How to agree with a QNP

This paper focuses on the great variety of φ-agreement patterns and case alternations quantified noun phrases trigger in Serbo-Croatian. Novel data from Serbo-Croatian are contributed, showing more agreement patterns than so far attested. Crucial for the analysis is an observation that draws a parallel between the agreement patterns of quantified noun phrases and conjoined noun phrases. We will show that the data can best be described by a strictly derivational agreement system based on rule ordering (Müller 2009; Murphy &Puškar 2018) and operating in narrow syntax. Existing case-based approaches (Pesetsky 1982; Franks 1994; Bošković 2003; 2006) and index-concord based feature systems (Wechsler & Zlatić 2000; 2003; Danon 2013) fail to account for agreement alternations in preand post-verbal position as well as in NP-topicalisation configurations.

(3) Hebrew (Danon 2013: 2) a. 30 axuz-im me-ha-maskoret holx-im / ?holex-et le-sxar.30 percent-m.plof-def-salary-f.sggoes-m.pl/ goes-f.sgto-rent '30 % of the salary goes to (paying the) rent.' (Q-Agree / ?N-Agree) b. Maxacit me-ha-tošav-im ovd-im / *oved-et be-xakla'ut.half-f.sgof-def-residents-m.plwork-m.pl/ work-f.sgin-agriculture 'Half of the residents work in agriculture.' (N-Agree / *Q-Agree) Different proposals have been made for analysing the optionality of agreement (Franks 1994;Wechsler & Zlatić 2000;2003;Bošković 2003;2006;Danon 2013;Despić 2013), most of which restrict the empirical coverage to only certain types of quantifiers.The attention is often directed at the question of case assignment and the difference between agreeing and non-agreeing subjects, analysing neuter singular as a repair strategy for the latter.Additionally, for Bošković (2003) the option of plural agreement is triggered by the semantics in special cases.Danon (2013) on the other hand proposes a maximally permissive system of agreement in which the features appearing on the verb depend on whether φ-features of the quantifier are intrinsically valued or receive the value from the noun.In this system, optionality is always available, but there is no default option.We contribute novel data from Serbo-Croatian, which show that in this South Slavic language agreement can alternate between agreement with the quantifier (henceforth: Q-Agree), agreement with the noun (henceforth: N-Agree), and default neuter singular agreement, across different types of quantifiers that assign genitive case to the embedded noun.Crucially, this optionality arises when the quantified noun phrase (henceforth: QNP) is in the pre-verbal position, but post-verbally, only Q-Agree and default agreement are available.In this sense, agreement with QNPs resembles closest vs. highest conjunct agreement patterns, described for South Slavic languages (Corbett 1991;Bošković 2009;Willer-Gold et al. 2016).Since case-based systems arguing for semantic agreement and Danon's system cannot account for these restrictions on agreement in Serbo-Croatian, we turn to the solutions proposed for conjunct agreement, more specifically to the derivational system based on rule ordering, proposed by Murphy & Puškar (2018).
Section 2 introduces the different types of QNPs available for Serbo-Croatian.In section 3 we point out several problems previous approaches to agreement with QNPs face, based on the data presented in section 2. The key observation regarding the parallelism between QNP agreement and conjunct agreement is presented in section 4. Section 5 compares two recent proposals made for conjunct agreement patterns in South Slavic and discusses their potential to be extended to QNP agreement patterns.We show that the rule-ordering system, developed for conjunct agreement by Murphy & Puškar (2018), can be faithfully extended to QNP agreement patterns, while also being able to account for additional NP-topicalisation.Section 7 summarises and concludes.

