Morphological Complexity and Prosodic Minimality

Abstract It is widely attested, cross-linguistically, for both words and prosodic morphemes to be required to be minimally bimoraic or disyllabic. Work since McCarthy and Prince (1986) argues that these minimality effects fall out from the Prosodic Hierarchy. Requiring the relevant morpheme to be a Prosodic Word and dominate a stress Foot automatically also imposes a two mora or two syllable minimality requirement. In this paper I show, based on a reanalysis of reduplication in Axininca Campa, that this Prosodic Hierarchy-based theory of minimality is inadequate. I argue instead that morphological minimality conditions are better explained as a form of Head-Dependent Asymmetry (Dresher and van der Hulst 1998). Head morphemes are enhanced by requiring more complex prosodic structure, mirroring their more complex morphological structure. This alternative approach not only provides a uniform account of minimality effects holding for Axininca Campa reduplication, it also solves the problems raised by McCarthy and Prince’s (1993, 1995) analysis of the data. Key words: compounds, head-dependent asymmetry, minimal word, minimality, onset, Optimality Theory, positional prominence, prosodic hierarchy, prosodic word, reduplication, stem; Axininca Campa, Diyari. * I would like to thank an anonymous reviewer, the editors of this volume as well as audiences at NYU, SUNY-Stony Brook, the 12th Manchester Phonology Meeting, OCP2 in Tromsø, and the University of Barcelona for thought-provoking comments and questions on earlier versions of this work. Both the presentation and content of the analyses have been improved as a result of responding to these comments. Any errors of fact or interpretation are, of course, my responsibility. Catalan Journal of Linguistics 4, 2005 83-106 Morphological Complexity and Prosodic Minimality* Laura J. Downing Zentrum für Allgemeine Sprachwissenschaft, Typologie und Universalienforschung (ZAS) Jägerstrasse 10-11, D-10117 Berlin (Germany) do[email protected] Table of Contents 1. Introduction 2. How the Prosodic Hierarchy accounts for minimality 3. Minimality and reduplication in Axininca Campa 4. An alternative approach to minimality: time for a pedicure! 5. Conclusion References Cat.Jour.Ling. 4 001-252 7/2/06 11:44 Página 83 1. Introduction As work like McCarthy and Prince (1986) shows, it is widely attested, cross-linguistically, for the lexical words of a language to be required to have a minimum size, typically two moras or two syllables. Prosodic morphemes, like reduplicants, also often have this same minimum size. The standard analysis of these minimality effects is that they fall out from the Prosodic Hierarchy (McCarthy and Prince 1986, 1993, 1999; McCarthy 2000; Hayes 1995; Prince and Smolensky 1993; Selkirk 1995): (1) Prosodic Hierarchy In this hierarchy, each Prosodic Word must contain at least one stress Foot; and each stress Foot must contain minimally (and maximally) two moras or two syllables. Therefore, any morpheme parsed as a distinct Prosodic Word must minimally contain one bimoraic or disyllabic stress foot. Minimality (and maximality) conditions on morphemes are then straightforwardly accounted for by parsing the relevant morpheme as a Prosodic Word. While this theory of minimality is very elegant, it faces recognized empirical problems. For example, work like Downing (1999, 2000, 2005) shows that the reduplicative morpheme in many Bantu languages is minimally disyllabic, yet tonal processes do not treat the reduplicative morpheme as a separate Prosodic Word from the Base. Similarly, Urbanczyk (1996) shows that the distributive reduplicative morpheme in Lushootseed is a CVC syllable, yet this syllable type is not a possible minimal foot in the quantity-insensitive trochaic stress system of the language. A further problem is that work like Itô (1990) and Ussishkin (2000) has shown that derived words are often subject to a disyllabic minimality condition while underived words are not, even though both are clearly Prosodic Words. The goal of this paper is to argue for an alternative theory of minimality conditions which addresses these problems. I follow Dresher and van der Hulst (1998) in proposing that morphological minimality conditions are better explained through the correlation between morphological and