Optimizing Verbal Agreement In Mordvin Rau´l Aranovich

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OPTIMIZING VERBAL AGREEMENT IN MORDVIN Rau´l Aranovich Abstract. In the Mordvin definite conjugation, portmanteau verbal affixes crossreference the person and number of both subject and object. This complex agreement system shows extensive syncretism, which is more acute among the most marked members of the paradigm. I argue that Optimality-Theory gives a more explanatory account of the pattern of neutralizations in the Mordvin verb than rule-based theories. Predictions of the analysis are tested against data from other Finno-Ugric and Uralic languages. 1. Introduction In Inflectional languages, it is common to see that the contrast between two or more members of a paradigm is neutralized. This is known as syncretism. This phenomenon is often regarded as too exceptional and unsystematic to deserve any consideration as a serious issue in morphology, but the frequent occurrence of syncretic forms in all kinds of inflectional paradigms underscores its importance. Moreover, syncretisms display some regular properties that require explanation, in particular the fact that syncretic forms tend to affect the more marked components of a paradigm. In this paper I examine a quite dramatic case of syncretism in the verbal paradigm of Mordvin, an Uralic (FinnoUgric) language of central Russia. I argue that the more marked an agreement morpheme is in Mordvin, the more likely it is to be syncretic. This hypothesis, I show, can be elegantly captured in an OptimalityTheoretic treatment of syncretism. The analysis is based on a ranking of faithfulness constraints partially motivated by a universal, multidimensional agreement hierarchy of person and number. My analysis assumes that syncretic morphemes are underspecified for certain features, an assumption shared with impoverishment theories of syncretism (Bonet 1995, Noyer 1998). But I argue that an OT treatment of syncretism is more explanatory than a rule-based impoverishment account, as well as an account based on rules of referral (Zwicky 1985, Stump 1993, 2001). My analysis also makes some cross-linguistic predictions, which I test against data from other members of the Finno-Ugric and Uralic family. In this paper I assume a realizational theory of morphology (Matthews 1972, Anderson 1992, Stump 2001). In realizational theories, there is a distinction made between morphemes, which are abstract specifications of morphosyntactic features, and the morphophonological units that realize them. Morphemes and their realizations are connected by rules of exponence. Realizational theories are better suited than sign-based Studia Linguistica 61(3) 2007, pp. 185–211.  The author 2007. Journal compilation  The Editorial Board of Studia Linguistica 2007. Published by Blackwell Publishing Ltd., 9600 Garsington Road, Oxford OX4 2DQ, UK, and 350 Main Street, Malden, MA 02148, USA 186 Rau´l Aranovich theories to deal with cases of multiple exponence (one morpheme expressed by more than one morph), or cumulative exponence (more than one morpheme encoded in one morph). This is relevant to a treatment of verbal inflection in Mordvin, given its heavily synthetic character: subject and object agreement are encoded in a single portmanteau suffix. 2. Verbal agreement: basic types and the Mordvin system Verbal agreement is a systematic covariation between verbal morphology and some characteristic features of its arguments, most frequently person and number (although agreement in gender or class is also possible). Agreement can be marked by verbal affixes or pronominal clitics. Turkish exemplifies a very common pattern, in which the verb agrees in person and number with its subject. Other languages (v.g. Classical Nahuatl) may have additional affixes to agree with a complement.1 (1) a. Ben mektubu okudu-m. I letter.acc read-1sg ÔI read the letter.Õ b. ni-mitz-itta. 1sg.subj-2sg.obj-see ÔI see you.Õ [TURKISH] (Underhill 1976) [NAHUATL] (Andrews 1975) Yet in other languages, subject and complement are not cross-referenced by independent affixes. Rather, a portmanteau affix is used to express agreement with a pair of subject-complement arguments. Aymara is a language with this kind of agreement. (2) Jum t’’aq-tam. you.acc look.for-3.subj.2obj.aor ÔHe was looking for you.Õ [AYMARA] (Hardman et al. 1988) Mordvin is a Uralic language spoken in the Russian republic of Mordva. Like other languages in the Uralic and Finno-Ugric family (i.e. Hungarian, Ostyak, etc.), Mordvin distinguishes an ÔindefiniteÕ set of agreement affixes (used for intransitives and transitives with indefinite objects) from a ÔdefiniteÕ set of agreement affixes (used for transitive sentences with definite objects). Morphologically speaking, Mordvin is the most complex language in its family. In the definite conjugation, portmanteau agreement suffixes inflect for person and number of subject and object. Some examples are given below, followed by a table listing 1 The following abbreviations are used for grammatical categories. subj: subject; obj: object; sg: singular; pl: plural; per: person; def: definite; acc: accusative; aor: aorist; loc: local; pol: polite; fam: familiar; gen: genitive.  The author 2007. Journal compilation  The Editorial Board of Studia Linguistica 2007. Optimizing verbal agreement in Mordvin 187 the past and non-past agreement suffixes in the Erza dialect (from Raun 1988).2 In the tables below, syncretic forms are in italics. The widespread syncretism in forms that agree with a plural argument is apparent.3 (3) a. sÕormada-n ÔI writeÕ b. sÕormada-sa ÔI write itÕ [MORDVIN] The non-past definite conjugation differs from the past definite conjugation by the presence of an additional affix, placed closer to the stem. The non-past affix has three allomorphs, conditioned by the person of the object: -sa- Ônonpast.1objÕ, -ta- Ônonpast.2objÕ, and -s(i)- Ônonpast.3objÕ. In addition, some formatives can be distinguished: dental stops characterize agreement with a second person, while nasals show up in some agreement affixes that mark 1st person. These formatives may be morphophonologically related to the system of personal pronouns (mon ÔIÕ, ton Ôyou (sg)Õ and son Ôhe/she/itÕ), suggesting that agreement morphemes are affixal forms with a pronominal origin (Honti 1998– 1999).4 Beyond the formative level, the inflected verb cannot be segmented into individual subject and object agreement suffixes. Even if formatives are analyzed as independent morphemes (which is not possible in all cases), the remnants cannot be clearly identified. Formatives may Table 1. Mordvin (Erza) agreement suffixes, non-past OBJECT fi Indefinite SUBJECTfl 1sg 2sg 3sg 1pl 2pl 3pl Definite 1sg -n -t -i -tano/-dano -tado/-dado -it¢ 2sg -tan -samak -samam -tanzat -tadiz¢ -samiz¢ -samiz¢ -tadiz¢ 3sg 1pl -sa -sak -si -sin¢ek -sink -sinz¢ -tadiz¢ -samiz¢ -samiz¢ -tadiz¢ -tadiz¢ -samiz¢ -samiz¢ -tadiz¢ 2 2pl 3pl -sin¢ -sit¢ -sinze -sin¢ek -sink -sinz¢ Mordvin has two dialects, Erza and Moksha, each with its own literary tradition. Since the differences between the two dialects are not relevant for the present study, I only give examples from the Erza dialect. The inflections in tables 1 and 2 differ slightly from the ones given by Ba´tori (1990) (e.g. -ik for -k Ôpast.2sg.subj.3sg.obj.Õ), probably due to the inclusion of a thematic vowel or orthographic conventions. There is some degree of allomorphy induced by vowel harmony and palatalization in Erza, which I will overlook in the present study. 3 In the past tense, Mordvin distinguishes perfective from imperfective. There is also a periphrastic future tense, in which subject agreement is expressed by an affix on the auxiliary verb, and object agreement by a possessive affix on the non-finite form of the main verb (Ackerman 2000). My analysis is limited to the synthetic tenses. 4 Honti argues this point against Keresztes (1998–1999). Keresztes claims that the definite conjugation in Mordvin originates out of a rudimentary Proto-Uralic object agreement suffix, which is still manifested in related languages. For other points of view see Mikola (1998–1999) and Redei (1998–1999).  The author 2007. Journal compilation  The Editorial Board of Studia Linguistica 2007. 188 Rau´l Aranovich Table 2. Mordvin (Erza) agreement suffixes, past OBJECT fi Indefinite SUBJECTfl 1sg 2sg 3sg 1pl 2pl 3pl Definite 1sg -n¢ -t¢ -s¢ -n¢ek -d¢e -s¢t¢ -mik -mim -miz¢ -miz¢ 2sg 3sg -t¢in¢ -ja -k -z¢e -n¢ek -nk -z¢ -n¢z¢it -diz¢ -diz¢ 1pl -miz¢ -miz¢ -miz¢ -miz¢ 2pl 3pl -diz¢ -n¢ -t¢ -n¢z¢e -n¢ek -nk -z¢ -diz¢ -diz¢ -diz¢ offer a glimpse of an older state of the language in which subject and object agreement where encoded in two distinct verbal affixes, the object agreement one preceding the subject agreement one and placed closer to the root. But from a synchronic point of view, it is better to analyze the Mordvin definite conjugation as consisting of portmanteau morphemes, similar to the Aymara pattern. 