Agreement can alternate
According to the generalisations made by previous reports on the agreement patterns with QNPs in Serbo-Croatian (Franks 1994;Wechsler & Zlatić 2000;2003;Bošković 2003), it is the quantifier's morpho-syntactic category that determines the agreement pattern.Quantifiers are divided by Wechsler & Zlatić (2003) into the following groups:

i. Adjectival quantifiers
This group consists of quantifiers like neki 'some', brojni 'numerous', svi 'all', svaki 'every' etc.They agree with the noun they modify.The features on the verb always match the features of the noun, so previous reports have interpreted this as "N-Agree only".ii.Nominal quantifiers Quantifiers such as većina 'majority', nekolicina 'few', niz 'sequence', deo/dio 'part', par 'pair, couple' etc. fall into this group.They are fully fledged nouns, with their own set of φ-features, therefore there is no concord with the noun they modify.Only Q-Agree was reported available with these quantifiers and the noun bears genitive case.
A subgroup of nominal quantifiers consists of quantifiers such as dva 'two', tri 'three', četiri 'four', and oba 'both'.Among them, only 'two' and 'both' show concord in gender with the noun: dva and oba for masculine and neuter nouns, and dve/dvije and obe/obje for feminine.A special kind of Q-Agree is reported as the only option: namely, 'two', 'three', 'four', and 'both' trigger paucal agreement, distinctive from the plural agreement by a different exponent on the participle.1 iii.Uninflecting quantifiers Uninflecting quantifiers do not inflect for gender, therefore it is assumed that they do not agree with the noun in genitive.This is the case for quantifiers mnogo 'many/much', malo 'a little', nekoliko 'a few', and numerals pet 'five', and higher.According to the literature, agreement can alternate only with these QNPs, between the default n.sg and plural N-Agree, with a remark that N-Agree is an option for some speakers.
Contrary to previous reports, the data collected in this paper show more patterns than so far attested.For QNP subjects in neutral pre-verbal position, the alternation is available regardless of the type of quantifier.
The data was collected through a pilot-survey in Google Forms, based on grammaticality judgements, on a 5-point scale (1 = completely bad, 5 = sounds excellent), reported here in form of average scores (medians) for every option.The judgements were given by 116 native speakers of Serbo-Croatian:2 75,7% non-linguists, and 24,3% linguists or philologists.
The sentences are in past tense active or present tense passive, because they require the same auxiliary (jesam 'to be'), agreeing in number and person, and a participle, agreeing in number and gender with the subject.Sentence subjects included quantified noun phrases, where the nouns used were both animate and inanimate.The participants were presented with sentences in a randomised order, interspersed with fillers consisting of multiple choice questions.

Adjectival quantifiers
For adjectival quantifiers, features on the participle always match the features on both the noun and the quantifier, due to internal concord between the quantifier and the noun.These quantifiers do not assign genitive case and do not affect the form of the verb that predicates over the modified noun, hence, only N-Agree is available in these cases: if the noun is n.sg, as in (4a), so is the participle; if the noun is m.pl,only the m.pl option is grammatical (4b (N-Agree: 5 / default: 1)

Paucal-triggering quantifiers
As previously mentioned, there is a subgroup of quantifiers which consists of only four members, numerals 2-4 and 'both'. 3Due to their special behaviour, we classify them as a separate group, between fully-agreeing adjectival and non-agreeing nominal quantifiers.
(5)  5), the numerals 'both', 'two', 'three' and 'four' exhibit different behaviour when it comes to agreement, namely they induce the emergence of paucal on the participle. 4Additionally, 'both' and 'two' inflect for gender, as shown in (5a), unlike 'three' and 'four', as shown in (5b).In addition, both plural and default are available (although with lower average rates) for these QNPs, contrary to what has been claimed in the literature.

Nominal quantifiers
Nominal quantifiers are similar to paucal-triggering quantifiers, in that they trigger Q-Agree on the participle, illustrated in (6a)5 for 'sequence ' and in (6b) for 'majority'.They have their own number and gender features, and thus behave as typical nouns.As mentioned above, the quantifying noun bears nominative case, whereas the quantified noun bears genitive case.Contrary to the reports by Wechsler & Zlatić (2003;2000), QNPs with nominal quantifiers can also exhibit N-Agree and default, shown in (6a) and (6b).

Uninflecting quantifiers
For the uninflecting quantifiers, illustrated by the examples below Wechsler & Zlatić (2003;2000); Bošković (2003); Šarić (2014) and others claim N-Agree to be available for some speakers as an alternative to the default pattern.The speakers' judgements in our case do show the default to be slightly better, which is a general tendency for all quantifiers.
( The availability of N-Agree could be argued to arise as the result of re-analysing uninflecting quantifiers as their adjectival counterparts, e.g.mnoge in (7a).Similar acceptability scores, however, are found with numerals above 5, for which, crucially, no adjectival version exists, see (8).

