Paerns of alignment in verb agreement* Balthasar Bickel, Giorgio Iemmolo, Taras Zakharko, & Alena Witzlack-Makarevich University of Zürich 1 Siewierska’s Problem A highly productive inquiry in typology concerns the alignment of argument roles, especially the identical vs. di erent treatment of the three core roles S, A, and P by the rules of case assignment and agreement marking. With regard to case marking, determining alignment is straightforward: one can simply check which argumental NPs are assigned the same case markers. With regard to agreement, the issue is more complex. Whereas argumental NPs exist independently of case marking, agreement consist of two components: (i) whether or not it exists (i.e. whether certain argument features like person, number of gender, show up at all in the verb morphology), and (ii) if agreement exists, how its markers align roles. In many cases, the answers to these question are still straightforward and one can easily observe that the agreement markers of, e.g. Latin show accusative alignment. However, when expanding the typological scope, one oen runs into what we call here “Siewierska’s Problem”: argument marking in agreement is oen complex and does not allow simple answers. As a maer of fact, the analysis of an agreement system as being primarily ergative, accusative or neutral heavily depends on which criteria one employs. As Siewierska (2003) notes in her seminal paper on the determination of the alignment of agreement in ditransitive constructions, in some instances the consideration of di erent criteria gives rise to con icting classi cations, i.e. the criteria may not converge in identifying a unique alignment type. Siewierska (2003:342) considers the following four criteria that apply to the determination the alignment of agreement:¹ * Earlier versions of this paper were presented at the Anna Siewierska Memorial Workshop in Leipzig, April 27, 2012, and at the conference “Syntax of the World’s Languages IV” in Dubrovnik, October 1-4, 2012. We thank the audiences for helpful comments and questions. We are also grateful for very useful comments and suggestions on a rst dra by Dik Bakker and Martin Haspelmath. Author contributions: B.B., G.I. and A.W.-M. conceived and designed the study and all contributed to the writing. B.B. conducted the statistical analysis. All authors were involved in discussion and interpretation of the results. G.I. and A.W.-M. contributed to data analysis and coded agreement data. T.Z. did most of the data extraction and aggregation work. We thank Lennart Bierkandt and Kevin Bätscher for help in data collection and encoding. ¹ A further criterion, not considered by Siewierska (2003), concerns the host(s) of agreement marker(s), i.e. auxiliaries, lexical verbs, etc. We will not consider this criterion here either. REVISED DRAFT – March 15, 2013 2 1. Trigger Potential: which argument(s) do and which do not trigger agreement marking (i.e. does agreement exist at all)? 2. Form: which argument(s) are covered by the markers with the same phonological form? 3. Position: which arguments trigger agreement in the same position relative to the verbal stem and/or relative to each other (e.g. pre, post, etc.)? 4. Conditions: which arguments trigger agreement under the same condition? As observed by Siewierska, typically these four factors converge in establishing an overall agreement paern, as e.g. in German in (1) below, where all the criteria listed above give a consistent alignment paern. In terms of Trigger Potential, German displays accusative alignment: only S and A trigger agreement. When we take into consideration the Form and Position criteria, we see that they comply with the Trigger Potential characterization: with respect to the Form criterion, the system is consistently accusative, with S and A marked di erently from P, since P is never overtly marked in German verb agreement.² Likewise, with regard to the Position criterion, we have again S=A≠P, since agreement is realized by means of an overt su x only for S and A. (1) German a. I d. I slaf-e. 1sNOM sleep-1sS/A ‘I sleep .’ b. Du släf-st. seh-e ‘I see her.’ e. Du sieh-st 2sNOM sleep-2sS/A ‘You sleep.’ c. Er släf-t. sie. 1sNOM see-1sS/A 3sF.ACC mi. 2sNOM see-2sS/A 1sACC ‘You see me.’ f. Er sieh-t di. 3sM.NOM sleep-3sS/A 3sM.NOM see-3sS/A 2sACC ‘He sleeps.’ ‘He sees you.’ However, in many other languages these criteria diverge in de ning the alignment of agreement, thus giving rise to discrepancies. e situation can be illustrated with English: most English verbs in the present indicative are marked with the su x -s when the subject is third person singular and are unmarked otherwise, as in (2): (2) a. ey like sailing. b. He like-s sailing. With respect to the Trigger Potential criterion, the English present indicative agreement system can be characterized as exhibiting accusative alignment. However, when the distribution of zero versus overt agreement markers is taken into account (i.e. the Form criterion), S/A is marked ² Here and in the remainder of the paper, we simplify. We only consider default lexical classes and do not discuss deviating valency classes such as experiencer verbs. Also see below on this point. REVISED DRAFT – March 15, 2013 3 di erently from P only in the third person singular, whereas the alignment is neutral (S=A=P) in the rest of the paradigm, as none of the argument roles triggers an overt agreement marker. More complex discrepancies arise in systems with multiple markers per argument. An illustration of such