phonological complexity that follows from Head-Dependent Asymmetries pervasive in phonological systems. More concretely, Head morphemes like Stem and Root are subject to minimality to satisfy a requirement that Heads branch, creating an asymmetry with non-branching nonHeads (Affixes). Derived words (Stems) can be subject to a disyllabic minimality 84 CatJL 4, 2005 Laura J. Downing Prosodic Word Foot σ µ Cat.Jour.Ling. 4 001-252 7/2/06 11:44 Página 84 requirement while underived words are not, as they have more complex morphological structure. The argument is organized as follows. Section 2 briefly presents reduplication in Diyari to illustrate the Prosodic Hierarchy-based theory of minimality. Section 3 presents McCarthy and Prince’s (1993, 1995) analysis of Axininca Campa reduplication, and shows that it in fact contradicts the central claim and predictions of the Prosodic Hierarchy-based theory of minimality. Section 4 develops an alternative theory of minimality, and illustrates it with a reanalysis of Axininca Campa reduplication. 2. How the Prosodic Hierarchy accounts for minimality The central claim of the Prosodic Hierarchy-based theory of minimality (McCarthy 2000; McCarthy and Prince 1993, 1994a, b, 1999; Prince and Smolensky 1993) is that any constituent (e.g., word or reduplicative morpheme) subject to a bimoraic/ disyllabic minimality condition is parsed as a distinct Prosodic Word. Markedness constraints define each Prosodic Word as minimally (and maximally) coextensive with a stress Foot, the constituent dominated by Prosodic Word in the Prosodic Hierarchy (1). To illustrate, in Diyari (an Australian language) the reduplicative prefix (underlined) is disyllabic: (2) Diyari reduplication (McCarthy and Prince 1994a: 350, fig. (29)) a. wíla wíla-wíla ‘woman’ b. kánku kánku-kánku ‘boy’ c. kúkuŋakúku-kúkuŋa ‘to jump’ d. tílparku tílpa-tílparku ‘bird sp.’ e. ŋánkantiŋánka-ŋánkanti ‘catfish’ As McCarthy and Prince (1994a, b, 1995, 1999) argue, we can account for this disyllabic size constraint without recourse to a reduplicative template. The reduplicant is labeled a Stem, so that the reduplicative construction is a Stem-Stem compound. The constraints in (3) correctly optimize its disyllabic minimal and maximal size: (3) a. STEM →PRWORD HOMOLOGY: Stem ≈Prosodic Word (McCarthy 2000) Align the left and right edges of every Stem with the left and right edges of some Prosodic Word. b. HEADEDNESS (Orie 1997; Selkirk 1995) Any prosodic category [of the Prosodic Hierarchy (1)] Cimust dominate a Ci-1 [e.g., Prosodic Word must dominate a Foot]. c. BINARITY (McCarthy and Prince 1993; Prince and Smolensky 1993; Orie 1997) A prosodic constituent contains exactly two daughters [i.e., Prosodic Word contains exactly 2 Feet; Foot contains exactly two syllables or moras; syllable contains exactly two moras]. Morphological Complexity and Prosodic Minimality CatJL 4, 2005 85 Cat.Jour.Ling. 4 001-252 7/2/06 11:44 Página 85 By transitivity, each Stem (reduplicative or other) must minimally contain two syllables or two moras. This approach is known as Prosodic Hierarchy-based Generalized Template Theory (GTT) because the general principles of constituent parsing and constituent size in (3) define the size constraints on reduplicative morphemes. No reduplicationspecific template is required. This theory of minimality makes the following predictions, all borne out by Diyari (McCarthy and Prince 1995, 1999; Poser 1989). All morphemes parsed as Prosodic Words satisfy the same minimality requirement. In Diyari, reduplicative morphemes, like other Prosodic Words are minimally disyllabic (Poser 1989). Each Prosodic Word is a stress domain (i.e., independently aligned with stress Feet). In Diyari, the reduplicative morpheme is assigned main stress, independent of the Base, like other Prosodic Words. All morphemes parsed as Prosodic Words undergo the phonological processes conditioned by the Prosodic Word domain (edge). In Diyari, the reduplicative morpheme ends in a vowel, a requirement holding for all Prosodic Word-final syllables. As McCarthy and Prince (1995, 1999) and Poser (1989) argue, defining the reduplicant as simply a Foot, rather than a Prosodic Word, would incorrectly predict that the reduplicant Foot and Base Foot would segmentally match, to give, for example: *(tjílpar) = (tjílpar)ku. In the next section, we