3. Syncretism in the Mordvin agreement system The fact that the Mordvin definite conjugation is heavily syncretic is in all likelihood related to the cumulative nature of its agreement system, a hypothesis that follows from Carstairs-McCarthyÕs (1987) Systematic Homonymy Claim. Forms with a first or second person plural object neutralize contrasts in subject person or number, and forms with a plural subject show no distinctions with respect to the number of the object. The result is a system in which there is one affix for all forms with a plural argument and a first person object, and another affix for all forms with a plural argument and a second person object. Forms with a third person object preserve distinctions in subject person and number, but the contrast between singular and plural third person objects is only overt in combinations where the subject is singular. Following some approaches to syncretism (Bonet 1995, Noyer 1998, Grimshaw 2001) I propose to deal with neutralizations of person and number in the Mordvin agreement system as underspecification (or feature deletion). Inflectional elements are only specified for features shared by the syncretic morphemes (in cases where more than one form can be selected to agree with a subject/object pair, the more specific form takes precedence). I propose the following conditions for Mordvin: (4) Agreement Underspecification Conditions: a) If the Mordvin verb agrees with a plural subject, then no number features are specified for object agreement. b) If the Mordvin verb agrees with an object that is a local person and plural, then no subject agreement features are specified.  The author 2007. Journal compilation  The Editorial Board of Studia Linguistica 2007. Optimizing verbal agreement in Mordvin 189 The fact that forms which agree with a plural subject and a local person singular object are syncretic with forms that agree with a singular subject and a local person plural object is a necessary consequence of the interaction of the two conditions in (4). A morpheme with a first or second person object, and plural subject and object, must be indistinguishable from a morpheme with a plural subject and a local person plural object (condition 4a), and indistinguishable from a morpheme with a singular subject and a plural local person object (condition 4b). The only arrangement in which these two requirements can be satisfied simultaneously is one in which a morpheme with a plural subject and a local person singular object is identical to a morpheme with a singular subject and a local person plural object. The pattern of syncretism in the Mordvin verb, then, is the result of two constraint acting in concert: one neutralizing object number contrasts, the other one neutralizing number and person contrasts in the subject. This ÔglobalÕ property of Mordvin morphology is naturally accounted for in OT, as I show in section (7). The feature specifications for the inventory of agreement morphemes in the Mordvin definite conjugation are as in Table 3 (see Ba´tori 1990 for a similar analysis). An alternative that needs to be considered is one in which the syncretism of all forms with a second person or a first person object and a plural argument is accounted for by one single condition. Such condition states that if the object is a local person, and either argument is plural, then contrasts in the person of the subject and in the number of the other argument are neutralized. This approach, however, has two shortcomings. First, the condition on the syncretism of forms with local person objects is a disjunctive condition in disguise. It says that a form Table 3. Mordvin agreement suffix inventory (definite object, past only) -t¢in¢: 1sg.subj 2sg.obj -mik: 2sg.subj 1sg.obj -mim: 3sg.subj 1sg.obj -n¢z¢it: 3sg.subj 2sg.obj -ja: 1sg.subj 3sg.obj -n¢: 1sg.subj 3pl.obj -k: 2sg.subj 3sg.obj -t¢: 2sg.subj 3pl.obj -z¢e: 3sg.subj 3sg.obj -n¢z¢e: 3sg.subj 3pl.obj -n¢ek: 1pl.subj 3obj -miz¢: 1obj -d ¢iz¢: 2obj -nk: 2pl.subj 3obj -z¢: 3pl.subj 3obj  The author 2007. Journal compilation  The Editorial Board of Studia Linguistica 2007. 190 Rau´l Aranovich like -mizÕ will be used if the object is 1st person and plural or if the object is 1st person and the subject is plural, or both. Disjunctions are often a sign that a generalization has been missed. Second, an additional condition to account for the neutralization in object number when the subject is plural must be introduced for third person objects. In this analysis, then, two independent conditions account for the fact that, with plural subjects, there are no distinctions in number regarding the object. One condition states this for first or second person objects, the other one for third person objects. This analysis is clearly missing a morphological generalization, and, from this point of view, an analysis based on the conditions in (4) gives a better explanation of syncretism in Mordvin. The conditions in (4) capture another remarkable property of syncretism in the Mordvin agreement system: its relational (or quasisyntagmatic) nature. The loss of contrast in an agreement feature for one of the arguments (i.e. number of the object) is not triggered by a feature of the same argument (i.e. person of the object), but rather by the same feature in the other argument (i.e. number of the subject). Likewise, features for agreement with the object (local person plural) trigger neutralization of subject person and number agreement. The cumulative nature of verbal agreement in Mordvin justifies an analysis of complex feature structures that specify subject and object properties. Thus, the relational nature of syncretism in Mordvin notwithstanding, I still approach this problem as a paradigmatic phenomenon.5 4. Markedness and syncretism in Mordvin A generally accepted claim about possible syncretic paradigms is that morphological contrasts tend to neutralize in the presence of marked features. The Mordvin definite conjugation offers a striking instantiation of this hypothesis. Little argument exists around the claim that plural agreement is more marked than singular agreement (Moravcsik 1988). The fact that all Mordvin syncretic forms occur when the verb agrees with a plural subject or object, then, is expected.6 When person features are considered, however, markedness is relative to their association with grammatical relations. In a well-known study of split ergative systems, Silverstein (1976) established that the local persons in the dialogic 5 Noyer (1998) discusses a case of ÔsyntagmaticÕ syncretism in the morphology of Nimboran. He argues that the environment for a feature deletion rule in one morpheme can be found in features of a sister morpheme. A critical element in his analysis is the fact that the syncretic morpheme and the triggering environment are syntagmatically distinct, which is not the case in Mordvin. 6 BaermanÕs (2004) typological study shows that syncretism in person features in the singular implies syncretism in the plural. Mordvin conforms to this pattern as well. BaermanÕs study, however, is limited to subject agreement. What my analysis of Mordvin suggests is that the same implicational universal is true for object agreement.  The author 2007. Journal compilation  The Editorial Board of Studia Linguistica 2007. Optimizing verbal agreement in Mordvin 191 Figure 1. Mordvin Agreement Markedness Lattice situation (i.e. 1st and 2nd) are less marked than the 3rd person when associated with the subject, but more marked that the 3rd when associated with the object.7 What is expected, then, is that agreement with a third person object will show less syncretism than agreement with a local person object, but that for subject agreement the opposite will be the case. Again, the Mordvin definite conjugation conforms to this pattern. To understand syncretism in the Mordvin verb, it is necessary to address markedness relations in agreement paradigms from a multidimensional perspective. Verbal agreement morphemes can be organized in a lattice according to markedness, as in Figure (1). 