Two representations of case: Evidence from numerals and relatives

This paper highlights a fundamental tension between the representations required for case syncretism versus the representations required for case priority. Case syncretism is captured with a feature decomposition based on the patterns established in Caha 2009. However, a different decomposition is required for case priority relations, which are instantiated in Bosnian/Croatian/Serbian (BCS) numeral constructions and in BCS and German relative constructions. The paper proposes that this conflict can be resolved by introducing two levels of representation into the case system: priority is determined by set structures in the syntax, while syncretism is analyzed following a post-syntactic unification operation.


Introduction
Numeral constructions and light-headed relatives (LHRs) in Bosnian/Croatian/Serbian (BCS) reveal a tension between representations of case syncretism and representations of case priority. Caha (2009) demonstrates that syncretism is possible only among adjacent cases ordered in a universal sequence and that this pattern can be captured through a hierarchical decomposition of case. Given the universality of the analysis, the syncretism patterns are applicable to BCS, as Caha indeed shows. However, the case interactions within both BCS numeral and relative

constructions -withadditionalsupportfromGerman-conflictwiththehierarchypredictedby
Caha's case sequence. 1 In particular, these examples indicate that the lexical cases (genitive, locative, dative, instrumental) clash with one another, and none can take priority over the others.
By contrast, Caha's decomposition predicts that instrumental overrides dative, which overrides locative, which in turn overrides genitive. To resolve this paradox, this paper proposes that the case system should be layered to accommodate both representations: priority is determined through containment relations of syntactic set structures, while syncretism is analyzed postsyntacticallyafter'flattening'ofthestructuresthroughaunificationoperation(seeAckema& Neeleman 2018). The following discussion reveals the conflict through examinations of both syncretism and priority in the relevant examples and then introduces the two-level solution. Caha (2009) formalizes the universal patterns of case syncretism as Universal Contiguity:
With reference to BCS, Caha adds the "prepositional" (locative) case to the sequence between genitiveanddative,notingthatitislargelysyncreticwithdativeapartfromminordifferences in stress. 2 While this may signal that locative is moving toward elimination from BCS, the data presented in the following sections indicate that locative does contribute to the priority paradigm and should be included in the current analysis. 3 Caha contends that a hierarchy of 1 Other works have discussed case syncretism while analyzing the priority patterns found in numeral constructions, such as the Jakobsonian feature-based analysis in Franks 2002. However, Caha (2019b points out that such approaches to syncretism overgenerate, instead advocating an analysis based on the hierarchical organization of case and cumulative decomposition of these cases into features. 2 Caha(2009)specificallyreferstoSerbianratherthanBCS,butthisdoesnotaffectthedata. features based on the cumulative decomposition of case is necessary to capture the adjacency constraint on syncretism (see also Caha 2019b). This hierarchy can be adapted to the layout in (2),whereeachcasesetisbuiltwiththeadditionofasingleidentifyingfeature.Atthispoint, it is worth mentioning that some analyses of case syncretism disagree with the organization of this hierarchy (e.g. Harðarson 2016;Graf 2019;Zompì 2019;Bárány 2021), suggesting that the feature decomposition may not be as incremental as Caha (2009) proposes. For now, I assume thatCaha'sdecompositioniscorrect,but §4reflectsonhowthetwo-levelaccountproposedinthis paper is compatible with these alternate views of syncretism, as well as with languages in which both the priority and syncretism patterns align with (2). I emphasize that the decomposition in (2)  node.Alternatively,someanalysesofsyncretismutilizeunderspecification,wheretheinserted form is a maximal subset of the necessary case features. Impoverishment also seems to be a valid option: deletion of the outermost feature of each successive case set in (2) would reduce that set to the features of the one before it. For the most part, the data in this paper do not bear on which method to use, but §4 contains some speculation regarding the use of impoverishment.