shall see how this theory attempts to account for minimality conditions on Axininca Campa reduplication (McCarthy and Prince 1993, 1995). In fact, it will become clear that the analysis of Axininca Campa raises serious problems for Prosodic Hierarchy-based GTT. 3. Minimality and reduplication in Axininca Campa1 3.1. The data to be accounted for Axininca Campa is an Arawakan language spoken in Peru. Verbs in Axininca Campa have the morphologically complex structure in (4): (4) Verb structure of Axininca Campa (Payne 1981; Wise 1986) As Payne (1981) shows, all verbs consist minimally of a Stem + Tense/Aspect suffix. The Stem ((Prefix) + Root) is the Base for reduplication (and inflectional 86 CatJL 4, 2005 Laura J. Downing 1. The data in the paper comes from Payne (1981), Spring (1990, 1991) and McCarthy and Prince (1993, 1995). Citations are mainly to McCarthy and Prince (1993, 1995), to facilitate comparison with their analysis. Verb Word Stem Suffix(es) (Prefix) Root Cat.Jour.Ling. 4 001-252 7/2/06 11:44 Página 86 affixation), and forms a distinct phonological domain from the rest of the word (Payne 1981; McCarthy and Prince 1993). While the Stem is canonically bimorphemic, prefixes do not occur in the infinitive. The data in (5) show that total Stem reduplication is productive for verbs. Note, though, that the Prefix is not reduplicated if the Root has two or more syllables. (In the following examples, «]» marks the right Stem edge; the reduplicative morpheme (RED) is underlined; prefixes are italicized; epenthesized material is also italicized.) (5) C-initial Stems of two or more syllables (McCarthy and Prince 1993: 63, fig. (1), 64, fig. (4); Spring 1990: 106) a. Without prefix b. With prefix kawosi]-kawosi-wai-t-aki ‘bathe’ noŋ -kawosi]-kawosi-wai-t-aki taaŋki]-taaŋki-wai-t-aki ‘hurry’ non -taaŋki]-taaŋki-wai-t-aki kinta]-kinta-wai-t-aki ‘tell’ noŋ -kinta]-kinta-wai-t-aki The role of minimality in Axininca Campa reduplication is illustrated by the monosyllabic and vowel-initial Roots in (6) and (7). As shown in (6), monosyllabic C-initial Bases are augmented either by epenthesis (6a) or by including the Prefix in the Base (6b). A further point illustrated by the prefixed forms is that the Base and reduplicative morpheme are both disyllabic if the Base is a bimorphemic Prefix-Root complex. Bimoraic Bases (and reduplicative morphemes) are not augmented to disyllabicity, though, showing that this is an alternative minimality target: (6) C-initial monosyllabic Stems (McCarthy and Prince 1993: 63, 64)2 a. Without prefix b. With prefix paa]-paa-wai-t-aki ‘feed’ no-wa]-nowa-wai-t-aki /p-/ naa]-naa-wai-t-aki ‘chew’ no-naa]-nonaa-wai-t-aki /naa-/ *no-naa]-naa-wai-t-aki nata]-nata-wai-t-aki ‘carry’ no-na]-nona-wai-t-aki /na-/ tota]-tota-wai-t-aki ‘kiss, suck’ non-to]-nonto-wai-t-aki /to-/ The vowel-initial roots in (7) confirm the role of a disyllabic minimality condition on the reduplicative morpheme. The data in (7a, b) show that the initial vowel of longer roots does not appear in the reduplicative morpheme, arguably to avoid hiatus between the Base and the reduplicative morpheme. However, the initial vowel of disyllabic Roots (7c, d) does appear in the reduplicative morpheme, even if the remainder would be bimoraic (compare the first two forms in (6a) with (7c)). The motivation for including the initial vowel must be to satisfy disyllabic minimality: Morphological Complexity and Prosodic Minimality CatJL 4, 2005 87 2. As McCarthy and Prince (1993: fn. 24) note, the Root-initial /p/ in the form for ‘feed’ in (6b) spirantizes to [w] after a prefixal vowel by a regular —though phonologically idiosyncratic— process of Axininca Campa. Cat.Jour.Ling. 4 001-252 7/2/06 11:44 Página 87 (7) V-initial Roots (McCarthy and Prince 1993: 63, 64) Roots of 3 or more syllables: a. Without prefix b. With Prefix osaŋkina]-saŋkina-wai-t-aki ‘write’ n-osaŋkina]-saŋkina-wai-t-aki osampi]-sampi-wai-t-aki ‘ask’ n-osampi]-sampi-wai-t-aki aacika]-cika-wai-t-aki ‘stop’ n-aacika]-cika-wai-t-aki Disyllabic Roots («||» indicates Prosodic Word break): c. Without prefix d. With prefix api || apii-wai-t-aki ‘repeat’ n-apii]-napii-wai-t-aki *api || pii-wai-t-aki asi || asi-wai-t-aki ‘cover’ n-asi]-nasi-wai-t-aki ooka || ooka-wai-t-aki ‘abandon’ n-ooka]-nooka-wai-t-aki As we can see, both the Base Stem and the reduplicative morpheme are subject to minimality requirements in Axininca Campa. A critical review of McCarthy and Prince’s (1993, 1995) analysis of these minimality effects is presented in the next section. 