7 In a typical split ergative system, local person pronouns may follow a nominative/ accusative pattern, while all third person arguments follow an ergative/absolutive pattern. Assuming that the marked cases are ergative and accusative, they signal the marked associations: local person with object, third person with subject. However, in Baerman (2004) many examples are given of syncretisms affecting 1st and 3rd person, and of a tendency to group 2nd and 3rd against 1st. BaermanÕs scepticism about the validity of person hierarchies as predictors of syncretism is tempered by the observation that exceptions are more common in ÔpartialÕ syncretisms, i.e. syncretisms that are not consistently found across all paradigms in a language. Systems with ÔcompleteÕ syncretisms, like Mordvin verb agreement, are more likely to show the effects of person hierarchies.  The author 2007. Journal compilation  The Editorial Board of Studia Linguistica 2007. 192 Rau´l Aranovich Each morpheme is represented in Figure (1) as an ordered pair of matrix features (for person and number). The morpheme at the bottom corner of the lattice is the least marked one, with singular for both subject and object, and a local person (1st or 2nd) subject along with a third person object. At the top of the lattice is the most marked agreement morpheme: one that has plural agreement for both arguments, a third person subject, and a local person object. In between are other combinations of features, arranged according to their relative degree of markedness. Each line connects a morpheme upwards with another one that exchanges an unmarked feature for a marked feature. The dotted and dashed lines cover those parts of the paradigm that are affected by syncretism. The dotted line represents neutralization of number contrasts in object agreement. The dashed line represents neutralization of subject agreement features. The overlap of the two lines, I will argue, is responsible for the widespread use of the syncretic morphemes -mizÕ and -dÕizÕ. But more importantly, this graph makes apparent the implicational relations that govern the forms that are subject to syncretism. If one member of the paradigm is syncretic, then all members of the paradigm that are more marked are affected by the same condition. I will argue that an OT analysis explains this implicational relation in a natural way. 5. An Optimality-Theoretical analysis of syncretism in Mordvin Optimality Theory (Prince & Smolensky 1993) is a constraint-based framework for linguistic theory. This framework has become dominant in phonological theory over the last decade, and is being extended to morphology and syntax with increasing success. From an OT perspective, syncretism involves the assignment of a common, underspecified output to two inputs with a shared set of features. This is the way Grimshaw (2001) approaches feature neutralization in the pronominal clitic systems of the Romance languages. Inputs are fully specified sets of person, number, gender, case, and reflexivity features. The constraint hierarchy puts some of these inputs in correspondence with underspecified outputs. Syncretic morphemes share the same underspecified output. In Spanish, for instance, the first person singular clitic me can be used as a direct (or indirect) object pronoun, regardless of gender, and also as a reflexive pronoun. For the third person, however, the direct object clitics are lo for the masculine, and la for the feminine, while the reflexive clitic is a distinct form se. In GrimshawÕs analysis, lo and la are fully specified, the first person clitic me is underspecified for case, gender, or reflexivity, and the clitic se is only specified as reflexive. The actual inventory of Spanish clitics, then, expresses only some of the morphological contrasts that universal grammar makes available. Here I adopt a similar approach to treat syncretism in the Mordvin agreement paradigm.  The author 2007. Journal compilation  The Editorial Board of Studia Linguistica 2007. Optimizing verbal agreement in Mordvin 193 Feature contrasts between inputs are affected by two constraint families in OT: faithfulness and markedness. Markedness constraints penalize outputs that have a certain feature, while faithfulness constraints require some sort of correspondence between input and output with respect to a certain feature. When a markedness constraint *F (read Ôdo not have feature FÕ) dominates a faithfulness constraint Faith(F), the feature F ceases to be distinctive. Contrasts between inputs are preserved in the outputs when faithfulness trumps markedness. These two constraint types can be employed to account for morphological syncretism: feature contrasts are preserved in a morphological inventory when faithfulness dominates markedness, and neutralized if the opposite happens. In syncretic paradigms, however, morphological features are not neutralized across the board. Rather, they are disfavored in combination with other features. In Spanish, for instance, gender distinctions are preserved only in third person non-reflexive clitics. Because of this, Grimshaw suggests, a grammar should have combinatory constraints, in addition to constraints that address features in isolation. The same is true for Mordvin. In Mordvin, then, the input is a fully specified set of subject and object agreement features. I represent the morphological information carried by an inflected verb as an ordered pair of person and number features, where the first member corresponds to subject agreement. Output candidates may be specified for some or all of those features, with an X in place of the underspecified feature. Markedness constraints penalize outputs with a particular feature class. The markedness constraints that are active in Mordvin are the following: (5) a. *obj[num]: Object agreement does not have number features. b. *subj[agr]: There is no agreement with the subject. The effect of (5a) is to neutralize contrasts in number for object agreement. Constraint (5b) neutralizes contrasts in person and number for subject agreement. Not all distinctions of person and number in the Mordvin agreement paradigm are lost, however. Some candidates are sheltered from the effects of the markedness constraints in (5a)-(5b) by faithfulness constraints that penalize potential outputs in which a feature of the input is not expressed. In Correspondence Theory, this role is played by Max constraints. In my analysis of Mordvin these constraints instantiate the schema in (6). The combinatory nature of the constraint in (6) ensures that subject and object agreement feature oppositions are preserved in combination with other features. (6) Max(per/num, per/num) To illustrate the analysis, I will discuss first the competitions with inputs that have 3rd person objects and local person subjects, i.e. the lower left quadrant of the Mordvin Markedness Agreement Lattice in Figure (1).  The author 2007. Journal compilation  The Editorial Board of Studia Linguistica 2007. 194 Rau´l Aranovich The agreement morphemes with plural subject features are included in the area delimited by the dotted line, indicating that they are syncretic with respect to object number. In a competition against forms underspecified for number agreement with the object, then, the fully specified morphemes inside the dotted line will lose. This suggests a ranking in which the markedness constraint *obj[NUM] outranks the faithfulness constraints that preserves number distinctions in object agreement in combination with a plural subject. But given that those distinctions are preserved when the subject is singular, the constraints M(loc/sg, 3/sg) and M(loc/sg, 3/pl) must dominate the markedness constraint, yielding the ranking in (7). (7) M(loc/sg, 3/sg) >> M(loc/sg, 3/pl) >> *obj[num] >> M(loc/pl, 3/sg) >> M(loc/pl, 3/pl). The tableaux below show that, for inputs with plural subject agreement features, the optimal candidate is the one underspecified for object number agreement. The candidate underspecified for object number in Tableau (1) is more harmonic than the fully faithful candidate even though the former violates the faithfulness constraint M(loc/pl, 3/sg), because the latter violates the higher-ranked markedness constraints *obj[num]. Candidates with underspecified object person and number features fare badly with respect to M(loc/pl, 3/sg) on two accounts, and therefore receive two violation marks. A similar competition selects a candidate underspecified for object number agreement in Tableau (2). Tableau 1. [1pl, 3sg] M LOC 3 SG ; SG
M LOC 3 SG ; PL
*obj[num] [1pl, 3sg] *! [1pl, xsg] *! + [1pl, 3x] M
M LOC 3 PL ; PL
M LOC 3 PL ; PL LOC 3 PL ; SG
* * [1pl, xx] **! Tableau 2. [1pl, 3pl] M LOC 3 SG ; SG
M LOC 3 SG ; PL
*obj[num] [1pl, 3pl] *! [1pl, xpl] *! M LOC 3 PL ; SG + [1pl, 3x] [1pl, xx]  The author 2007. Journal compilation  The Editorial Board of Studia Linguistica 2007. * * **!