Interim summary
All cases considered, there is consistent variation within QNP agreement in Serbo-Croatian between Q-Agree (singular or paucal), default n.sg, and N-Agree (plural) on the other.The relational properties between the quantifier and the embedded noun, as well as the attested agreement patterns with QNP in pre-verbal position, can be summarised as in Table 1.
Several new observations can be made from the Table 1.First, contrary to previous claims, both N-Agree and default in Serbo-Croatian can occur with all quantifiers.Second, at least in the context of QNPs, there seems to be no correlation between N-Agree and genitive case assignment -the genitive does not render the features of the noun invisible for agreement.Third, there is a correlation between concord and genitive case assignment (except for 'two', 'both') -genitive case is marked on the noun if the quantifier does not show concord.Pesetsky (1982); Franks (1994) and Bošković (2003;2006) derive agreement alternations with QNPs from positional differences (a high position which enables spec-head agreement and a low position which does not), resulting from a categorical distinction (DP/NP vs. QP) and/or the need to acquire (nominative) case.They focus on adjectival quantifiers, which allow only one agreement option (pl), and uninflecting quantifiers (5 and up), which allow for an additional default sg agreement option.While for Russian Pesetsky (1982) and Franks (1994) diagnose a height difference between agreeing subjects (pl) and non-agreeing subjects (sg), based on different subjecthood tests such as binding, control, and comp-trace effects, the agreement alternations in Serbo-Croatian do not seem to be sensitive to different pre-verbal positions of the subject.There is, however, a restriction that arises from pre-verbal vs. post-verbal subject positions -an effect we will make use of in our own account.Agreeing subjects in Russian, they argue, move to a high position to receive case, while non-agreeing subjects stay low because, by assumption, they do not need case.In contrast, Serbo-Croatian subjects move to a higher position in any case, but agreement fails for independent reasons, resulting in default sg agree.Bošković (2006) drops the categorical difference and ties the agreement option to case: nominative case assignment and φ-agreement are licensed in SpecIP.Thus, uninflecting quantifiers in Russian trigger pl agreement if they get assigned zero nominative marking, while case-less uninflecting quantifiers trigger default sg marking.For Serbo-Croatian, Bošković (2003) proposes that case assignment does not have to be licensed in a specific position.Rather, uninflecting quantifiers are always case-less and trigger default sg agreement, whereas pl agreement arises as a special form of "semantic" agreement.For Šarić (2014), the default n.sg with uninflecting quantifiers results from the featural deficiency of these lexical items.

Case-based accounts and attraction theories
Semantic agreement corresponds to the N-Agree option, described in the previous section.As is shown in the examples in section 2, not only number but also gender is exponed by the participle.Since the meaning of the embedded noun cannot be argued to encode natural feminine gender, it must be grammatical gender information that the participle expresses.An example with a nominal quantifier that excludes a natural gender interpretation is repeated in (9).
A further problem emerges with the third option occurring with nominal and paucal quantifiers, shown in sections 2.2 and 2.3.Since case-based approaches focus on the difference between adjectival quantifiers, for which only N-Agree is available, and uninflecting quantifiers, which alternate between N-Agree and default, a third option such as Q-Agree for nominal quantifiers and pauc for paucal quantifiers is, without further assumptions, not accounted for.
Finally, another argument against semantic N-Agree can be brought forward with respect to topicalisation, a syntactic operation which seems to be able to block N-Agree, as the following examples show. 6,7  (10) Većin-a klijenat-a: je kupil-a / su majority-f.sg.nom client-m.pl.gen aux.3sg bought-f.sg/ aux.3pl kupil-i / je kupil-o knjigu.bought-m.pl/ aux.3sg bought-n.sgbook 'The majority of clients bought the book.' (Q-Agree: 5 / N-Agree: 3 / default: 3) a. Klijenat-a: je knjigu kupil-a većin-a.client-m.pl.gen aux.3sg book bought-f.sgmajority-f.sg.nom 'As for the clients, the majority of them bought the book.' (Q-Agree: 2) b. *Klijenat-a: su knjigu kupil-i većin-a.client-m.pl.gen aux.3pl book bought-m.plmajority-f.sg.nom 'As for the clients, the majority of them bought the book.' (N-Agree: 1) 6 The low average grades of the topicalisation examples all-in-all might be a consequence of the design of the pilot-study itself.Namely, these structures contain a word order rather unusual for sentences uttered out-ofthe-blue, as these examples were presented to the speakers without any context.We expect higher acceptability rates if presented with suitable contexts, such as in (i).Nevertheless, a dispreference for N-Agree with respect to other agreement options in the examples in (10) is noticeable.
(i) Context: At a promotion event for a new book about nutrition, primarily intended for the author's clients but also open to the public, A asks B how many books were sold to the clients.