3.2. McCarthy and Prince’s (1993, 1995) analysis McCarthy and Prince (1993, 1995) develop a detailed analysis of Axininca Campa reduplication. This section summarizes their treatment of the minimality conditions holding for the reduplicative morpheme and the Base. The data in (6) show that bimoraic Roots must satisfy a minimality condition on the Base, as they are not augmented. This is accounted for by the constraint in (8) defining the Base for suffixation (including reduplication) as a Prosodic Word: (8) ALIGNSFX: Align(L, Suffix; R, Prosodic Word) The left edge of every suffix coincides with the right edge of some Prosodic Word (McCarthy and Prince 1995: 300). As the minimal stress Foot in Axininca Campa is minimally bimoraic, Prosodic Words must also be minimally bimoraic (McCarthy and Prince 1995). The constraint in (8), then, is consistent with Prosodic Hierarchy-based GTT in accounting for the minimality conditions on the Base by parsing it as a Prosodic Word. The constraint in (9) accounts for why CV Bases are augmented to two syllables rather than only two moras: augmenting to two moras by lengthening the input vowel would misalign the input stem with a syllable. (9) ALIGN-R: Align(Stem, Right; σ, Right) The right edge of every [lexical] stem coincides with the right edge of some syllable (McCarthy and Prince 1995: 306). 88 CatJL 4, 2005 Laura J. Downing Cat.Jour.Ling. 4 001-252 7/2/06 11:44 Página 88 These points are illustrated by the tableau in (10): (10) Candidate (10a) is optimal, as it only violates constraints against epenthesis into the Base. Not epenthesizing, as in candidate (10b), is non-optimal because this violates ALIGNSFX (8): the Base is not a bimoraic Prosodic Word. RT-ANCHORBR requires material at the right edges of the Base and the reduplicative morpheme to match. It is violated when epenthetic material in Base does not appear in RED, as candidate (10c) illustrates. Candidate (10d) is non-optimal, as lengthening the Base vowel misaligns the input stem /to-/ with the output syllable, in violation of ALIGNR(9). As we saw in (6) and (7), there is a disyllabic minimality condition on the reduplicative morpheme. As Prosodic Words are only required to be minimally bimoraic, McCarthy and Prince (1993) propose that a distinct minimality constraint is required to account for this, namely, the reduplication-specific constraint, DISYLL: (11) DISYLL (McCarthy and Prince 1993: 87, fig. (49)): The left and right edges of the Reduplicant [RED] must coincide, respectively with the left and right edges of different syllables. The constraint ranking, DEP-BR/DEP-IO » DISYLL » RED#ROOT, optimizes copying the prefix to satisfy disyllabic minimality. (The constraint RED#ROOT accounts for the fact that prefixes are only copied in order to satisfy disyllabic minimality.) The tableau in (12) exemplifies the analysis with a prefixed form of the verb in (10): (12) Notice that the winning candidate, (12a), violates only RED#ROOT by copying prefixal material. Other candidates violate higher-ranked constraints. The reduMorphological Complexity and Prosodic Minimality CatJL 4, 2005 89 /to-RED-/ ALIGNSFX ALIGN-R RT-ANCHOR-BR DEP-IO MAX-BR ☞a. tota]-tota]- ** b. to]-to]- *! c. tota]-to]- *! ** ** d. too]-too]- *! * RT-ANCHOR-RED# MAX- /non-to-RED-/ ALIGNSFX BR DEP-IO DISYLL ROOT BR ☞a. non-to]-nonto]- * b. non-to]-tota]- *! *** c. non-to]-to]- *! *** Cat.Jour.Ling. 4 001-252 7/2/06 11:44 Página 89 plicative morpheme in candidate (12b) satisfies DISYLL by epenthesizing material not found in the Base, in violation of RT-ANCHOR-BR. The reduplicative morpheme in candidate (12c) violates DISYLL. Tableau (13) shows why it is optimal not to augment bimoraic Bases: (13) Candidate (13a) is optimal, even though it violates DISYLL, as competing candidates violate higher-ranked constraints. Because bimoraic Bases satisfy ALIGNSFX (8), augmentation of a bimoraic Base incurs gratuitous DEP violations. This is why candidate (13c) is non-optimal. Augmenting only the reduplicative morpheme to a disyllable leads to a violation of RT-ANCH-BR, as shown by non-optimal candidate (13b). The prefixed forms in the second candidate