Optimizing verbal agreement in Mordvin 195 Tableau 3. [1sg, 3pl] M LOC 3 SG ; SG
M LOC 3 SG ; PL
+ [1pl, 3pl] *obj[num]
M LOC 3 PL ; PL
M LOC 3 PL ; PL M LOC 3 PL ; SG M LOC 3 PL ; SG
* [1pl, xpl] *! [1pl, 3x] *! [1pl, xx] **! * Tableau 4. [1sg, 3sg] M LOC 3 SG ; SG
M LOC 3 SG ; PL
*obj[num]
* + [1pl, 3sg] [1pl, xsg] *! [1pl, 3x] *! [1pl, xx] **! * The result is an inventory without contrast in object number agreement when the subject is plural, since the inputs [1/pl,3/pl] and [1/pl,3/sg] are in correspondence with the same underspecified output. If the subject is singular, however, the fully faithful candidates win, in spite of the negative effect of *obj[num] (Tableaux 3, 4). The faithfulness constraints M(loc/sg, 3/sg) and M(loc/sg, 3/pl) trump *obj[num], and this ensures that agreement morphemes with singular subjects contrast in number for object agreement. 6. An OT account of markedness in the Mordvin agreement system The relative ranking of the faithfulness constraints in (7) accounts for the fact that the syncretic forms are the more marked members of the verbal agreement paradigm. The ranking of faithfulness constraints mirrors the relations defined in the Mordvin Markedness Agreement Lattice in Figure (1), so that faithfulness to the less marked feature combinations takes precedence over faithfulness to more marked combinations. This yields the universal faithfulness sub-hierarchies in (8). (8) Universal faithfulness sub-hierarchies (partial): a) M(loc/sg, 3/sg) >> M(loc/sg, 3pl) >> M(loc/pl, 3/pl) b) M(loc/sg, 3/sg) >> M(loc/pl, 3/sg) >> M(loc/pl, 3/pl) When the markedness constraint penalizing object number agreement features is ranked above M(loc/pl,3/sg), it also dominates the faithful The author 2007. Journal compilation  The Editorial Board of Studia Linguistica 2007. 196 Rau´l Aranovich ness constraint M(loc/pl,3/pl), given the universal sub-hierarchy in (8b). Syncretism between the two most marked elements of the paradigm follows from this. The faithfulness constraint M(loc/sg, 3/pl), on the other hand, is ranked above *obj[num], and so must M(loc/sg, 3/sg) given the sub-hierarchy in (8a). Thus, the paradigm will show no syncretism with respect to object number agreement between its less marked members. But not all relative rankings in Mordvin follow from the universal sub-hierarchies in (8). The faithfulness constraint ranking M(loc/sg, 3/pl) >> M(loc/pl, 3/sg) has to be stipulated or made to follow from other principles, a matter I return to in a following section. Also, the ranking of the markedness constraints relative to the faithfulness hierarchies is particular to Mordvin. This freedom in relative ranking is the source of a great deal of cross-linguistic variation in verb agreement, an issue that I explore in detail in section 8. Some logically possible rankings, however, are ruled out as empirically impossible by the universal faithfulness hierarchies in (8). A markedness constraint like *obj[num] may not dominate the constraints requiring faithfulness to less marked feature combinations without dominating the constraints requiring faithfulness to more marked combinations, because the resulting constraint hierarchy would infringe on the universal faithfulness ranking constraints projected from the lattice in Figure (1). The treatment of syncretism I am proposing, then, when further restricted by the universal hierarchies in (8), makes the prediction that syncretism between two members of a paradigm implies syncretism between more marked members of the same paradigm. The verbal system of Mordvin conforms to this principle. The use of the relations in Figure (1) to derive universal constraint sub-hierarchies is a variation of the harmonic alignment technique proposed in Prince and Smolensky (1993) for phonology, and applied to the syntax of voice in Aissen (1999). Harmonic alignment starts from two scales like a > b > ... > n and X > Y (one of the scales has to be binary). The first member of the binary scale is associated with the members of the other scale in increasing order to build a Ôharmony scaleÕ like X/a  X/b  ...  X/n. The harmony scale is then reversed to derive a universal sub-hierarchies of markedness constraints: *X/n >> ... >> *X/b >> *X/a. Another harmony scale is built by associating the second member of the binary scale with the members of the other scale in decreasing order. Harmonic alignment is not rich enough to capture markedness relations based on the combination of several dimensions of asymmetric oppositions, like the ones that define the agreement paradigm of Mordvin (number, gender, and grammatical relation). Aissen (2003) faces a similar problem in her account of differential object marking, and her solution is to project a universal sub-hierarchy of constraints based on the product of two harmony scales relating definiteness to animacy. In the same spirit, I am using a lattice of  The author 2007. Journal compilation  The Editorial Board of Studia Linguistica 2007. Optimizing verbal agreement in Mordvin 197 markedness relations to derive universal sub-hierarchies of faithfulness constraints.8 When the complete set of paradigmatic oppositions in the Mordvin verb are considered, the number of faithfulness constraints grows. For each feature combination, there is a constraint requiring a correspondence between it and the output candidates. These constraints are also subject to universal rankings that mirror the markedness relations in Figure (1). The faithfulness constraint associated with the most marked morpheme [3/pl, loc/pl] is placed at the end of all the universal subhierarchies in this extended family. Other constraints are ranked with respect to each other depending on the relative degree of markedness of their feature combinations. The resulting sub-hierarchies are spelled out (in abbreviated form) in (9). In the next section I show what happens when they interact with markedness constraints in Mordvin. (9) Universal Faithfulness sub-hierarchies (full) a) M(loc/sg, 3/sg) >> M(loc/sg, 3/pl) >> M(loc/pl, 3/pl) >> M(3/pl, 3/pl) >> M(3/pl, loc/pl) b) M(loc/sg, 3/sg) >> ... >> M(loc/pl, loc/pl) >> M(3/pl, loc/pl) ... n) M(loc/sg, 3/sg) >> M(3/sg, 3/sg) >> M(3/sg, loc/sg) >> M(3/sg, loc/pl) >> M(3/pl, loc/pl) 7. Generalizing the OT analysis of syncretism in Mordvin One consequence of the sub-hierarchies in (9) is that the markedness constraint *obj[num] forces a neutralization of object number contrasts in all forms that are more marked than the feature combination [loc/pl, 3/sg]. This is so because *obj[num] outranks M(loc/pl, 3sg) (as already determined), and M(loc/pl, 3sg) outranks all faithfulness constraints with more marked feature combinations. The ranking in (10a), then, results in syncretism for number of the object in all forms that have a plural subject. Except for morphemes with the features local and plural for agreement with the object (to which I will return below), all other morphemes with singular subjects display no syncretism. Thus, the associated Max constraints must dominate *obj[num]. 8 My approach contrasts in this respect with the proposals in the works cited (and also to Grimshaw 2001), because their sub-hierarchies are of markedness constraints. Universal faithfulness constraint sub-hierarchies have been proposed in phonology (DeLacy 1999), and there is no reason why they should not exist. It should be noted that there are two senses of the term ÔmarkednessÕ: one is the typological sense, and the other one the more technical sense it takes in OT, as output constraints. The fact that this term has these two senses may create the misleading impression that the only way to capture the markedness relations observed in linguistic typology is through hierarchies of markedness constraints.  The author 2007. Journal compilation  The Editorial Board of Studia Linguistica 2007. 198 Rau´l Aranovich (10) a. *obj[num] >> M(loc/pl, 3sg) >> ... >> M(3/pl, 3/sg), M(loc/pl, loc/sg) >> ... >> M(3/pl, loc/pl) b. M(loc/sg, 3/sg) >> M(loc/sg, 3/pl) >> ... >> M(3/sg, 3/pl), M(3/sg, loc/sg) >> *obj[num] Some faithfulness constraint rankings are not motivated by the markedness relations in Figure (1). From the hierarchies above, for instance, it follows that M(3/sg, 3/pl) outranks M(loc/pl, 3/sg) (by transitivity, with respect to *obj[num]). But there is no measurable sense in which the feature combination [3/sg, 3/pl] is more or less marked than [loc/pl, 3/sg]. The ranking M(3/sg, 3/pl) >> M(loc/pl, 3/sg), then, has to be stipulated or made to follow from some other principle. Syncretism among the morphemes with a local person plural subject is the work of the markedness constraint *subj[agr]. This constraint dominates M(loc/sg, loc/pl), which is associated with the least marked combination of features with a local person plural object, resulting in the ranking in (11). The result is that no agreement forms with local plural object display a contrast in subject agreement features. (11) *subj[agr] >> M(loc/sg, loc/pl) >> M(3/sg, loc/pl), M(loc/pl, loc/pl) >> M(3/pl, loc/pl) With the exception of M(loc/pl, loc/sg) and M(3/pl, loc/sg), which are also dominated by *subj[agr], all faithfulness constraints with singular or 3rd person objects outrank this markedness constraint, as in (12). Morphemes with singular or 3rd person objects, then, will not be syncretic with respect to subject agreement features. (12) M(loc/sg, 3/sg) >>... >>M(3/sg, loc/sg) >> M(3/pl, 3/pl) >> *subj[agr] The markedness constraints *obj[num] and *subj[agr] have to be applied globally to a candidate set to account for the pattern of syncretism among morphemes with local person objects, i.e. the fact that all morphemes with a first (or second) person object get the same exponent when one of the arguments is plural. The constraint hierarchy will assign candidates only specified for object person to those morphemes. A tableau may serve to better illustrate how the constraints interact to select the same output candidates for the syncretic inputs. To simplify the exposition, the tableau has a selection of the most relevant constraints for a given input. The candidate set is expanded to include all possible arrangements of deleted input features in the outputs. Tableau 5 shows that the output that corresponds to a [3pl, 2sg] input is one in which all but object person features are deleted. *obj[num] and *subj[agr] narrow the field to two candidates: [XX, 2X] and [XX, XX]. M(3/pl, 3/sg) insures that the least faithful one is selected.  The author 2007. Journal compilation  The Editorial Board of Studia Linguistica 2007.  The author 2007. Journal compilation  The Editorial Board of Studia Linguistica 2007. *! [xpl, xx] [xx, xx] [xx, xsg] *! *! [3x, xx] + [xx, 2x] *! [3pl, xx] * [xx, 2sg] *! *! [3x, 2x] * [3x, xsg] *! *! [xpl, 2x] * *! * * * * *subj[agr] [xpl, xsg]
3 3 PL ; SG *! *! [3x, 2sg] M [3pl, 2x] *! [3pl, xsg] *obj[num] *!