Representations of priority
In addition to syncretism, case hierarchies are commonly used to address priority patterns (Vogel 2001). This section reviews the behavior of case in both BCS numeral constructions as well as BCS and German relative constructions, which each produce the decomposition in (3) (5), the result is ungrammatical whether the nominal form is genitive or dative (similarly with instrumental). The overall distribution of numeral constructions thus suggests that genitive can override nominative and accusative but clashes with both dative and instrumental.
As it happens, the BCS LHRs discussed below provide independent evidence of the same clashes (see Citko 2004). The crucial evidence for case priority comes from the examples in which the light head is omitted. We will see that a genitive head cannot be omitted when the wh-pronoun is either dative or instrumental (and vice versa), indicating a clash between these cases. By contrast, a nominative head is always optional, and an accusative head is optional with a wh-pronoun realizing any of the lexical cases. This possibility of omitting the head suggests that the case of the wh-pronoun is allowed to take precedence, again predicting the sequence nominative < accusative < lexical.
We now turn to a case-by-case discussion of the paradigm. Given the contrived nature of these examples, there is some variability in judgments, which is discussed in the footnotes to avoid complication. Beginning with (6), the matrix clause is nominative, while the relative clause is manipulated to assess the six case combinations. Here, the light head ono is always optional. 4 Since nominative is not required to surface in the construction via the head, it appears that all cases can take priority over nominative. This is because without the head, the case of the 4 Thedatareflect18responses,distributedacrossBosnian,Croatian,andSerbianinformants.Regarding(6),11agreed thattheheadcouldbeomitted,while7indicatedadifficultywith(6b-f),thoughtheycouldomittheheadinother examples in line with the predictions of (3). This variation need not cause concern, as there is reportedly a meaning shiftduetoanimacywiththeomissionoftheheadin(6).Additionalresearchisnecessary,butthereisindependent evidence of a similar effect in BCS što-relative clauses. Goodluck & Stojanović (1996) report a link between the optionality of a resumptive clitic and the inanimacy of the head it refers to. If a similar idea is extended to the examples in (6), an inanimate reading tied to the omission of the head could be marked in the nominative matrix clause, where the subject is more naturally interpreted as animate. Regarding (6a), all informants' ability to omit the head may be attributed to the frequency of this expression. relative clause surfaces on the relative pronoun, while the nominative case of the matrix clause is not realized.  (7b) when both clauses realize accusative. In (7a), however, the head is required, suggesting that nominative cannot override accusative despite the fact that što is a nominative/accusative syncreticform.Theconflictin(7a)thatwouldresultfromomittingtheheadcruciallydiffers fromthebehaviorofBCSfreerelatives(FRs),whichallowrepairbysyncretism(Milićević2011).
This fundamental contrast may be attributed to a difference in syntactic structure (see Citko 2004 for a related discussion of Polish). 5 5 UnlikeLHRs,BCSFRsrequirestrictcasematchingbetweenclauses(Gračanin-Yuksek2008),butmismatchesare toleratediftherelativepronounrealizesasyncreticform(Milićević2011).WiththeLHRin(7a),thenom/acc form of štodoesnotseemtohaveanimpact.Thiscontrastinrepairpotentialmaybeattributedtoadifferenceinstructure between LHRs and FRs. In LHRs, distinct words (the head and wh-pronoun) spell out distinct syntactic positions; in FRs, the relative pronoun seems to spell out two syntactic positions for the matrix and relative clauses. The form of the relative pronoun in FRs could result from the fusion of two feature sets into one spell-out, potentially through the process of spanning (Svenonius 2012). This would create a context for deletion that is absent in LHRs. §4 explores how impoverishment may be well-suited to address this potential for repair limited to certain constructions. In the genitive examples, the head is optional only when both the matrix and relative clauses are genitive. This further substantiates the claim that genitive takes priority over nominative and accusative but not vice versa, since nominative and accusative wh-pronouns cannot appear without the head (8a-b). 6 Similarly, the inability of locative, dative, and instrumental wh-pronouns to occur without the head in (8d-f) indicates that the lexical cases cannot take priority over genitive. The same is true for the remaining locative, dative, and instrumental examples in the appendix (with additional comments): the head is optional only with case matching between clauses. When nominative or accusative occurs on the wh-pronoun, or when any two lexical cases are paired, the headcannotbeomitted.Altogether,theseLHRsdemonstrateasequenceofcaseprioritywhere nominative is overridden by accusative which is overridden by the lexical cases. Moreover, the interaction of genitive with the other cases exactly parallels the numeral constructions.
Remarkably, German FRs provide a non-Slavic parallel of the BCS LHRs, though without instrumental case since German does not distinguish it morphologically. While some speakers adhere to strict case matching in FRs (Vogel 2001;Vogel & Frisch 2003), others display the pattern in (9) where a more complex case in the relative clause can override the matrix case. AswithBCS,thecaseofthepronounin(9a-b)revealsthatnominativeisoverriddenbyaccusative, which is overridden by genitive. The ungrammaticality of (9c-d) indicates a clash between genitive and dative, as neither form of the wh-pronoun is grammatical. 7 Since the priority pattern is not restricted to either BCS or numeral constructions, these examples suggest that case priority is indeed prevalent and should be considered alongside patterns of syncretism. Moreover, Caha (2009) shows that German syncretism patterns conform to Universal Contiguity; thus, German, like BCS, displays a priority/syncretism paradox.
The containment relations between the cases in (3) easily capture the observed patterns of priority. 8 These feature sets allow all cases to override nominative, since it is contained in 7 Himmelreich'sexampleswereverifiedbyfourinformants.Tworated(9d)withthedat-gen pairing as questionable ratherthanstrictlyungrammatical.Areviewerpointsoutthatthisquestionabilitymaystemfromthefactthatthe genitive appears to be fading in German. Regardless of the explanation, it seems that genitive does not straightforwardly override dative, similar to BCS. One of these two speakers suggested that (9d) would be better as:

2017usingagraftinganalysisinwhichthepronounissimultaneouslypartofbothclauses.BergsmaemploysCaha
2009's nanosyntactic view of case and its decomposition, but grafting could potentially work with the analysis proposed here if the structures in (10) are inserted as bundles on the pronoun. When the more complex case originates from the relative clause, the feature bundle on the pronoun contains the less complex case of the matrix clause, allowing it to be accessed. If lexical cases are paired, a clash is predicted due to a lack of containment. Similar reasoning applies to the LHRs; if the matrix case is accessible via the feature bundle on the pronoun, the head is optional.
For case-matching languages, Bergsma must add two restrictions: Only graft highest node and Keep spellout. These restrictions are not directly generated by nanosyntax nor do they translate directly to a feature-bundle analysis, and further work is required to determine the implementation needed in this type of account. In terms of languages in which the matrix clause requires the more complex case on the pronoun, Bergsma uses the nanosyntactic framework to merge additional case nodes. Thus, an equivalent feature-bundle account would have to allow for the addition of case features-a task I leave to future research. While the two-level account proposed in this paper does not address all sets. Genitive, locative, dative, and instrumental also override accusative, since all contain the set of accusative features. However, the individual sets of genitive, locative, dative, and instrumental are predicted to clash with each other, as none of them fully contain the features of theothers.Crucially,thislackofcontainmentamongthelexicalcasesdiffersfromthesyncretism configurationgivenin(2).Usingthesystemin(3),thereisnoobviouswaytocaptureUniversal Contiguity. Take the paradigm in Table 1 for example: the apparent dative/instrumental syncretism cannot be analyzed here using supersets, subsets, or impoverishment, since neither set contains the other. On the other hand, the system in (2) does not capture the priority patterns observed in the numeral and relative constructions, as both dative and instrumental are predicted to override genitive. This fundamental conflict between priority and syncretism suggests that thetwopatternsmayrequiredifferentanalyses,thoughthedistributionofcasefeaturesshould ideally remain constant throughout.