set in (13) show the independent roles of ALIGNSFX (8) and DISYLL (11) in choosing the optimal candidate. In non-optimal (13e), the Base satisfies minimality (ALIGNSFX), but the reduplicative morpheme violates the reduplicative minimality constraint (DISYLL). While the analysis works, it is obvious that DISYLL (11) violates the principles of Prosodic Hierarchy-based GTT. All minimality constraints should fall out from parsing the relevant morpheme as Prosodic Word. Construction-specific size constraints like DISYLL (11) are never to be resorted to. The analysis of the vowel-initial forms in (7) emphasizes why the reduplicative morpheme cannot be parsed as a Prosodic Word to account for disyllabic minimality. Prosodic-Word initial position is the one place where onsetless syllables are tolerated in Axininca Campa (Payne 1981; Spring 1990; McCarthy and Prince 1993). If the reduplicative morpheme were a Prosodic Word, it would be optimal to copy the initial vowel. Yet, the data shows that the initial vowel is only copied to satisfy DISYLL (11). These points are made clear by the tableau in (14), where the «||» notation indicates that the Base and the reduplicative morpheme have been parsed into separate Prosodic Words:3 90 CatJL 4, 2005 Laura J. Downing 3. Prosodic Word-initial ONSET violations are not counted in (14) and (15) as an abbreviatory convention to keep the tableaux to a more manageable size. In McCarthy and Prince’s (1993) full analysis, ONSET violations in Prosodic Word-initial position do not count in choosing optimal RT-ANCHOR-RED# MAX- /naa-RED-/ ALIGNSFX BR DEP-IO DISYLL ROOT BR ☞a. naa]-naa]- * b. naa]-naata]- *! c. naata]-naata]- *!* RT-ANCHOR-RED# MAX- /no-naa-RED-/ ALIGNSFX BR DEP-IO DISYLL ROOT BR ☞d. no-naa]-nonaa]- * e. no-naa]-naa]- *! ** Cat.Jour.Ling. 4 001-252 7/2/06 11:44 Página 90 (14) Analysis of disyllabic V-initial Root In the optimal candidate (14a), the reduplicative morpheme begins a new Prosodic Word. This allows it to satisfy the ONSET constraint, as only ONSET violations which are not in Prosodic Word-initial position are counted. The initial vowel allows this candidate to also satisfy DISYLL.4Candidate (14b), which omits the initial vowel in the reduplicative morpheme, violates DISYLL, while candidate (14c), with a suffixal reduplicative morpheme, violates ONSET. (ALIGNSFX (8) is omitted in this tableau and the next. The inputs satisfy the constraint, so it cannot play a role in choosing optimal candidates.) The analysis of the disyllabic vowel-initial verb stems cannot be extended straightforwardly to longer vowel-initial stems, however. The problem is, if the Base and the reduplicative morpheme can be parsed in separate Prosodic Words, the pattern found with longer verb stems in (7a, b), where the reduplicative morpheme omits the initial vowel, should not be optimal. This is shown by the tableau in (15): (15) Analysis of longer V-initial Roots Morphological Complexity and Prosodic Minimality CatJL 4, 2005 91 candidates for the usual OT reason: a higher-ranked constraint requires left-edge alignment of Prosodic Word and Stem. RIGHT-ANCHOR-BR is also left out of these tableaux, as it is too highranked to play a role in choosing the optimal candidates. 4. In candidate (14a), the input Base long vowel is shortened as it occurs word-finally, by a regular process of Axininca Campa phonology (Payne 1981; McCarthy and Prince 1993). /apii-RED-/ ONSET DEP-IO DISYLL RED # ROOT MAX-BR ☞a. api || apii]- b. apii]-pii]- *! * c. apii]-apii]- *! /n-apii-RED-/ ONSET DEP-IO DISYLL RED # ROOT MAX-BR ☞d. n-apii]-napii]- * e. n-apii]-pii]- *! ** f. n-apii]-apii]- *! * /osaŋkina-RED-/ ONSET DEP-IO RED # ROOT MAX-BR a. osaŋkina]-saŋkina]- *! b. osaŋkina- || osaŋkina]- c. osaŋkina]-osaŋkina]- *! /n-osaŋkina-RED-/ ONSET DEP-IO RED # ROOT MAX-BR d. n-osaŋkina]-saŋkina]- *!