B:
Klijenat-a: je knjigu kupil-a većin-a, ali bil-o je client-m.pl.gen aux.3sg book bought-f.sgmajority-f.sg.nom but were-n.sgaux.3sg i nek-ih drug-ih kupac-a.and some-m.pl.gen other-m.pl.gen buyer-m.pl.gen 'As for the clients, the majority of them bought the book, but there were some other buyers, too.' B's answer not only addresses A's question but signals the presence of a more general question salient in the context of the form How many of who bought the book?This interpretation is in line with contrastive topics in English, discussed by Büring (2003) and Wagner (2012). 7The attentive reader will notice that topics are split in post-verbal position, while the baseline presents a pre-verbal subject position.The subject position with respect to the participle indeed plays an important role in the current theory and will be addressed in more detail in the next section.
c. Klijenat-a: je knjigu kupil-o većin-a.client-m.pl.gen aux.3sg book bought-n.sgmajority-f.sg.nom 'As for the clients, the majority of them bought the book.' (default: 2.5) If N-Agree were the result of the semantic interpretation of QNPs, we would not expect it to be sensitive to topicalisation, contrary to what (10) shows for nominal quantifiers.
The last point of this section concerns potential language processing accounts of agreement alternations with QNPs in Serbo-Croatian.A different way to explain the N-Agree option is to attribute the occurrence of number and gender features to attraction effects happening in speech processing and production (Harrison 2004;Badecker & Kuminiak 2007;Lorimor et al. 2008;Malko & Slioussar 2013;Slioussar & Malko 2016;Ristić et al. 2016).The sentence in (11) provides an example for number attraction in English.
Under an attraction account, the Q-Agree option, shown in section 2, is the result of agreement with the hierarchically highest argument, whereas N-Agree is triggered by an erroneous agreement source in the local context. 8Under such an analysis, the judgements in section 2 would suggest that attraction errors do not only occur in production, as previous studies have reported, but they also have a significant effect in acceptability judgements, since both agreement options seem to be equally available for most types of quantifiers.
What is even more surprising under this view, however, is the low acceptability rate of N-Agree in the topicalised structures in (10).If attraction errors are due to a competing local agreement goal and the only linearly available goal is the embedded noun, attraction errors are expected to increase rather than decrease.On the contrary, what we find with structures like (10) is a clear preference for Q-Agree and default.

