Feature Split.Footnote ^25, Footnote ²⁶ It is no surprise to the proposed Realization OT model that a morphosyntactic or semantic feature value can be multiply realized.

2.4 Problems in other languages

Noyer's and Stump's models encounter problems in other languages, such as Barasana, Batsbi, and Lezgian. This section continues to illustrate the problems of rule blocks and a distinction between primary and secondary exponents with data from these languages.

In Barasana (a Tukanoan language of Colombia and Brazil), a number of suffixes can affect stem tone. The Non3rdSubj suffix -b causes H(igh tone) to align all the way to the right in words containing it, while the interrogative suffix -ri causes H to align all the way to the left (Gomez-Imbert & Kenstowicz Reference Gomez-Imbert and Kenstowicz2000, Pycha Reference Pycha2008, Inkelas to appear). See (16), in which the stem baa- ‘swim’ contains a lexical tone H+L(ow tone). Noyer's (Reference Noyer1992, Reference Noyer1997) model would ascribe the tonal changes in (16) to morphologically conditioned phonology or secondary exponence because he assumes that ‘[f]eature-changing rules (overwriting affixes) are always secondary exponents, which are expressed by dynamic rules’ (Noyer Reference Noyer1997: liv).

1. (16)

   1. (a) baa- ‘swim’

      HL

   2. (b) baa-b ‘I/you/we swam’

      HH H

   3. (c) baa-ri ‘did he/she/they swim?’

      H

Interestingly, the joint feature set {Non3rdSubj, int} is realized by both the tone of {Non3rdSubj} and the suffix -ri. Consider (17). The tone in (17b) is the only exponent of {Non3rdSubj}, so it must be a primary exponent. Therefore, the tone of {Non3rdSubj} is paradoxically either a primary or secondary exponent, depending on the context.

1. (17)

   1. (a) *baa-ri-b , *baa-b -ri ‘did I/you/we swim?’

   2. (b) baa-ri ‘did I/you/we swim?’ HH H

Not surprisingly, additional mechanisms could be introduced to circumvent this paradox. For example, a zero morpheme could be added to (17b) (either baa-ri-Ø or baa-Ø-ri) so that the tone in (17b) still accompanies a primary zero exponent. Such a use of zeroes would make Noyer's model unfalsifiable.

Both the extended exponence in (16b) and the non-occurrence of -b in (17b) can be accounted for under the following Realization OT grammar.Footnote ²⁷ We assume that {1} and {2} form a natural class {part(icipant) (in the speech act)} (see Siewierska Reference Siewierska2004). *Feature Split is outranked by the two constraints realizing {part, subj}, one of which spells out the suffix -b and the other of which requires H to occur throughout. This derives the extended exponence in (16b). Additionally, we refer to the phonological constraint Wd-Binary (Broselow & Xu Reference Broselow, Xu, Boersma and Cutillas2004), which requires a word to consist of two syllables. Both Wd-Binary and {int}: -ri block the occurrence of -b in (17b).

1. (18) Wd-Binary, {int}: -ri >>{part, subj}: -b , {part, subj}: HHH >> *Feature Split

The tableaux illustrating the above grammar are presented in (19). In (19a) Candidate b is ruled out because H does not occur throughout. In (19b) Candidate b is ruled out because it is trisyllabic and therefore violates Wd-Binary. Candidate c is ruled out because {int} is not realized.

1. (19)

   1. (a) baa-b (HHH) ‘I/you/we swam’

      

   2. (b) baa-ri (HHH) ‘did I/you/we swim?’

      

Noyer's distinction between primary and secondary exponents encounters difficulties in Batsbi (a language of the Nakh-Dagestanian family) as well. Harris (Reference Harris2009) argues convincingly that gender and number in verbal agreement are realized in Batsbi by the same morph that iteratively occurs in a word. In a Batsbi sentence, a verb agrees in gender and number with a noun that takes an absolutive case. Harris places Batsbi nouns into eight classes based on the corresponding agreement marker of a verb. Each of the classes assigns a distinct set of agreement markers to a verb. See the following paradigm, in which ex is a verbal stem, -o is a present tense marker, and anŏ is an evidential marker. When ex agrees with a first class singular noun, for example, it will take an agreement marker v-, which may iteratively precede each of the affixes that follow the verbal stem ex. Noyer would presumably consider the initial agreement marker a primary exponent of gender and number and the following repetitions secondary, so that they won't be blocked by the primary exponent. If so, we have to assume that the initial agreement marker and its following repetitions within the same word (e.g. v-ex- v-o- v-anŏ) are distinct morphemes, given their varied morphemic information, even if they are phonologically identical. This is an undesirable result, because it sacrifices the simpler generalization that the phonological form of the same agreement morpheme iterates across a Batsbi verb. Additionally, there is no reason other than mechanical necessity why a distinction between primary and second exponents is made among these phonologically identical markers. We should therefore resort to other formalisms to account for the Batsbi data and will return to this data in Section 3.

1. (20) Paradigm of d-ex-d-o-d-anŏ ‘evidently she/he/they destroyed it’ in the evidential (Harris Reference Harris2009: 299)

   

Lezgian negation markers pose a problem for Stump's (Reference Stump2001) model, which disallows discontinuous bleeding. Haspelmath (Reference Haspelmath1993: 127) remarks that in Lezgian ‘the participles, the converbs, the Infinitive, the Masdar, and the Periphrasis forms are non-finite, and that the remaining verb forms are finite. Within the group of finite verb forms, the Hortative, the Optative, the Imperative, and the Prohibitive will be said to be non-indicative, the others are indicative’. Haspelmath also said (p. 133) that ‘[f]inite indicative verb forms are negated by means of the suffix -č’. The remaining verb forms, which cover various categories that do not easily fall into a natural class, are negated by the ‘elsewhere’ prefix t-. Since the two negation markers t- and -č occupy distinct position classes with respect to the stem, they belong to different rule blocks in Stump's model. Stump's model cannot explain the complementary distribution of t- and -č in the environment of, for example, the verb awun (21) or rule out an illicit form like *t-ijí-zwa-č, in which -č is expected to block t-, given that blocking of exponents does not apply across rule blocks in Paradigm Function Morphology.Footnote ²⁸

The blocking of t- by -č is easily accounted for under the Realization OT grammar: *Feature Split>>{neg, ind}: -č>>{neg}: t-. See the tableau in (22) below for an illustration of this grammar. We assume that an input consists of a stem ijí and {–perf, ind, neg}. We propose the constraint {–perf}: -zwa to realize the imperfective feature.

1. (21) awun ‘do’ (adapted from Haspelmath Reference Haspelmath1993: 135)

   

1. (22) Lezgian ijí-zwa-č