* e. n-osaŋkina- || osaŋkina]- * f. n-osaŋkina]-nosaŋkina]- *! Cat.Jour.Ling. 4 001-252 7/2/06 11:44 Página 91 verbs illustrated in (5). (ALIGNPRSTEM (23) is omitted from the tableaux in this section, however, as it is never violated and so never chooses the optimal candidate.) Recall that the monosyllabic C-initial stems in (6) and the vowel-initial stems in (7), above, provide evidence for minimality requirements on the Base and reduplicative Stems. As we can see from this data, the Base and the reduplicative Stems are usually identical in size, and the reduplicative Stem matches the augmentation strategy of the Base. Both the Base and the reduplicative Stems are mostly minimally disyllabic, and the disyllabic minimality requirement is never violated when the Base contains a prefix. This is, indeed, what we expect, as the Base and the reduplicative morpheme are defined as minimally disyllabic by PROSODICSTEM (22b). However, we can see that, in a few cases when the Base is a monomorphemic Root, the Base and reduplicative Stems can be bimoraic. Bimoraic Base stems are not augmented, and consonantal stems, like /p-/ ‘feed’, are augmented to a bimoraic monosyllable not a disyllable. These conflicting minimality constraints on the Base Stem — bimoraic vs. disyllabic— reflect that the Base for reduplication is only optionally bimorphemic. When it does not contain a prefix, it can be bimoraic, the minimum size required for Roots by HEADSBRANCH (20a). When the Base Stem does include a prefix, it is always minimally disyllabic, satisfying PROSODICSTEM (22b). The role of these conflicting minimality requirements in accounting for Axininca Campa reduplication patterns is defined by the constraint ranking: HEADSBRANCH (20a) » DEP-IO » PROSODICSTEM (22b). HEADSBRANCH (20a) outranks DEP-IO, as moras (and segments to realize the moras) are optimally epenthesized to satisfy the bimoraic minimality requirement on monomorphemic Bases. DEP-IO outranks PROSODICSTEM (22b), as only material present in the input is recruited to satisfy the disyllabic minimality requirement imposed on Prosodic Stems. (DEP-IO and DEP-BR evaluate moras and associations between segments and moras in this analysis, rather than segments as in McCarthy and Prince’s 1993, 1995 analysis. The motivation for this is that material is being epenthesized to satisfy constraints on the prosodic, rather than the segmental, composition of these forms.) The analysis of the bimoraic C-initial Roots is exemplified in (26). (In the analysis in this section, «[ ]» indicates Prosodic Stem edges.) (26) 98 CatJL 4, 2005 Laura J. Downing HEADS DEP-IO ALIGN /naa-PrStemRED-/ BRANCH DEP-BR PRSTEM PREFIX MAX-BR ☞a. [naa]-[naa]- ** b. [naa]-[naata]- *!(BR) * c. [naata]-[naata]- *!(IO) HEADS DEP-IO ALIGN /no-naa-PrStemRED-/ BRANCH DEP-BR PRSTEM PREFIX MAX-BR ☞d. [no-naa]-[nonaa]- * e. [no-naa]-[naa]- *! ** f. [no-naa]-[naata]- *!(BR) ** Cat.Jour.Ling. 4 001-252 7/2/06 11:44 Página 98 In the first candidate set, the bimoraic Base (containing only a Root) satisfies high-ranked HEADSBRANCH, so it is optimally not augmented (candidate (26a)). Competing candidates with disyllabic Bases and/or reduplicative morphemes are non-optimal as they gratuitously violate DEP, the constraint banning augmentation. In the second candidate set, we see in candidate (26d) that including the prefix in the Base Prosodic Stem and copying it in the reduplicative Prosodic Stem is optimal, as this allows both to satisfy the disyllabic minimality requirement (PROSODICSTEM (22b)). Candidate (26e) is non-optimal, as it violates PROSODICSTEM (22b). Candidate (26f) incurs gratuitous DEP violations, as it satisfies PROSODICSTEM (22b) by epenthesis rather than copying the Base. (In the tableau, candidates (26b, c, f) earn one violation each of DEP, because in each case only one mora has been inserted.) This tableau shows that in this approach there is no need for a distinct disyllabic size requirement on the reduplicative morpheme comparable to DISYLL (11) in McCarthy and Prince’s analysis. Instead, the disyllabicity requirement falls out from the Prosodic Stem status of both the Base and the reduplicative morpheme, motivated by the canonical bimorphemic structure of the Base. As shown by the data in (6), some monomorphemic Bases are augmented to disyllabicity. In McCarthy and Prince’s (1993, 1995) analysis, a special constraint, ALIGN-R (9), was required to account for this. As shown by the tableau in (27), no new constraints are required in this analysis: (27) In the first candidate set, the monomoraic Root is optimally augmented by epenthesizing a mora (candidate (27a)) to satisfy HEADSBRANCH (20). Not augmenting, as in candidate (27b), violates this constraint. Since the Stem consists only of a single morpheme, the Root, we might expect it to be optimal to augment it to a single bimoraic syllable by lengthening the vowel, as in candidate (27c). While lengthening satisfies HEADSBRANCH, it fatally incurs extra DEP violations. Lengthening an input vowel involves not only inserting a mora (as in (27a)) but also changing the moraic linking of an input segment. As we can see, disyllabicity is optimal in (27a) for phonotactic reasons, not because the morphological strucMorphological Complexity and Prosodic Minimality CatJL 4, 2005 99 HEADS DEP-IO ALIGN /to-PrStemRED-/ BRANCH DEP-BR PRSTEM PREFIX MAX-BR ☞a. [tota]-[tota]- *(IO) b. [to]-[to]- *!