Two sets of ϕ-features: Danon (2013)
Based on the observation that agreement in Modern Hebrew alternates between Q-Agree and N-Agree, Danon (2013) adopts the proposal by Wechsler & Zlatić (2003), originally implemented in HPSG framework, that lexical items are specified with two distinct sets of φ-features.Index features reflect the noun's semantics, and are relevant to subjectpredicate agreement.concord features are related to the noun's morphology, and are relevant to NP-internal concord.Not only is it possible that concord and index features mismatch on one and the same lexical item, but any of them can enter the derivation unvalued.This is determined by an external mechanism, 9 related to the semantics of the entire sentence.Quantifiers are assumed to take a case-assigning FP as a complement, which in turn takes NP as its complement.The chosen option of agreement depends on whether the features of Q enter the derivation valued or not.If they are valued, as in (12), the QNP's index features get projected up from Q to get copied onto T. If the index features of Q are unvalued when Q enters the derivation, as in (13), they get valued by the index features of the embedded NP.The QNP still gets the index features via Q, but now they originate on the noun.Depending on whether the quantifier enters into a concord relation with the noun, concord features can additionally be unvalued on Q. Danon's (2013) system is, thus, free of assuming structural ambiguity of QNPs in alternating QNP agreement patterns (in contrast to case-based approaches), but it requires a complex feature system and an additional external mechanism to constrain the valuing of the index features on the quantifier.An important suggestion is made for default agreement in Serbo-Croatian: agreement is always successful, and default is a result of a fixed n.sg default value for the index feature of the Q head.This system does not tie successful φ-agreement to the presence of a case feature and default agreement to the absence of a case feature as previous analyses have done.Rather, φ-agreement always happens with the entire QP, which is marked for nominative and gets its index feature from Q.One potential counter-argument against this type of approach can be raised with respect to the exponents of concord and index features.In cases where we see concord between the quantifier and the noun, as well as Q-Agree on the participle, the exponents on the quantifier and the participle are identical, see ( 14) for an example with paucal quantifiers.If there were different slots for index and concord features, one would potentially expect different exponents for concord and index agreement.A second, more serious, problem arises with default agreement.A possible scenario for default insertion to be required would be an unvalued index feature on Q.However, there is no way Q can ever end up with index: □ after it is merged with FP, since Q either contributes its own feature or relies on N for index to be valued.Default can therefore not result from an unvalued index feature. 1011 Additional problems for the Danon system emerge with quantifiers that show concord and undergo NP-topicalisation, i.e. adjectival quantifiers and the paucal quantifiers 'two' and 'both', see ( 15) and ( 16).As was shown in (10), N-Agree is blocked if the QNP is discontinuous with the quantifier occuring in the left periphery.The unavailability of N-Agree can be accounted for under the assumption that topic splits are base-generated: if there is no step in the derivation in which the quantifier and the embedded noun are merged in a sufficiently local configuration, there is no way for Q to value its index feature by N. While this solution might work for nominal quantifiers in (10) which do not show concord with the embedded noun, ( 15) and ( 16) strongly suggest that quantifier and noun start-off in a local configuration and are subsequently split via movement.
( There is further independent evidence against base-generation, arguing in favour of topicalisation as feature-driven syntactic movement.Topicalised NPs e.g.reconstruct for binding.In ( 17), the possessive is bound by the quantifier, requiring the topicalised NP to be interpreted in its base position.12(i) Svoj-ih i/*j / Njen-ih i/j klijenat-a: Sara i mrzi većin-u.refl.poss-m.pl.gen / poss-m.pl.gen client-m.pl.genSara-f.sg.nom hate.3sgmajority-f.sg.acc 'As for her i/j clients, Sara i hates the majority of them.' Advokat-∅ je imao-∅ mnogo olovak-a: i nekoliko attorney-m.sg.nom aux.3sg had-m.sgmany pen-f.pl.gen and few svezak-a:.notebook-f.pl.gen 'The attorney had many pens and a few notebooks.'(22) *Svezak-a: je advokat-∅ imao-∅ mnogo olovak-a: notebook-f.pl.gen aux.3sg attorney-m.sg.nom had-m.sgmany pen-f.pl.gen i nekoliko.and few 'As for the notebooks, the attorney had many pens and a few of them.' Split topic structures are information structurally marked, they require a context in which the referent of the noun is not only previously mentioned but also contrasts with another alternative in the context, see footnote 6.In line with many movement accounts on topicalisation (Chomsky 1977;Rivero 1978;Authier 1991;Grohmann 2003;Frey 2006;Frascarelli & Hinterhölzl 2007;Miyagawa 2017), we propose a left peripheral head, either C or a dedicated Top head, carrying a feature [•top•] which attracts contrastive topics to its specifier.
Having established that topic splits are derived by movement, the ban on N-Agree in (10b) on the one hand and the concord data from ( 15) and ( 16) on the other forces one to assume that extraction takes place after concord but before index features are valued on the quantifier.However, as we argued above and in footnote 6, topic splits are featuretriggered by a left peripheral head which arguably enters the derivation too late to extract the quantifier before it can undergo index agreement.
The final observation with respect to Danon's (2013) proposal relates to the position of the participle.If the QNP follows the participle, only Q-Agree and default are available -a configuration that has not received much attention in the literature. 14This is illustrated in the following examples, in (23) for the paucal-triggering 'three', in (24) for the nominal 'majority', and for uninflecting quantifiers in (25), for 'six'.Since Danon locates the source of the agreement alternations on the index feature of Q, there is no way to account for a pre-verbal v. post-verbal distinction. (23) Isporučen-a su / *isporučen-i su / isporučen-o je delivered-m.paaux.3pl / delivered-m.plaux.3pl / delivered-n.sgaux.3sg tri kačket-a.three cap-m.pa'Three caps were delivered.'(paucal: 5 / plural: 1 / default: 4) (24) Na nju je lajal-a / *su lajal-i / je lajal-o at her aux.3sgbarked-f.sg/ aux.3pl barked-m.pl/ aux.3sg barked-n.sgvećin-a pas-a:.majority-f.sgdog-m.pl.gen 'The majority of dogs barked at her.' (Q-Agree: 4 / N-Agree: 1 / default: 3) (25) U prvoj smeni je radil-o / *su radil-i šest in first shift aux.3sg worked-n.sg/ aux.3pl worked-m.plsix konobar-a:.waiters-m.pl.gen 'Six waiters worked in the first shift.'(default: 5 / N-Agree: 1) Summing up, Danon's index-concord agreement system is able to account for the various agreement patterns that can be found with different types of quantifiers in Serbo-Croatian.However, the theory overgenerates with respect to the post-verbal data given in ( 23)-( 25), while it undergenerates generally in terms of default agreement.Moreover, the account has to assume a counter-cyclic topicalisation operation to derive the agreement options in (10) and concord in ( 15) and ( 16).