A possible solution: Two levels of representation
While the feature sets in (2) address syncretism, they fail to predict the priority patterns captured by the sets in (3). However, the use of two distinct sets of case features within a single language does not contribute to a contentful theory. Instead, (10) shows that it may be possible to derive the general shape of the priority relations in (3) from the features of (2). The structural cases (nominative and accusative) remain sets of atomic features as we saw in (2) and (3); the lexical cases (genitive, locative, dative, and instrumental) contain an embedded set in addition to the nom and accfeatures. This decomposition provides a basis for the case clashes.  Rather than considering all cases as sets of atomic features as in (2), (10) suggests that the priority relations can be derived through a decomposition into features and embedded sets. In both (10) and (3), nominative is composed of one element, accusative of two, and genitive, locative, these typological alternations, Bergsma points out that further research is required to determine their motivations. Overall, Bergsma's analysis does well in recognizing these alternations, but without adaptation the solution does not seem to be able to account for the priority/syncretism paradox observed here. It is unclear how to resolve this within a single language without employing two case levels.
dative, and instrumental of three elements. 9 If we maintain that a case C 1 overrides another C 2 when C 1 is composed of all elements of C 2 , then (10) correctly captures the observed patterns of case priority. For example, dative overrides accusative since it includes the nom and acc features that define accusative. However, dative clashes with genitive due to a lack of containment.
Genitive is composed of the features nom,acc, and gen, but dative does not contain gen as an atomic feature, only as a member of the embedded set {gen,loc,dat}.
Theconflictbetweenpriorityandsyncretismcanthenberesolvedifpriorityrelationsare determinedbysetrelationsinthesyntax.Thesesetstructuresarepost-syntactically'flattened'to the sets of features in (2), after which spell-out takes place and potentially leads to syncretism. 10 Flattening amounts to a unification of the outermost and embedded sets through removal of internalstructure;assuch,isnotadifficultassumptiontomakebecausenocomplexmechanisms are added to the grammar. Information is simply removed, but the content of each case remains constant throughout.
Let us consider how this unfolds in the BCS examples. We have seen that a case clash occurs when the head is omitted in examples such as (8d), where the head realizes genitive and the wh-pronoun realizes locative. This outcome can be illustrated with the structure below, which loosely follows Citko's (2004) analysis of LHRs. Priority is determined through containment relations in the syntax.
In (11), the features of the head are not recoverable from the features of the wh-pronoun because there is no containment between the genitive and locative cases at this level. Both cases include the nom and accfeatures,buttheydifferwithregardtogen. In the composition of genitive, gen is an atomic feature, while in locative it only appears as a member of the embedded set {gen,loc}.
Since the composition of genitive is not fully contained within the composition of locative, the features of head are not recoverable, and it cannot be grammatically omitted.
Post-syntactic representation of BCS LHR Thus far, it has not been necessary to know precisely which method is used to analyze syncretism, thecriticalpointbeingthattheflattenedsetsarerelatedthroughcontainment.However,itnow seems that impoverishment may best accommodate this repair potential in the two-level system, at least for a subset of the examples. This is because impoverishment can be precisely formulated to address idiosyncrasies, and constructions that do not exhibit repair potential simply lack the necessary deletions. If the clash in (11) were repairable through syncretism, one could imagine a rule such as (13) that reduces the flattened set of locative features to genitive in a specific context, such as on the wh-pronoun in the environment of a genitive light head. 11 It would then be possible to omit the head since its features match those of the wh-pronoun. Note that in order to derive the correct syncretism predictions, impoverishment must be restricted to the outermost feature of a case set, perhaps through a requirement on the well-formedness of case sets with respect to (2). Zompì (2019) proposes a similar constraint using Graduality.
This repair is not observed in BCS LHRs, so the rule in (13) is merely hypothetical. Flattening does occur in the derivation, but case override is restricted to the syntax, so the priority relations 11 Repair is limited to certain constructions, so impoverishment would likely have to make some reference to the syntax. Since (13) is a hypothetical deletion, I am not concerned about its precise formulation. More data regarding the available repairs would be required to determine best formulation for these rules. stand as they did in (11). This shows that cases may clash, but at the level of spell-out, they form unifiedsetsthatcanbemanipulatedtoderiveasyncreticformiftherelevantrulesexist.
Forcertainrepairs,itisconceivablethatimpoverishmentwouldhavetooccurpriortoflattening to repair the mismatch at the correct case level. Though impoverishment is typically considered a morphological operation, Keine (2010) argues for the possibility of syntactic impoverishment.
Given Zompì's (2019) Graduality, it seems that impoverishment of the embedded sets would only be able to reduce the case sets in (10)  This predicts that the lexical cases override genitive, which overrides nominative and accusative, roughly corresponding to the hierarchy predicted by Universal Contiguity. The priority data alonearenotsufficienttodeterminethepreciseorderofalllexicalcaseswithrespecttoeach other, but in Caha's investigation, there is no strong evidence to suggest that the syncretism and priorityhierarchiesvarywithinasinglelanguage.Again,itispossiblethatthebehaviorofthese languagescouldbeaccommodatedinthecurrentsystembyadjustingthetimingoftheflattening operation. Since priority relations are determined in the syntax, languages such as Russian could haveflatteningearlyinthederivationsothatpriorityisdeterminedonthebasisoftheflattened casesets.Otherwise,theselanguagesmaycontainonlytheflattenedlevelofcase.Ileaveitto future research to determine the exact implementation that would be required to address this typological variation within the system proposed here.

Conclusion
This paper highlights a conflict between representations of case syncretism and case priority through an examination of numeral constructions and relative constructions in BCS, with added supportfromGerman.Theconflictisresolvedbyintroducingtwolevelsofcaserepresentation, where the syntactic interactions of set structures define priority relations and post-syntactic flatteningyieldssetsofcasefeaturesthatdeterminesyncretism.Suchasolutionpredictsthatcase syncretism cannot be analyzed with a purely syntactic account-at least in languages containing this priority/syncretism paradox-with implications for syncretism more generally. The solution seems to be incompatible with the nanosyntactic view of syncretism in Caha 2009 where each case is a projecting head, but further research is required in this area.