* ** c. [too]-[too]- **!(IO) ** HEADS DEP-IO ALIGN /non-to-PrStemRED-/ BRANCH DEP-BR PRSTEM PREFIX MAX-BR ☞d. [non-to]-[nonto]- * e. [non-to]-[to]- *! * *** f. [non-to]-[tota]- *!(BR) *** Cat.Jour.Ling. 4 001-252 7/2/06 11:44 Página 99 ture requires it. In the second candidate set, (27d) is optimal for the same reasons discussed for the prefixed candidate in tableau (26). A bimorphemic Base is also disyllabic, satisfying PROSODICSTEM (22b). Copying the prefix is the optimal way for the reduplicative morpheme to also satisfy PROSODICSTEM (22b). Recall from tableaux (14) and (15), above, that the vowel-initial stems were especially problematic for McCarthy and Prince’s (1993, 1995) analysis. In this analysis, we need just one additional constraint, to account for the fact that an initial vowel is not copied for longer stems. I follow Downing (1998a, b) in proposing that the initial vowel is not copied because the Prosodic Stem, the Base for reduplication (see (23)), must be left-aligned with an Onset: (28) ALIGNONSET: AlignL(PrStem, σ) ∩ONSET.8 Ranking this constraint below DEP-IO and PROSODICSTEM (22b) optimizes making the initial vowel extraprosodic —i.e., parsed outside the Prosodic Stem (the string for evaluation by MAX-BR)— except to satisfy minimality. The analysis of the V-initial Roots is exemplified in tableaux (29) and (30):9 (29) Analysis of V-initial Root with more than two syllables Candidate (29a) is optimal in the first set. This candidate violates none of the constraints, as the initial vowel is optimally excluded from the Base Prosodic Stem to satisfy ALIGNONSET (28), and the reduplicative Prosodic Stem matches the resulting Base. In the second candidate set, it remains optimal to exclude the initial vowel from the reduplicative morpheme. Including it would require also reduplicating the prefix, in violation of ALIGNPREFIX (25), to avoid an ALIGNONSET violation. As a result, candidate (29d) is non-optimal. 100 CatJL 4, 2005 Laura J. Downing 8. See Downing (1998b) for detailed arguments in favor of formalizing this constraint as a logical conjunction, and for more examples of the role of Onset alignment in reduplication and other prosodic phenomena. 9. HEADSBRANCH is omitted from tableaux (29) and (30) as it is not violated by any of the outputs, and so plays no role in choosing the optimal candidate. DEP-IO ALIGN ALIGN MAX- /osaŋkina-PrStemRED-/ DEP-BR PRSTEM ONSET PREFIX BR ☞a. o[saŋkina]-[saŋkina]- b. [osaŋkina]-[osaŋkina]- *!* DEP-IO ALIGN ALIGN MAX- /n-osaŋkina-PrStemRED-/ DEP-BR PRSTEM ONSET PREFIX BR ☞c. [n-osaŋkina]-[saŋkina]- ** d. [n-osaŋkina]-[nosaŋkina]- *! Cat.Jour.Ling. 4 001-252 7/2/06 11:44 Página 100 As shown in (30), the same constraints and ranking straightforwardly optimize including the initial vowel in the Prosodic Stem of disyllabic vowel-initial verb stems: (30) Analysis of disyllabic V-initial Root Candidate (30a) is optimal when the Root is unprefixed. Even though it violates ALIGNONSET, all the other constraints are satisfied. This candidate shows that PROSODICSTEM (22b) crucially outranks ALIGNONSET (28). Not copying the initial vowel, as in candidate (30b), violates higher-ranked PROSODICSTEM. (As noted above, independent constraints account for word-final shortening in (30a).) This candidate also shows why the relationship between branching morphological structure and the disyllabic minimality requirement, PROSODICSTEM (22b), can be an indirect one. Since both the Base and the reduplicative morpheme are defined as Prosodic Stems, they are subject to PROSODICSTEM (22b) minimality, even when the Base is monomorphemic. However, as PROSODICSTEM (22b) is ranked below DEP, it plays a role in motivating a disyllabic Base Prosodic Stem only in this particular case: when the Base Stem provides a second syllable without