[xpl, 2sg] 3 LOC SG ; SG *! M [3pl, 2sg] [3pl, 2sg] Tableau 5. M 3 LOC SG ; PL
3 LOC PL ; SG ****! *** *** *** *** ** ** ** ** ** ** * * * * M
M 3 LOC PL ; PL
Optimizing verbal agreement in Mordvin 199 200 Rau´l Aranovich Since *obj[num] and *subj[agr] dominate M(3/sg, loc/pl) and M(3/pl, loc/pl), all morphemes with a second person object and a plural feature for either subject or object agreement correspond to the same output, which is realized as -dÕizÕ (subject person contrasts are neutralized in the same way). The remaining constraint that requires faithfulness to a combination of third person subject and a local person object is more prominent than either markedness constraint. If the input is a morpheme like [3sg, loc.sg], then, the winning candidate will be a fully faithful output, which is realized as -nÕzÕit. It is interesting to also consider the role of M(3/pl, 3/sg). This faithfulness constraint is flanked by the two markedness constraints. If the input is a [3pl, 3sg] morpheme, the corresponding output will be underspecified for object number, but it will keep the specifications for subject agreement features. This morpheme will be syncretic with the [3pl, 3pl] morpheme, but it will be realized differently from a [3pl, 2sg] morpheme. Taking another look at the lattice in Figure (1), now, it is clear that each morpheme is associated with a combinatory faithfulness constraint. Markedness relations among feature combinations determine the ranking of the faithfulness constraints. The dotted line determines which faithfulness constraints are dominated by the markedness constraint *obj[num], and the dashed line those that are dominated by *subj[agr]. For any morpheme that is included within one of the lines, every morpheme that is more marked is also included. This is why a grammar is more likely to preserve feature contrasts in the less marked members of the paradigm. The overlap of the lines also indicates the relative ranking of the markedness constraints. Given that *obj[num] dominates *subj[agr], every node that is included in the dashed line will also be included in the dotted line. These are the morphemes that are syncretic with respect to every agreement feature, except object person. Not all dominance relationships among constraints follow directly from the markedness relations in the lattice. For instance, *obj[num] dominates M(loc/sg, loc/pl) by transitivity, since *obj[num] dominates *subj[agr], and *subj[agr] dominates M(loc/sg, loc/pl). The relative prominence of M(loc/sg, loc/pl) with respect to other faithfulness constraints *obj[num] dominates, v.g. M(loc/pl, 3/sg), is not universally determined, because the two faithfulness constraints are not necessarily ranked with respect to each other by the comparative markedness of the feature combinations. Of more interest, however, is the fact that *subj[agr] dominates M(loc/pl, loc/sg). I suggest that this order derives from an independently motivated sub-hierarchy of faithfulness constraints, based on the following schema: (13) M(i/sg, j/pl) >> M(i/pl, j/sg) that is, a constraint that requires faithfulness to a combination of singular subject-plural object features always outranks a combinatory constraint  The author 2007. Journal compilation  The Editorial Board of Studia Linguistica 2007. Optimizing verbal agreement in Mordvin 201 with plural subject-singular object features, if the two are in combination with the same arrangement of person features. This ranking can be observed across the board. For instance, M(loc/sg, 3/pl) outranks M(loc/pl, 3/sg), since morphemes with plural subjects are syncretic, but morphemes with singular subjects are not. The schema in (13) puts the faithfulness constraint M(loc/pl, loc/sg) behind M(loc/sg, loc/pl), which requires faithfulness to the least marked combination with local person plural object features. The constraint *subj[agr] must dominate M(loc/sg, loc/pl) to capture the insight that neutralization of subject agreement features is triggered by agreement with a local person plural object. The order *subj[agr] >> M(loc/pl, loc/sg) follows by transitivity. The schema in (13) captures a generalization about relative rankings between faithfulness constraints in Mordvin. The question that remains is whether this is also motivated by markedness relations between morphemes. In a recent exchange of opinions with Bresnan and Aissen (2002) about the merits of functionally-motivated OT, Newmeyer (2002) casts doubts on the claim that the universality of constraints in OT can be justified on a functional basis. In spite of his criticism of a functional motivation for person or animacy hierarchies like the ones used in Aissen (1999, 2003), there is reason to believe that constraints about the alignment of person features with subject and object are easily justifiable in functional terms. First and second person are more likely to act on a third person, for instance, given that they are necessarily animate, sentient, etc. First and second person subjects, then, are unmarked with respect to third person subjects, and the markedness values are reversed with respect to objects. Markedness of plural with respect to singular is also functionally motivated, since singular entities are cognitively more simple than aggregates. A universal constraint ranking like Faith(sg) >> Faith(pl), then, is also justifiable in functional terms. But why should there be a functional preference for aligning singular with the subject and plural with the object over the opposite configuration? Is there any reason to consider that a single individual is more likely to act on a plurality of individuals than the other way around? I have found no argument in favor of a functional motivation of the constraint schema in (13), so I am inclined to agree with NewmayerÕs claim that not all OT constraints or rankings thereof can be justified on functional grounds. But I disagree with his conclusion that OT is therefore bankrupt as a syntactic theory. The reason why an OT analysis is sound and successful has less to do with the functional motivation of the constraints or their relative order than with their ability to capture interesting linguistic generalizations and make predictions about grammatical phenomena. As long as the constraint schema in (13) achieves this goal, an analysis that includes it is a sound one, regardless of functional justifications. Nevertheless, the fact that in Mordvin singular  The author 2007. Journal compilation  The Editorial Board of Studia Linguistica 2007. 202 Rau´l Aranovich subjects seem to be less marked than singular objects should prompt an inquiry into the functional underpinnings of different alignments between number and grammatical relations, which is outside the reach of this paper. 8. Universal constraints on syncretism and cross-linguistic variation Among the features that make OT an appealing linguistic theory is the way in which it accounts for cross-linguistic variation. In OT, constraints are universal. Languages do not differ from one another by the presence or absence of a constraint. Rather, cross-linguistic variation results from changing constraint rankings. Moreover, the soundness of an OT analysis of a linguistic phenomenon is tested against its accuracy in predicting the range of possible languages from the allowed variations in constraint ranking. From my analysis of Mordvin, different agreement systems can be obtained by promoting or demoting the markedness constraints, while maintaining the ranking of the combinatory faithfulness constraints relative to each other. In languages like Turkish, for instance, there is no person or number agreement with the object. This results from a system in which *obj[agr] outranks all the faithfulness constraints. To preserve person and number contrasts in subject agreement, however, the constraint *subj[agr] must be inactive, i.e. it must rank below all agreement faithfulness constraints. Turkish has the ranking below: (14) Turkish: *obj[agr] >> M(loc/sg, 3/sg) >> ... >> M(3pl, loc/pl) >> *subj[agr] In Aymara, there is agreement with object and subject, but only in person (There is an additional contrast between inclusive and exclusive first person, which I will gloss over to simplify the exposition). *obj[num] and *subj[num], then, dominate the faithfulness constraints. *obj[per] and *subj[per] are inactive, as shown below. (15) Aymara: *obj[num], *subj[num] >> M(loc/sg, 3/sg) >> ... >> M(3pl, loc/pl) >> *obj[per], *subj[per] Thus, the same set of inputs, with all person and number features specified for subject and object agreement, is made available to Turkish, Aymara, and Mordvin by the generative component of the grammar, as is the set of output candidates. The same markedness and faithfulness constraints are also available to all languages. The difference in their particular morphological inventories comes about after different constraint rankings evaluate the candidate set in each language, with different results. Examined from this point of view, the verbal paradigm of Turkish can be said to be syncretic with