a system comes from the imperfective agreement paradigm found in Tirmaga (Surmic; Bryant 1999), which has three slots of agreement marking: one pre x and two su x slots. Table 1 shows the paradigms separately for each of the three roles S, A, and P. e appliPerson pf sf1 sf2 pf sf1 sf2 pf sf1 sf2 1s 1pi 1pe 2s 2p 3s 3p kkk- - -i -(G)o -i -(G)o -(G)ɛ kkk- - -i -(G)o -i -(G)o -(G)ɛ - -aɲ -ey -ey -aɲ -oŋ - - S A P Table 1: Agreement paradigms for S, A, and P in the Tirmaga Imperfective aspect cation of the criteria to the Tirmaga paradigm provides con icting evidence on the alignment paern. When one considers the Trigger Potential criterion, the resulting alignment is neutral, since all the three roles S, A, and P display some kind of agreement marking, at least in part of the system. With regard to the Position criterion, Tirmaga shows accusative alignment, since S and A are marked in the pre x (‘p’) slot and in the second su x (‘sf2’) slot respectively, as opposed to the markers for P, which occupy the rst su x (‘sf1’) slot. Under the Form criterion, nally, one considers the phonological shape of individual markers and asks which argument roles are marked by identical vs. distinct markers. Unlike the other criteria, the Form criterion does not establish a unique alignment paern in the Tirmaga paradigm: the pre x position shows accusative alignment in the rst person (S and A is marked with k- and thus di erently from P), whereas other persons have zero exponence which covers all roles alike, thereby constituting neutral alignment. In the rst su x slot non-third person argument is accusatively aligned due to the su xes -aɲ, -ey, -oŋ, whereas the absence of overt markers for the third person arguments establishes neutral alignment. In the nal su x slot, there is again a number of markers (-i, -(G)o, -(G)ɛ) which establish the accusative alignment, whereas arguments of those referential categories which have zero exponents for all three argument roles (i.e. the rst person plural inclusive and the third person singular) align neutrally. e alignment paerns established on the basis of these three criteria and the observed discrepancies are summarized in (3). REVISED DRAFT – March 15, 2013 4 (3) Tirmaga agreement alignment a. Trigger Potential: S=A=P b. Form: S=A≠P, S=A=P c. Position: S=A≠P With the exception of Siewierska (2003), discrepancies like these have received lile attention in the typological literature or in the description of individual languages. is paper intends to explore the distribution and in uence of such discrepancies in the determination of the alignment in agreement systems, focusing speci cally on discrepancies between alignments in terms of Trigger Potentials and alignments in terms of Form. We explore two research questions: 1. How frequent and how strong are these discrepancies cross-linguistically? 2. Do these discrepancies have an impact on our generalizations about the distribution of alignment systems? We begin by describing the database used for this study and then address these questions in turn. 2 Data, analysis and coding methods We surveyed 260 languages and coded their agreement systems for alignment paerns as part of the AUTOTYP database of grammatical relations.³ Unlike Siewierska (2003), whose focus was on person agreement only, we also considered instances of gender, number and honori city agreement. To keep our dataset manageable in size, however, we treated gender-di erentiating agreement markers as if they were just one marker, i.e. we did not track the di erence between for example third person masculine vs. feminine agreement, but simply third person gender agreement. We considered a particular person-number-gender combination as overtly marked if it is overtly marked for at least one gender. Also departing from Siewierska, we only looked at grammatical agreement in the sense of Bickel & Nichols (2007), i.e. we only coded verbal markers of argument properties that can in principle co-occur with a coreferential noun phrase in the same clause (regardless of whether this co-occurrence is frequent or rare in discourse). Grammatical agreement in this sense corresponds to what Siewierska (2004) treats as the union of syntactic and ambiguous agreement. Cliticized or incorporated pronouns that cannot co-occur with co-referential noun phrases were not analyzed as instances of agreement. For coding alignments, we considered only the coding of S, A, and P argument roles and excluded arguments of ditransitive verbs from our present purview. S, A, and P are de ned by numerical valency and semantic entailment properties of lexical predicates, following earlier ³ e dataset used in this study is available for download at http://www.spw.uzh.ch/autotyp/available. html REVISED DRAFT – March 15, 2013 5 proposals of ours (Bickel & Nichols 2009, Bickel et al. 2010, Bickel 2011a, Witzlack-Makarevich 2011). We furthermore limited our aention to lexical predicates that qualify as open, default classes of their language and excluded predicates with non-canonical agreement paerns, other special behavior, or lexical constraints of any kind. We analyzed the alignment of agreement systems under the two criteria of (i) Trigger Potential, i.e. which argument(s) trigger(s) agreement; and (ii) identity of Morphological Marking, which implies identity of both phonological form and morphological slot. e formulation of the second criterion is similar to Siewierska’s Form and Position criteria but departs from her original proposal in so far as we took into