epenthesis. In the second candidate set, the prefix is optimally copied, as shown by candidate (30d). Competing candidates either violate higher-ranked PROSODICSTEM (candidate (30e)) or incur gratuitous DEP violations (candidate (30f)). (MAX-BR is omitted from this tableau, as it plays no role in choosing the optimal candidate.) To sum up the analysis of Axininca Campa reduplication, I have shown that minimality constraints on the Base and the reduplicative morpheme follow from proposing that both are optimally disyllabic Prosodic Stems (22b). This analysis improves on McCarthy and Prince’s (1993, 1995) analysis of Axininca Campa in the following ways. No reference is made to Prosodic Word to define minimality, so there is no need to parse strings into Prosodic Words at one level to account for prosodic well-formedness, and reparse them at a separate level to account for all other phonological processes. Moreover, McCarthy and Prince’s (1993, 1995) minimality constraint on the reduplicative morpheme, DISYLL (11), violates the basic Morphological Complexity and Prosodic Minimality CatJL 4, 2005 101 DEP-IO /apii-PrStemRED-/ DEP-BR PRSTEM ALIGNONSET ALIGNPREFIX ☞a. [api] || [apii]- ** b. a[pii]-[pii]- *!* c. a[pii]-[piita]- *!(BR) * DEP-IO /n-apii-PrStemRED-/ DEP-BR PRSTEM ALIGNONSET ALIGNPREFIX ☞d. [n-apii]-[napii]- * e. [n-apii]-[pii]- *! f. [n-apii]-[piita]- *!(BR) Cat.Jour.Ling. 4 001-252 7/2/06 11:44 Página 101 tenet of Generalized Template Theory, which bans construction-specific size constraints. In the morphology-based alternative, the minimality requirements for both the Base and the reduplicative morpheme fall out from the general constraints requiring (Prosodic) Stems to satisfy HEADSBRANCH (20) and PROSODICSTEM (22b). As a result, this analysis better fulfills the goal of Generalized Template Theory: to account for minimality requirements through general morphological and prosodic principles. 4.3. Diyari, a slight return The Axininca Campa analysis has emphasized that the morphology-based theory of minimality predicts disyllabic minimality to hold primarily for derived Stems (or constructions based on canonically derived Stems). The Diyari reduplication pattern in (2) appears to be problematic for this proposal. We saw that there is a disyllabic minimality condition on the Prosodic Word reduplicant (and other Prosodic Words of the language), even though Prosodic Words can be monomorphemic Roots in Diyari. The theory developed here seems to predict they should be monosyllabic, as this would satisfy the MORPHEME-SYLLABLE CORRELATION in (19). I suggest that phonotactic factors independent of stress favor the disyllabic (21a) satisfaction of HEADSBRANCH in Diyari. There are no long vowels in Diyari, so the branching representation in (21b) cannot define a possible minimal word. And words cannot end in a consonant in Diyari, so the branching representation in (21c) also cannot define a possible minimal word. Therefore, disyllabic (21a) is the only representation which both satisfies the branching requirement on Head morphemes like Roots and also satisfies constraints on possible (word-final) syllables in this language. 5. Conclusion In conclusion, I have shown that the Prosodic Hierarchy-based account of morpheme minimality does not provide an adequate analysis of Axininca Campa verb reduplication. In the Prosodic Hierarchy-based theory, minimality should fall out from parsing a morpheme as a Prosodic Word, containing a stress Foot, yet neither the Base nor the reduplicative morpheme are independent Prosodic Words in Axininca Campa. I have proposed that an alternative, morphology-based approach to minimality provides a better analysis. In this approach, stems and other morphologically derived constructions have a tendency to be minimally disyllabic because they are minimally bimorphemic. This falls out from the MORPHEMESYLLABLE CORRELATION (19). Lexical monomorphemes (Roots) are also subject to minimality conditions because of the HEADSBRANCH (20a) requirement. In Axininca Campa, defining the Base for reduplication and the reduplicative morpheme as Prosodic Stems straightforwardly accounts for why they are subject to a disyllabic minimality constraint: the Base is a canonically bimorphemic stem. The Base can, however, consist only of a Root. 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