respect to person and number in object agreement, and Aymara to be syncretic with respect to number in subject and object agreement. What makes Mordvin interesting is that  The author 2007. Journal compilation  The Editorial Board of Studia Linguistica 2007. Optimizing verbal agreement in Mordvin 203 syncretism is not uniform across its paradigm, requiring faithfulness and markedness constraints to be interspersed. Of course, an important difference between Turkish and Aymara on one side, and Mordvin on the other, is that only the latter marks a distinction between definite and indefinite objects in its agreement system. In Turkish the verb never agrees with a complement, regardless of its semantic status. In Aymara, a verb must agree with a complement, whether definite or indefinite. The agreement system of Mordvin, then, reflects a sort of differential object marking, which is expressed in other languages through the case system (Bossong 1998). An OT treatment of the role of case in differential object marking is developed in Aissen (2003). I suspect that a similar approach can succeed in accounting for the use of agreement to mark the difference between definite and indefinite objects in Mordvin. Such an analysis may require the introduction of another feature, [+/) definite], which combines with person and number agreement features. I have to leave the details of this analysis for another occasion. I should point out, however, that the nature of the semantic feature that triggers object agreement in Mordvin (and in other Finno-Ugric and Uralic languages) is an open matter. Some have claimed that the definite conjugation is related to completive aspect (Keresztes 1998–1999, Mikola 1998–1999), but Alhoniemi (1996) refutes a similar claim based on lexical-semantic evidence, and on data showing that the definite conjugation can have durative and frequentative uses. A detailed discussion of the semantic mature of the definite conjugation in these languages, however, is beyond the scope of this paper. Using the approach to cross-linguistic variation outlined above, it is possible to get a panoramic picture of the agreement systems of the Finno-Ugric and Uralic language family (see Ba´tori 1990 for an overview). A first group includes Finnish, Estonian, Sa´mi, Cheremis, and the Permian languages, in which only subject agreement is contrastive. A verb does not agree with an object, whether definite or indefinite. These languages have a constraint ranking similar to the Turkish one in (14). Another group includes the Ob-Ugrian languages Ostyak and Vogul. In this group there is person and number agreement with the subject, and also agreement with a definite object.9 (16) a. wels-em kill.past-1sg.subj/sg.obj ÔI killed you (sg), him/her/itÕ b. wels«-lam kill.past-1sg.subj /pl.obj ÔI killed you (pl), themÕ [N. Ostyak] (Nikolaeva 1999) 9 Nikolaeva (1999) suggests that information structure plays a more important role in the distribution of object agreement in Ostyak than definiteness.  The author 2007. Journal compilation  The Editorial Board of Studia Linguistica 2007. 204 Rau´l Aranovich From the glosses of the examples above, however, it can be observed that object agreement is limited to number, making it different from Mordvin (in some Ostyak dialects there is an additional contrast with dual number, which I will not discuss here). In the ranking for the Ob-Ugrian languages, then, the only markedness constraint to outrank the faithfulness constraints is *obj[per]. (17) Ob-Ugrian: *obj[per] >>M(loc/sg, 3/sg) >> ... >> M(3pl, loc/pl) >> *obj[num], *subj[agr] A fourth group within this family (counting Mordvin as a third group) contains Hungarian and the Samoyedic languages. Like Mordvin and the Ob-Ugrian languages, these languages agree in person and number with the subject, and they distinguish an indefinite conjugation (18a) from a definite conjugation (18b). (18) a. La´t-ok egy ha´zat see-1sg a house ÔI see a house.Õ b. La´t-om a ha´zat see-1sg.def.obj a house ÔI see the house.Õ [HUNGARIAN] The traditional view on these languages is that they do not make any distinctions of person or number in object agreement, as shown in (19a). However, in Hungarian there is a distinct agreement suffix, -lak, for first person singular subject and a second person object, used in familiar contexts (Rounds 2001). An example is given in (19b). (19) a. La´t-om: ÔI see you (sg/pl.pol), him/her/it, them.Õ b. La´t-lak: ÔI see you (sg/pl.fam).Õ In Hungarian, then, there is a minimal distinction in person with respect to object agreement, which contrasts second and third person in combination with first person singular subject. For agreement with a second person in the polite register, Hungarian adopts the common cross-linguistic strategy of using a third person form (cf. Spanish canta Ôsing.3sgÕ or Ôsing.2sg.polÕ, which contrasts with cantas Ôsing.2sg.famÕ). I suggest that this reflects an inventory in which agreement morphemes with first person singular features can also bear a feature specification for object person features, while all other morphemes are underspecified for object agreement features (except, of course, to mark definiteness). The feature specification [1sg, 3x], realized as -om, contrasts with the feature specification [1sg, 2x], realized as -lak. In the constraint ranking of Hungarian, then, the markedness constraint *obj[per] outranks all combinatory faithfulness constraints except for those with a 1sg subject specification. This analysis requires a  The author 2007. Journal compilation  The Editorial Board of Studia Linguistica 2007. Optimizing verbal agreement in Mordvin 205 refinement of the markedness relations defined in Figure (1), decoupling first from second person. The Hungarian ranking, then, is as follows: (20) Hungarian: *obj[num] >> M(1sg, 3sg) >> M(1sg, 3pl), M(1sg, 2sg) >> M(1sg, 2pl) >> *obj[per] >> M(2sg, 3sg), M(1pl, 3sg) >> ... >> M(3pl, 1pl) >> *subj[agr] By re-ranking markedness constraints penalizing agreement features with respect to a hierarchy of faithfulness constraints, the range of crosslinguistic variation in subject and object agreement is accounted for. When a markedness constraint *F (i.e. a constraint penalizing a feature F in the output) ranks above all the agreement faithfulness constraints, the result is a language which makes no distinctions for F. If the markedness constraint partially dominates the set of faithfulness constraints, this results in a language in which some morphemes will be syncretic for the feature F. In those cases where this happens, the principle stating that syncretisms are more likely to affect the more marked members of a paradigm follows from the universal faithfulness sub-hierarchies in (9). This makes the right predictions for Mordvin, and also for Hungarian: contrasts in the person of the object are only expressed in morphemes with first person singular features, which are the least marked ones. Restricting possible rankings to those that abide by the universal subhierarchies in (9) also makes predictions about which languages cannot exist. No language will have a ranking in which faithfulness to a more marked combination of agreement features outranks faithfulness to a less marked one. Given that syncretism is triggered by a markedness constraint dominating a relevant set of faithfulness constraints, the prediction is that a language in which a feature contrast is preserved among the more marked morphemes in the paradigm while being neutralized among the less marked ones is not a possible language. The theory does not predict whether there will be syncretism in a particular language, or which features a paradigm will be syncretic with respect to, since the ranking of the markedness constraints relative to the faithfulness sub-hierarchy is not universally restricted. But if a feature contrast is neutralized, there are clear predictions as to which members of the paradigm will be syncretic. Given the range of cross-linguistic variation this seems to be the right approach. 9. Alternative approaches to syncretism The constraint-based, comparative approach to syncretism I propose must be compared to rule-based analyses, such as the one that employs rules of referral (Zwicky 1985, Stump 1993, 2001). A rule of referral specifies that the realization of a particular morpheme (one of the syncretic terms) should be dealt with by the rule that realizes another morpheme (the other syncretic term). Stump (2001) argues that rules of  The author 2007. Journal compilation  The Editorial Board of Studia Linguistica 2007. 