consideration individual slots in which given phonological forms appear in the string of morphemes, rather than a binary pre x vs. su x distinction. e two criteria basically equate the Trigger Potential with syntax and Morphological Marking with morphology, allowing us to frame the question in terms of possible discrepancies between how argument roles are aligned in agreement syntax as opposed to agreement morphology. Agreement syntax in this sense refers to whether or not the verb – or more generally, any predicate complex that heads a clause – registers features contained in S, A or P and therefore systematically interacts with these arguments. If a speci c argument does not trigger agreement at all (e.g. P arguments in German), this means that the verb does not interact with this argument at all in the syntax. Such questions of verb-argument interaction are fundamental for the organization of syntax, typically requiring speci c modeling in formal theories. is conceptualization of Trigger Potentials and Morphological Marking as two dimensions of agreement does not match traditional grammar, where they are not kept separate. For data like those from Tirmaga in Table 1, one would traditionally focus on the form and position of markers and argue that the paradigms show (mostly) accusative alignment. e fact that all three arguments behave alike in triggering agreement would not be considered an interesting fact. For other languages, however, traditional grammar would focus precisely on triggering behavior and not consider form and position criteria. For German for example, one would traditionally say that only S and A arguments trigger agreement; one would not say that German is accusatively aligned because S and A have overt agreement markers whereas P shows zero markers. Applying di erent criteria in Tirmaga and in German is typologically inconsistent, as Siewierska has noted. Furthermore, it is essential to keep apart cases (i) where an argument has a Trigger Potential but the morphology happens to be zero in speci c category (such as third person singular in Tirmaga) and (ii) where an argument never triggers agreement (like German P arguments). In type (i), the grammar of the verb has to check for the presence of speci c features in all arguments, and as a result, the verb enters a speci c morphosyntactic relationship with all arguments. e same morphosyntactic relationship does not exist between the verb morphology and arguments that never trigger verb agreement, i.e. in type (ii). In other words, there is a fundamental di erence between accusative alignment in a language like Tirmaga and accusative alignment An alternative approach would be to take into account just phonological properties, abstracted, if possible, across positions. While possible and interesting, we leave the exploration of this alternative for another occasion. REVISED DRAFT – March 15, 2013 6 in a language like German, and this di erence can only be captured by following Siewierska’s innovation and consider Trigger Potentials independently of Morphological Marking. Trigger Potential is a notion that is uniquely tied to agreement: it is only for agreement that it makes sense to ask whether there exists a speci c syntactic relationship between the verb and features of a speci c set of arguments. ere is no equivalent of this in case assignment: the syntactic relationship that is marked by case exists independently of case assignment, as argumental NPs always bear a syntactic relationship to the predicate since they are assigned a semantic role by it. e relationship is not established by the presence of case morphology, and so one would not say that P arguments in, say, ai bear no syntactic relation to the verb just because there is no case marking. Instead, case morphology can be said to mark the existing relationship. As a result of this, the absence of case morphology is equivalent to zero marking and not to the absence of syntactic relationships. erefore, in contrast to agreement marking, case marking can be fully determined by considering Morphological Marking; the Trigger Potential has no role to play here. When looking at Morphological Marking in agreement, we considered which roles trigger overt agreement morphology per referential category (i.e. per every person/number combination) in every relevant morphological slot in the predicate. Consider the data in (4) from the Uto-Aztecan language Pipil: (4) Pipil (Uto-Aztecan language; Campbell 1985) a. ni-panu 1sS/A-pass ‘I pass’ b. ni-mits-ita-k 1sS/A-2sP-see-PST ‘I saw you’ c. ti-ne-ita-k d. panu [3S/A-]pass ‘he passes’ e. ki-neki [3S/A-]3sP-want ‘he wants it’ f. ni-k-neki 2sS/A-1sP-see-PST 1sS/A-3sP-want ‘You saw me’ ‘I want it’ If we consider the morphological realization of agreement in the rst pre x slot in Pipil, we observe S=A≠P alignment for the rst person singular: there is ni- ‘1sS/A’ for S in (4a) and for A in (4b), but zero exponence for the rst person singular P role in this slot, as (4c) shows; rst person singular P is instead marked in the second slot (-ne in 4c). e situation is identical for the rst person plural and for the second person. However, when we consider the morphological marking of the third person within the rst pre x slot, we observe that three roles behave alike (S=A=P) in that none of them shows up with an overt morphological trace in this slot (be it as dedicated marker or as a portemanteau a x, cf. 4d-4f). e markers in the rst pre x slot here only register rst person (4f). is is di erent for the second pre x position, lled by mits- in (4b), and ki- in (4e) and (4f). Here one obtains S=A≠P alignment, since the markers that appear in this slot encode the P argument, as opposed to S and A, which leave no overt morphological trace in this slot. e situation is again di erent in the su x position. Here we have neutral alignment for singular arguments, since this category never results in overt morphology across all persons. REVISED DRAFT – March 15, 2013 7 For plural arguments, however, there is an opposition between overt marking of S and A (cf. -t in 5a and 5b) vs. no marking for P (5c), again across all persons: (5) Pipil (Uto-Aztecan language; Campbell 1985) a. panu-t b. te-ita-ke-t c. ni-kin-ita-k [3S/A-]pass-pS/A 1pP-see-PST-pS/A 1sS/A-3pP-see-PST[-pP] ‘they pass (S)’ ‘they saw us (A)’ ‘I saw them (P)’ e example of Pipil also shows that alignment can di er across referential categories. In the rst pre x we get S=A=P for the third person and S=A≠P elsewhere; in the su x slot, we get S=A=P in the singular and S=A≠P in the plural. e second pre x slot, by contrast, shows consistent S=A≠P alignment for all referential categories. In case a language has multiple allomorphs of agreement markers (e.g. conditioned by inectional classes), we proceeded as follows: morphologically overt allomorphs were encoded as the same marker for the present purposes. If one of the allomorphs has zero exponence, we considered the size and productivity of individual in ectional classes. Only the major paern of marking – either in terms of the number of in ectional classes or, where the information is available, in terms of the class size – was considered. For instance, for Latvian three conjugation classes with several subclasses are di erentiated. Class II (also referred to as “long”) and the overwhelming majority of verbs in Class I (called “short”) have zero exponence for the second person singular present, whereas the verbs of Class III (“mixed”) use the su x -i in this context. As the most productive and numerous class is Class II, the exemplar paradigm selected for Latvian has no overt marker in the second person singular present (cf. Holst 2001, Mathiassen 1997, Nau 1998). For easy data entry, we only coded overt markers. e distribution and semantics of zero exponents was then automatically inferred with the help of an ancillary database that tracks all referential features that an agreement system is sensitive to. us, in the case of the Pipil rst pre x slot, zero exponence of S/A agreement for third person forms is not explicitly coded in the database, but it can be inferred from the list of the referential types of Pipil which includes three persons and two numbers. e same holds for the singular arguments in the su x slot. Since agreement systems sometimes undergo splits conditioned by temporal-aspectual properties of the clause (e.g. past vs. non-past, perfective vs. imperfective) we tracked the e ects of these conditions in the database and considered the a ected alignment paerns as individual datapoints. We refer to these paerns as constituting agreement ‘systems’ within a language in the following. e database thus contains a total of 289 systems from 260 languages. 3 Does it make a difference? ere are many languages where the alignment of Trigger Potentials deviates from the alignment of Morphological Marking. e extent of such discrepancies can be quanti ed by counting how oen Morphological Marking shows alignment that is identical to the alignment of All data processing, analysis and visualization was done in R (R Development Core Team 2012), with the added packages lattice (Sarkar 2010) and vcd (Meyer et al. 2009). REVISED DRAFT – March 15, 2013 8 Number of systems the Trigger Potential. In the English present tense, for example, one marker (-s) di ers and one marker (zero) is identical with the alignment of the Trigger Potential (which is S=A≠P), resulting in an identical alignment proportion of .5 for this system. e histogram in Figure 1 shows the frequency of identical alignment proportions binned into ten intervals running from [0,.1] to (.9,1]. e rightmost interval consists almost completely of systems with no discrepancy at all (111 systems with an identical alignment proportion of 1, compared to 2 systems with a proportion between .9 and 1); the lemost interval contains 19 systems with no identical alignment at all and 46 systems with identical alignment proportions greater than 0 and smaller or equal to .1. 100 80 60 40 20 0 0.0 0.2 0.4 0.6 0.8 1.0 Figure 1: Histogram of the proportions of identical alignment between agreement morphology and trigger potentials in each system (N = 289) In total, almost two thirds (N = 178) of the 289 systems in our database show at least some kind of discrepancy between alignments in terms of Trigger Potentials and alignments in terms of Morphological Marking. e histogram furthermore shows that discrepancies tend to be severe: 43% (N = 125) show an identical alignment value below (or equal to) .5. ese ndings suggest that Siewierska’s Problem is a serious one. It is imperative that typologies of alignment in agreement be clear on whether they refer to trigger potential or to agreement morphology and apply criteria consistently across languages. e two ways of looking at alignment di er substantially. While this is an important insight with many practical consequences for typology’s day-to-day business, the theoretically more pressing question concerns the source and consequences of such discrepancies between syntax and morphology. We take up this issue in the following. 