206 Rau´l Aranovich referral are suitable for syncretism of the ÔstipulatedÕ kind, and not so adequate for ÔunstipulatedÕ syncretisms. The simplest case of stipulated syncretism is the directional one. In directional syncretisms, one member of the paradigm, the dependent one, adopts the exponent of another member of the paradigm.10 In Russian feminine nouns, for instance, the genitive plural is identical to the bare stem (e.g. komnat Ôroom.acc.plÕ), and the accusative plural adds a suffix (komnat-y Ôroom-gen.plÕ). Animate nouns, however, adopt the genitive form for the accusative case (e.g. korov Ôcow-acc/gen.plÕ). In this example, the accusative plural is clearly the dependent member. In unstipulated syncretisms, on the other hand, there is no distinction between dependent and determinant members. In Mordvin, for instance, the suffix -nk expresses agreement with a second person plural subject and a third person object, whether plural or singular. There is no reason to assume that one of the syncretic morphemes gets the exponent that the other one independently has. An unstipulated syncretism like this one, Stump suggests, arise as the result of a realizational rule that disregards the feature that would otherwise distinguish the syncretic morphemes. Rules of referral are not needed in this case. A different approach to syncretism is based on the notion of morphological ÔimpoverishmentÕ (Bonet 1995, Noyer 1998). Rather than having realizational rules that are sensitive to only the common features among the syncretic morphemes, or having rules of referral, impoverishment theory sees syncretism as the result of feature deletion (perhaps followed by the introduction of default features, as in NoyerÕs approach). Bonet uses impoverishment in this way to deal with unstipulated syncretism in the clitic system of Romance, and this approach can be extended to the syncretism in the Mordvin definite conjugation. In the case of the Mordvin plural subject agreement syncretic forms, an impoverishment analysis results in those morphemes not having number features for the object.11 In the realizational approach based on rules of referral, on the other hand, the two morphemes are indeed distinguished by their morphological features, i.e. they are fully specified. It is the rule of exponence that looks at a sub-set of those features. The OptimalityTheoretic analysis of the Mordvin verbal agreement system I propose is closer in spirit to the impoverishment approach, since feature deletion has the effect of narrowing the morphological inventory of Mordvin. GrimshawÕs (2001) analysis of the Romance clitic system is also an OT 10 Other types of stipulated syncretism are the bidirectional kind and the symmetrical kind, which is nondirectional. This type of syncretism needs to be stipulated because the syncretic morphemes do not form a natural class (Stump 2001). 11 Noyer (1998) approaches impoverishment in a different way. Besides rules deleting morphological features, he suggests that redundancy rules fill the missing feature with a default value. This additional step seems unnecessary for unstipulated syncretisms, although it may be needed for the stipulated cases.  The author 2007. Journal compilation  The Editorial Board of Studia Linguistica 2007. Optimizing verbal agreement in Mordvin 207 implementation of impoverishment theory. In this approach, the realizational component of the grammar is greatly simplified, because it is always the case that morphemes that are distinguished by one or more features are associated with different exponents. The OT approach to syncretism, however, has advantages over both rule-based theories. Referral theory can find some clever ways to achieve the right result for the syncretic forms with local person objects,12 but a serious problem arises when considering the neutralization of number distinctions in object agreement when the verb agrees with a plural subject. These unstipulated syncretisms are dealt with by means of realizational rules that are insensitive to the features that distinguish one member of the syncretic pair from the other. In the case of the Mordvin plural subject agreement morphemes, however, three such rules are needed, since there is a contrast between first, second, and third person plural subject agreement. Each rule is stated independently of the other. Thus, the generalization that number distinctions in third person object agreement are neutralized when the verb agrees with a plural subject is lost. In the impoverishment analysis, on the other hand, the fact that all three plural subject agreement morphemes are syncretic with respect to the number of a third person object is not an accident. It follows from a single rule that deletes the feature [number] from all agreement morphemes that also have the value plural for subject number. On this account, then, impoverishment theory is more explanatory than referral theory. A rule-based impoverishment approach to syncretism, however, faces problems of its own to explain the pattern found in Mordvin local person object agreement morphemes. Impoverishment theory is caught in an Ôunderspecification paradoxÕ. LetÕs assume first an impoverishment rule that deletes the object agreement feature [number] in the context of plural subject agreement. The conditioning environment for the other impoverishment rule (the one responsible for the syncretism between morphemes that agree with local plural objects) has to be stated in a disjunctive form. As an effect of the first impoverishment rule, neutralization of subject number and person takes place if the object is a local person and plural, or a local person underspecified for number.13 If, on the other hand, an impoverishment rule deleting subject agreement 12 A possible analysis of the Mordvin system would have a realization rule insensitive to the contrast in object number features when subjects are plural, followed by a directional rule of referral stipulating that the realization of the morphemes with local person plural objects and singular subjects is identical to the realization rule for morphemes with local person objects and plural subjects. Such interaction between rules of exponence is allowed in the theory, but it is unclear what is gained by it. 13 The alternative is to use a negative characterization like not singular, but the gains of such approach are illusory. The negation of singular is equivalent in this analysis to the disjunction plural or underspecified, so not much is gained in terms of capturing a generalization.  The author 2007. Journal compilation  The Editorial Board of Studia Linguistica 2007. 208 Rau´l Aranovich features in morphemes that agree with local person plural objects is stated first, then the rule deleting number features from object agreement has to be formulated as a disjunction. That is, in a rule-based approach to impoverishment in Mordvin, one rule destroys the natural class of features that characterizes the triggering environment for the other rule. An optimality-theoretical approach to syncretism like the one I have defended here avoids the underspecification paradox. Because OT is parallel and global, the effect of the two constraints that penalize agreement features in the output (*obj[num] and *subj[agr]) work in concert to select the most harmonic candidate. The violable nature of constraints in OT avoids the need to state cumbersome triggering environments for the impoverishment rules. Rather than specifying when feature deletion should take place, the approach I have chosen to follow specifies the cases in which it is better for a morpheme to retain a feature, violating the markedness constraints. This is what happens when a faithfulness constraint violation outranks the markedness constraint violation. The underspecification paradox does not arise in the referral approach, because rules of referral do not delete morphological features. In this sense, it is as explanatory as the OT approach, but the latter, like the impoverishment approach, has a natural way to capture the fact that the syncretism among third person agreement morphemes when the subject is plural occurs in a general way. This is the result of a single constraint, *obj[num], dominating the faithfulness constraint M(loc/pl, 3/sg). Since faithfulness constraints requiring maximal expression of features in more marked morphemes are also dominated by *obj[num], the neutralization of the contrast in object number agreement when the subject is plural follows naturally. In this sense too impoverishment theories and OT accounts are superior to referral theories. As Noyer (1998) points out, rules of referral are not good at capturing the markedness implicit in syncretism. A rule of referral can arbitrarily pick any feature or combination thereof, whether marked or unmarked, as the subordinate features in a syncretism. Realization rules can also be underspecified for any feature combination, regardless of markedness. Impoverishment theory, on the other hand, is explicit in stating that the features to be deleted (and to be replaced by default specification rules, in NoyerÕs analysis) are sensitive to markedness relations. In the OT account I propose here, this is the result of the universal constraint on the ranking of faithfulness constraints projected on it by the harmonic lattice. The Optimality-Theoretic approach to syncretism I have proposed for Mordvin, then, shares the insights of impoverishment theory, and it is more explanatory than referral theory in the same ways. But the OT analysis does not suffer from the Ôunderspecification paradoxÕ that afflicts the impoverishment analysis, because instead of a rule-based serial approach it adopts a constraint-based, parallel approach.  