4 Sources of the discrepancies Two causes of discrepancies are trivial. First, if a referential type, e.g. third person singular, is always zero-marked (i.e. in any role) in a particular slot, its alignment is neutral, while overt markers can be distributed both according to neutral as well as according to any other alignment paern. Second, tripartite alignment (S≠A≠P) is logically possible only with Morphological Marking. Trigger Potentials can never have this type of alignment: if all roles trigger agreement, REVISED DRAFT – March 15, 2013 9 this leads to neutral (S=A=P) alignment, no maer how diverse the morphological shapes and positions may be; if only a subset triggers agreement, this leads to accusative (S=A≠P), ergative (S=P≠A) or horizontal (S≠A=P) agreement, again regardless of the morphological structure. is situation can be illustrated with the mrophology of second person agreement in the Mayan language Ch’orti’: (6) Ch’orti’ (Mayan; izar 1994) a. i-wayan. b. a-ira-en. c. in-ira-et. 2sS-sleep 2sA-see-1sP 1sA-see-2sP ‘you sleep (S)’ ‘you see me (A)’ ‘I see you (P)’ In the incompletive aspect there are two dedicated markers for the second person singular S (6a) and A arguments (6b). e P argument is not marked with a pre x, but with a su x instead (6c). us, although the individual markers are di erent for the three argument roles S, A, and, P, in terms of Trigger Potential the alignment is neutral, since all three argument roles equally trigger agreement. Excluding all instances of zero exponence and of tripartite alignment in morphology brings down the proportion of systems with at least one discrepancy to 122 (42%) out of 289 systems (from 178 or 62%, cf. above). ese remaining discrepancies are empirical observations, and not logically derivable from how alignment is de ned. In other words, it could well be the case that languages would tend to favor similar alignments in the morphology as in the syntax, perhaps in response to iconicity principles. In that case, we would expect, for example, that neutral alignment in the syntax would tend to go together with neutral alignment in the morphology, so that we would nd neutral markers in most morphological slots. Systems like this are apparently rare. What comes closest corresponds to what is sometimes called hierarchical agreement. A case in point is agreement pre xes in Plains Cree. Here, categories like second person trigger agreement in all three roles, and these roles receive exactly the same morphological marking (the pre x ki-): (7) Plains Cree (Algonquian; Dahlstrom 1991) a. ki-pimipahtā-n. b. ki-pēhtaw-i-n. 2-run-sSAP 2-hear-2￫1-sSAP ‘you (sg) run (S)’ ‘you (sg) hear me (A)’ c. ki-pēhtaw-iti-n. 2-hear-1￫2-sSAP ‘I hear you (sg) (P)’ But this seems to be very strongly disfavored worldwide and markers tend to di erentiate roles, leading thus to discrepancies. Discrepancies can arise independently in every slot of the agreement morphology and in every referential category: while in Cree, the alignment of the pre x slot is identical to the alignment of the Trigger Potential for the rst and second person, the su xes show various discrepancies. Consider, for example, the distribution of the second person plural su x -nāwāw in one of the su x slots (su x slot 5): (8) a. ki-pimipahtā-nāwāw. b. ki-wāpam-i-nān. c. ki-wāpam-iti-nāwāw. 2-run-2p 2-hear-2￫1-1p 2-hear-1￫2-2p ‘you (pl.) run (S)’ ‘you (pl.) see us (A)’ ‘I see you (pl.) (P)’ REVISED DRAFT – March 15, 2013 10 Whereas the S and P arguments of this referential type are marked with -nāwāw, as in (8a) and (8c), the A argument of the same referential type is not marked in this slot; instead we nd a rst person su x -nān (8b). is results in ergative alignment. In general, each agreement category in each slot allows for maximally four types of how overt morphology can align roles (S=A=P, S=A≠P, S≠A=P, S=P≠A) if we exclude tripartite alignment (following the reasoning above). erefore, the range of logically possible opportunities for discrepancies rises with the number of agreement categories and agreement slots. For instance, Jero (Opgenort 2005) has 11 referential categories for the S argument (three person categories, three number categories and inclusive vs. exclusive distinction in the rst person of both dual and plural). Each of the marking of the A argument of these 11 types can be conditioned by the P arguments which again are of these 11 types (e.g. A of the rst person singular when acting on the second person singular P, A of the rst person singular when acting on the second person plural P, etc.). In the same fashion, the marking of the P argument across all 11 referential types varies with respect to the A argument and its referential types. To calculate alignment we take an S argument of a particular referential type and compare it with the A argument of the same referential type under one of the 11 conditions and with the P argument of the same referential type under one of the 11 conditions (Witzlack-Makarevich 2011, Witzlack-Makarevich et al. 2011). is results in 113 alignment statements per agreement slot. Jero has 3 slots relevant for agreement and the number of alignment statements for each of them is theoretically 113 , that is, 113 × 3 = 3993 alignment statements in total. e actual number of alignment statements is, however, somewhat lower than this amount of combinatorial possibilities, as particular referential categories or referential category combinations are non-existent or belong to a di erent (e.g. re exive) paradigm. Nevertheless, there is still a very large space of opportunity for discrepancies, easily extending into several thousands when there are many categories and a complex system of morphological slots. Interestingly, languages seem to exploit these possibilities to a substantial extent: Figure 2 plots the proportion of discrepancies, i.e. alignment statements that di er between Morphological Marking and Trigger Potential, per system against the number of category/slot combinations that are distinguished by that system. e data are limited to nontrivial cases of non-identical alignments, i.e. following the reasoning above, we consider here only overt morphology and exclude tripartite alignment. e plot suggests that the opportunity space for discrepancies becomes heavily, and oen fully, exploited with systems that contain more than 6 categories (67% discrepancies with 7 categories in 6 systems, 34% with 8 categories in 17 systems, 88% with 9 categories in 8 systems etc.). Systems with fewer categories tend to show alignments that match the alignment of agreement trigger potentials either completely (displayed in the graph as thin horizontal lines at 0% with systems of 1, 2, 4 or 5 categories) or to a large extent (12.5% discrepancies with 3 categories in 8 systems, 14% with 6 categories in 14 systems). See Witzlack-Makarevich et al. (2011) on deriving basic alignment types from systems with hierarchical and coargument conditioned systems of alignment. Note that a language a like English counts as having 1 agreement category in the non-past (third person singular), i.e. we counted the number of overtly marked categories, not the number of feature values in oppositions. REVISED DRAFT – March 15, 2013 Proportion discrepancies 11 1.0 0.8 0.6 0.4 0.2 0.0 1 2 3 4 5 6 7 8 910 102 103 104 Number of category/slot combinations (plotted on a log10 scale) Figure 2: Proportion of alignment discrepancies in overt agreement morphology vs. agreement trigger potentials (y-axis) in correlation with the number of category/slot combinations de ned per agreement system (x-axis, ploed on a log₁₀ scale). Barwidth is proportional to the count of systems (from the total of N = 289) within each given number of category/slot combinations. It is not immediately clear why languages exploit the opportunity space for discrepancies so strongly. One possibility is that complex morphological systems may have developed through repeated accretion of freshly grammaticalized markers, each giving rise to new alignment patterns somewhere in the system. For example, if a language develops P agreement based on accusatively-marked pronouns, one expects the morphology to keep the emerging agreement markers separate and in a di erent position from older agreement markers. e result would be neutral alignment in terms of trigger potentials, but S=A≠P alignment in the morphological structure for this position. is is a plausible scenario and can be observed, for example, throughout Romance. e question whether this is a universally valid scenario, however, must be le for detailed research on the extent to which agreement systems re ect layered grammaticalization of case-marked pronouns. For now, we conclude that richer paradigms lead to more discrepancies and that 7 categories represent the critical threshold for this. 5 Implications for typological generalizations Another question that arise from our ndings concerns the kinds of alignment where discrepancies are concentrated. Table 2 gives an overview of the distribution of alignments types in overt Morphological Marking and among Trigger Potentials, excluding again non-tripartite alignment. e strongest deviation, alone accounting for 51% of the total χ2 -deviation (284.41), comes from the increased proportion of neutral alignments among agreement Trigger Potentials (with 41% as compared to 14% in the morphology). While these discrepancies are not logically necessary, they re ect the widespread paern in agreement systems illustrated by the Tirmaga, Pipil and Ch’orti’ examples above: although there is agreement morphology for all three arguments, the morphology makes distinctions, mostly aligning A with S. REVISED DRAFT – March 15, 2013 12 Morphological Marking Trigger Potential S=A=P S=A≠P S=P≠A S≠A=P 0.14 0.41 0.37 0.55 0.21 0.03 0.28 0.01 Table 2: Proportion of alignments in overt morphology compared to trigger potentials, excluding tripartite alignment (N = 289) Proportion of S=A(=P) alignments e ip side of this is a heavily increased proportion of ergative and S≠A=P alignments in Morphological Marking (together 49% vs. 4% in Trigger Potentials). is could potentially challenge the relatively well-established principle that verb agreement is strongly biased against S≠A alignment paerns (e.g. Siewierska 2004). Given the discrepancies we noted above, it is possible that such an anti-ergative bias only holds for relatively simple agreement systems where discrepancies are more limited (cf. Figure 2). Figure 3 appears to con rm this suspicion since more complex systems (to the right on the graph) indeed tend to have a lower proportion of S=A(=P) alignments, i.e. more S≠A paerns. Decreased S=A(=P) proportions are less common among simpler systems (to the le of the graph), where the only notable exception consists of a few radically ergative systems with one single agreement category (e.g. gender agreement in Nakh-Daghestanian, represented here by 5 systems ). 