The author 2007. Journal compilation  The Editorial Board of Studia Linguistica 2007. Optimizing verbal agreement in Mordvin 209 A constraint-based analysis is more advantageous than either rule-based analysis because it offers a better explanation for the complexities of the Mordvin agreement system. 10. Final summary The Mordvin definite conjugation presents a challenge of the first class for any morphological theory, because of the richness of the distinctions it encodes (person and number in object and subject agreement) and its intricate pattern of neutralizations. Since Carstairs-McCarthy (1987) posed the question of what are possible syncretisms, different answers have revised our simplistic assumptions about the relationship between morphemes and their morphophonological realizations, and the nature of feature co-occurrence restrictions inside and across morphemes. These are some of the staples of morphological theory, so it is clear that syncretism is a good area to test different approaches to the treatment of inflection. The issues that are raised by a morphological system with the complexity of the Mordvin verbal agreement paradigm show that the study of syncretism is not an exercise in cataloguing exceptions, but an area of linguistics that demands well-thought explanations for interesting generalizations.14 In this paper I have claimed that syncretism (at least the unstipulated kind) has to be treated as feature deletion (or underspecification). I have developed an Optimality-Theoretic account of the problem, based on the interaction of markedness constraints and combinatory faithfulness constraints. These faithfulness constraints penalize feature deletion in the output candidates, while the markedness constraints demand it. By ranking the markedness constraints in the appropriate way with respect to the faithfulness constraints, the right underspecified outputs are selected. This is how I have accounted for the pattern of neutralization in agreement features in Mordvin. This pattern, I have argued, does not lend itself well to be analyzed in serial, rule-based theories like impoverishment theory or referral theory. A parallel constraint-based approach like the one Optimality Theory provides is better equipped to explain how the interaction of two simple constraints (one against object number features, another one against subject number and person features) derive the complex distribution of the affixes -mizÕ and -dÕizÕ. OT is a linguistic theory inherently geared to the comparative study of grammar, and to the formulation of explicit typological analyses. The possible ranking permutations among a set of constraints define a space 14 As Baerman (2004) reminds us, however, formal models of syncretism cannot be so rigid as to exclude the results of descriptive work that reveals significant exceptions to alleged universals.  The author 2007. Journal compilation  The Editorial Board of Studia Linguistica 2007. 210 Rau´l Aranovich of possible variation in human languages. This is often referred to as a Ôfactorial typologyÕ. Factorial typologies can be constrained by fixing the relative ranking of some constraints, making predictions about what kind of linguistic structures, categories, or phenomena will not be found among the languages of the world. On occasions, fixed rankings are motivated by functional considerations. I have claimed that aspects of syncretism in Mordvin reflect markedness relations among agreement features and grammatical relations, and I have implemented that observation in my OT analysis through a rigid hierarchy of faithfulness constraints that mirrors such markedness relations. This analysis makes predictions about what sort of cross-linguistic variation can be found regarding verbal agreement. I have tested these predictions on the FinnoUgric and Uralic family, with positive results. More work remains to be carried on in this area, since more agreement systems are predicted to exist than the ones I have observed. Extending this line of research to languages rich in verbal agreement morphology, such as Tibeto-Burman, Austronesian, Muskogean, Tupı´ -Guaranı´ , etc., should be a goal of future studies. References Ackerman, F. 2000. Syntactic expression as morphological exponence. Papers from the Regional Meetings, Chicago Linguistic Society 36, 1–12. Alhoniemi, A. 1996. On the use of the object conjugation in Mordvin [Zur Verwendung der Objektkonjugation im Mordwinischen]. Acta Universitatis Upsaliensis: Studia Uralica Upsaliensia 26. Aissen, J. 1999. Markedness and subject choice in Optimality Theory. Natural Language and Linguistic Theory 17, 673–711. Aissen, J. 2003. Differential object marking: Iconicity vs. economy. Natural Language and Linguistic Theory 21, 435–483. Anderson, S. 1992. A-morphous morphology. Cambridge: Cambridge University Press. Andrews, R. 1975. Classical Nahuatl. Austin: University of Texas Press. Baerman, M. 2004. Typology and the formal modelling of syncretism. Yearbook of Morphology 2004, ed. G. Booij & J. van Marle, 41–72. Dordrecht: Springer. Ba´tori, I. 1990. Object marking of verbs in Mordvin: Morphological underspecification and homomorphy [Die Markierung des Objekts am Verb im Mordwinischen: morphologische Unterbestimmtheit und Homomorphie]. Nyelvtudomanyi Kozlemenyek 91, 15–23. Bonet, E. 1995. Feature structure of Romance clitics. Natural Language and Linguistic Theory 13, 607–647. Bossong, G. 1998. Le marquage diffe´rentiel de lÕobjet dans les langues dÕEurope. Actance et Valence dans les Langues de lÕEurope, ed. J. Feuillet, 193–258. Berlin/ New York: Mouton de Gruyter. Bresnan, J. & Aissen, J. 2002. Optimality and functionality: Objections and refutations. Natural Language and Linguistic Theory 20, 81–95. Carstairs-McCarthy, A. 1987. Allomorphy in inflection. London: Croom Helms. De Lacy, P. 2002. The formal expression of markedness. Doctoral dissertation, University of Massachusetts, Amherst.  The author 2007. Journal compilation  The Editorial Board of Studia Linguistica 2007. Optimizing verbal agreement in Mordvin 211 Hardman, M, Va´squez, J. & Yapita, J. D. D. 1988. Aymara: Compendio de estructura fonolo´gica y gramatical. La Paz: Instituto de Lengua y Cultura Aymara. Honti, L. 1998–1999. On the Proto-Uralic background of the objective conjugation in Mordvin. [Gondolatok a mordvin targyas igeragozas urali alapnyelvi hattererol]. Nyelvtudomanyi Kozlemenyek 96, 106–119. Grimshaw, J. 2001. Optimal clitic position and the lexicon in Romance clitic systems. Optimality-Theoretic syntax, ed. G. Legendre, J. Grimshaw & S. Vikner, 205–240. Cambridge: MIT Press. Keresztes, L. 1998–1999. On the Development of Determinative Conjugation in Mordvin [Gondolatok a mordvin determinativ igeragozas kialakulasarol]. Nyelvtudomanyi Kozlemenyek 96, 90–105. Matthews, P.H. 1972. Inflectional morphology. Cambridge: Cambridge University Press. Mikola, T. 1998–1999. Remarks on the history of objective conjugation in Mordvinian [Megjegyzesek a mordvin targyas igeragozas tortenetehez]. Nyelvtudomanyi Kozlemenyek 96, 120–123. Moravcsik, E. 1988. Agreement and markedness. Agreement in natural language, ed. M. Barlow & C. A. Ferguson, 89–106. Palo Alto: CSLI. Newmeyer, F. 2002. Optimality and functionality: A critique of functionallybased Optimality-Theoretic syntax. Natural Language and Linguistic Theory 20, 43–80. Nikolaeva, I. 1999. Object agreement, grammatical relations, and information structure. Studies in Language 23, 331–376. Noyer, R. 1998. Impoverishment theory and morphosyntactic markedness. Morphology and its relation to phonology and syntax, ed. S. Lapointe, D. Brentari & P. Farrell, 264–285. Palo Alto: CSLI. Prince, A. & Smolensky, P. 1993. Optimality Theory: Constraint interaction in Generative Grammar. RuCCS Technical Report #2. Piscataway: Rutgers University Center for Cognitive Science. Raun, A. 1988. The Mordvin language. The Uralic languages, ed. D. Sinor, 96–110. Leiden: E. J. Brill. Redei, K. 1998–1999. On the objective conjugation in the Uralic languages [Gondolatok az urali targyas igeragozasrol]. Nyelvtudomanyi Kozlemenyek 96, 124–128. Rounds, C. 2001. Hungarian: An essential grammar. London/New York: Routledge. Silverstein, M. 1976. Hierarchy of features and ergativity. Grammatical categories in Australian languages, ed. R. M. W. Dixon, 112–-171. Canberra: Australian Institute of Aboriginal Studies. Stump, G. 1993. On rules of referral. Language 69, 449–479. Stump, G. 2001. Inflectional morphology. Cambridge: Cambridge University Press. Underhill, R. 1976. Turkish grammar. Cambridge: MIT Press. Zwicky, A. 1985. How to describe inflection. Proceedings of the Berkeley Linguistic Society meeting 11, 372–386. Recieved April 6, 2005 Accepted May 17, 2006 Rau´l Aranovich Deptartment of Linguistics University of California Davis One Shields Avenue Davis, CA 95616 USA [email protected]  The author 2007. Journal compilation  The Editorial Board of Studia Linguistica 2007.