1.0 0.8 0.6 0.4 1 2 3 4 5 6 7 8 910 102 103 104 Number of category/slot combinations (plotted on a log10 scale) Figure 3: Proportion of S=A(=P) alignments in overt agreement morphology (y-axis) in correlation with the number of category/slot combinations de ned per agreement system (x-axis, ploed on a log₁₀ scale). Barwidth is proportional to the count of systems (from the total of N = 289) within each given number of category/slot combinations. e only other cases in our database are ergative agreement in Nias (Austronesian) and in Hurrian, and S-only agreement in Tuvaluan (Austronesian), which results in S≠A=P alignment. REVISED DRAFT – March 15, 2013 13 However, as shown by the thin bar widths on the righthand side of Figure 3, more complex systems are much rarer than simpler systems (at least in our database, but we believe this to be fairly representative of worldwide distributions). Also, they tend to be concentrated only in a few families: in our database of 289 systems, there are only 4 families (Algonquian, Nilotic, Tacanan and the Kiranti group of Sino-Tibetan) and the family-level isolate Ainu which contain at least one system that is complex in the sense that it contains at least 60 category/slot combinations. When one surveys the proportions of S=A(=P) alignments in these systems (see the Appendix for a complete list), one notices that they hardly ever fall below 50%. is re ects a general trend, also found in families with members showing moderate complexity: Table 3 lists the mean proportions of S=A(=P) (and if applicable, standard deviations) for all families where this mean is below 1. ere are only seven further families that have mean proportions of S=A(=P) below or equal 0.5, i.e. families that show a possible trend favoring ergative alignments. Nakh-Daghestanian and Algonquian are the only families in the table where this trend is relatively compact and suggestive of a family-wide feature. At the same time, these two families show relatively complex systems (with between 8 and over 10’000 category/slot combinations). e other families in Table 3 with mean proportions below or equal 0.5 either show large standard deviations (Mayan, Macro-Ge) or are represented only by single members (Hurrian, Zuni, Muskogean). Family N (systems) N (cat./slot comb.) µ Hurrian Nakh-Daghestanian Zuni Mayan Algonquian Macro-Ge Muskogean Kiranti Tacanan Ainu Sepik Austronesian Nilotic Indo-European 1 5 1 11 10 2 1 29 1 1 5 16 5 1 1 (1,1) 6 (8, 17) (2266, 10047) (4, 6) 8 (457, 1889) 66 85 (1, 9) (1, 14) (1, 210) (1, 13) 0.00 0.00 0.00 0.39 0.40 0.50 0.50 0.63 0.68 0.75 0.80 0.81 0.87 0.95 std. dev. 0.00 0.49 0.09 0.71 0.10 0.45 0.40 0.18 0.22 Table 3: Mean proportions µ of S=A(=P) in overt morphology below 1 in families, ordered by proportions. N (cat. comb) shows the range of number of category/slot combinations across all members of the family in our database 60 is a reasonable threshold for calling a system ‘complex’ because there is a natural gap in Figure 3 between systems up to 30 and systems with more than 60 categories/slot combinations. REVISED DRAFT – March 15, 2013 14 is suggests that decreased S=A(=P) proportions are limited to only few families and is hardly ever a dominant trait of entire families. Given this, we expect that paradigm complexity has lile impact on the universal trend towards S=A alignment in agreement morphology, i.e. that the correlation noted in Figure 3 only re ects e ects in very few languages and systems and is not a robust principle of typology. To test this hypothesis, we applied Bickel’s (2011b, in press) Family Bias Method to our data. is method estimates statistical signals for diachronic biases from their expected synchronic results: if S=A alignments outnumber S≠A alignments signi cantly (under binomial testing) in a family, a change towards S=A alignments in this family was more likely than a change away from it (either because the proto-paradigm(s) showed S=A, which then hardly ever got lost, or because S=A was not there and then it was innovated early or oen in the family). If there is no signi cant synchronic preference, by contrast, no signal can be inferred because, in this case, there was either no diachronic bias towards a particular structure, or the di erence in biases was too small to leave a signal, or the family is too young to allow a signal to show up. Using extrapolation methods, signals for diachronic biases can also be estimated for isolates and small families.¹⁰ In order to nd out whether paradigm complexity has an e ect on diachronic biases towards or against S=A alignments in agreement morphology, families were grouped into simple (between 1 and 5 categories), moderately complex (between 6 and 30 categories or category combinations) and highly complex (above 60 categories or category combinations). e choice of cut-o points is arbitrary but it is based on the fact that 6 categories is the rst point (aer 1) at which S=A proportions fall below 1.0 in Figure 3 and that, as noted earlier, there is a gap between systems with up to 30 and systems with more than 60 category combinations.¹¹ Figure 4 summarizes the results. Almost all families are diachronically biased towards S=A(=P) alignments in their agreement morphology, and this preference is observed to a comparable extent across degrees of paradigm complexity.¹² e summary gure also includes the results of a separate analysis of diachronic biases in trigger potentials (rightmost bar), and the preference for S=A(=P) alignment is in the same ballpark here as well. We can conclude that agreement systems strongly prefer S=A(=P) alignments in both Morphological Marking and Trigger Potential. Deviations from this are limited to a few groups and languages with high (such as Algonquian) and moderate complexity (such as Mayan). ¹⁰ e method is implemented in and available as an R package (Zakharko & Bickel 2011 ). We used the method with the default seings of the package. ¹¹ When families were diverse with regard to these categories of complexity (e.g. Indo-European or Austronesian, cf. the range of category counts in Table 3), we split the family into smaller groups that fell consistently into one or the other group. Whenever possible, such groups were based on known genealogical subgroups, as de ned in Nichols & Bickel (2009). ¹² A likelihood ratio χ2 test comparing a loglinear model with vs. without an interaction between bias direction × complexity type suggests independence: χ2∆ = 2.29, df = 2, p = .32. REVISED DRAFT – March 15, 2013 15 no bias bias towards S≠A bias towards S=A simple moderately complex highly complex trigger potentials Figure 4: Proportion of estimated diachronic family biases towards S=A(=P) vs. S≠A alignments in Morphological Marking across di erent degrees of paradigm complexity, and among agreement Trigger Potentials. Tile sizes are proportional to frequencies (Meyer et al. 2009); a small circle indicates zero counts. 6 Conclusions Siewierska (2003) raised an important issue for typologies of alignment. Looking at alignment paerns in agreement systems in terms of the type of roles that can trigger agreement in the syntax (i.e. Trigger Potential) leads to very di erent characterizations than when one examines alignment paerns for speci c agreement markers in speci c morphological positions (i.e. Morphological Marking). Discrepancies are in fact severe, and it is imperative that typology carefully distinguish between di erent notions of alignment in agreement systems. Some of the sources of these discrepancies are trivial and have to do with the logic of determining alignments. However, we also observed (Section 4) that a substantial proportion of discrepancies is empirical in nature: agreement morphology could in principle be more in line with agreement syntax. At present it is not clear to us why morphological systems should exploit the possibility for discrepancies as strongly as they do, but we suspect that this has to do with the complex histories of grammaticalizing layer aer layer in agreement systems. Such a scenario would explain why discrepancies become stronger the more complex paradigms are in terms of the number of referential categories and category combinations they are sensitive to. While the study of discrepancies that Siewierska called for gives new insights into possible historical scenarios on how alignment paerns have developed in agreement systems, it could in principle challenge received universal principles on preferred alignments in such systems. As we showed in Section 5, however, confounding e ects are severely limited: there are only very few language families in the world where there seems to have been a bias away from S=A and towards S≠A alignments, and this is true regardless of whether one looks at agreement syntax or agreement morphology. ere is a slight preference for S≠A alignments in more complex paradigms, but it is only in a handful of language families that this is a signi cant and REVISED DRAFT – March 15, 2013 16 diachronically relevant trend (e.g. in Algonquian). In all other families, there is a very strong overall bias towards S=A, even when paradigms are exceedingly complex, as, for instance, in Kiranti. REVISED DRAFT – March 15, 2013 17 Appendix: Proportion of S=A(=P) in overt morphology and number of category/slot combinations per system in families where at least one system has more than 60 combinations Family Language System Ainu Algonquian Algonquian Algonquian Algonquian Algonquian Algonquian Algonquian Algonquian Algonquian Algonquian Kiranti Kiranti Kiranti Kiranti Kiranti Kiranti Kiranti Kiranti Kiranti Kiranti Kiranti Kiranti Kiranti Kiranti Kiranti Kiranti Kiranti Kiranti Kiranti Kiranti Kiranti Kiranti Kiranti Kiranti Kiranti Kiranti Kiranti Kiranti Kiranti Nilotic Nilotic Nilotic Nilotic Tacanan Ainu Arapaho Atikamekw Blackfoot Cheyenne Cree (Plains) Menomini Micmac Munsee Ojibwa (Eastern) Passamaquoddy Athpare Bahing Bahing Bantawa Belhare Camling Chintang Dumi Hayu Hayu Jero Koyi Koyi Kulung Kulung Kõic Kõic Limbu Limbu Lohorung Lohorung Old ulung (Mukli) Old ulung (Mukli) Puma ulung (Mukli) ulung (Mukli) Wambule Yakkha Yamphu Nandi Nandi Teso Turkana Reyesano INDEP INDEP.NPST INDEP INDEP.PRS.IND INDEP INDEP INDEP.IND INDEP.NPST INDEP.PRS INDEP.PRS IND NPST.IND PST.IND IND IND IND NPST.IND NPST.IND NPST.IND PST.IND IND NPST.IND PST.IND NPST.IND PST.IND NPST.IND PST.IND NPST.IND PST.IND NPST.IND PST.IND NPST.IND PST.IND NPST.IND NPST PST IND IND IND NONSNPST SNPST Pr(S=A) N (category/slot comb.) 0.753 0.287 0.450 0.578 0.338 0.517 0.372 0.353 0.381 0.350 0.421 0.676 0.626 0.540 0.589 0.721 0.503 0.658 0.479 0.519 0.665 0.536 0.602 0.605 0.633 0.606 1.000 0.794 0.640 0.642 0.592 0.592 0.626 0.625 0.656 0.708 0.701 0.535 0.656 0.670 1.000 1.000 0.742 0.619 0.682 85 2495 8117 2817 3354 8845 2266 10047 2467 3391 2726 1761 951 859 1621 1772 1247 1822 1057 682 811 941 850 901 922 903 471 457 1889 1847 1238 1238 1052 989 1668 1016 973 1071 1606 1391 10 8 186 210 66 REVISED DRAFT – March 15, 2013 18 References Bickel, Balthasar. 2011a. 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