Key observation
The pre-verbal data from section 2, together with the post-verbal structures, given in ( 23)-( 25), constitute an agreement pattern that is reminiscent of closest vs. highest conjunct agreement in South Slavic (Corbett 1991;Bošković 2009;Marušič et al. 2015;Willer-Gold et al. 2016).The structures in ( 26)-( 31) present the basic pattern for nominal quantifiers with minimal examples: while agreement with QNPs in the pre-verbal position can alter-nate between Q-Agree, N-Agree, and default, as shown in ( 26) and ( 28), subject QNPs positioned post-verbally only allow for Q-Agree and default, cf.(29) vs. ( 31).
The parallel of QNP agreement to conjunct agreement is provided in ( 32)-( 37), examples taken from Willer-Gold et al. (2016: 193). 15Pre-verbal agreement with coordinated subjects can alternate between agreement with the first (32) or with the last conjunct (33), and resolved m.pl agreement (34).

QNPs as coordinations
We will discuss two types of accounts of conjunct agreement: one is based on the notion of agreement as a process that is distributed across different modules of grammar so that linear order can have an influence on the availability of agreement goals (Bhatt & Walkow 2013;Marušič et al. 2015), while the second account is purely syntactic and makes use of the idea that operations such as Agree and Merge can be applied in different orders if they are triggered by the same head (Müller 2009;Georgi 2014;Assmann et al. 2015;Murphy & Puškar 2018).Since the decision between agreement options in the latter approach happens strictly locally, syntactic operations such as topicalisation, which are arguably triggered at a late stage in the syntactic derivation, are predicted to not have an effect on N-Agree vs. Q-Agree.The distributed approach, however, derives the post-syntactic agreement pattern from output representations, in which topicalisation operations will make a difference.QNP topicalisation structures, thus, provide a unique window into the (post)-syntactic properties of pre-verbal vs. post-verbal agreement strategies in Serbo-Croatian.
For the following discussion, we will assume that QNPs have the structure shown in (39), parallel to what has been claimed for conjoined NPs (Johannessen 1998;Zhang 2010) The functional head K assigns genitive case to to its complement, i.e.NP (see also Bošković 2006;Danon 2013), and takes QP as its specifier.Note that this assumption ties QNP agreement alternations to the presence of genitive case.If there is only one agreement option, independent of the position of the participle, as it is the case with adjectival quantifiers, genitive case on the embedded noun is also absent, see Table 1.Both of those properties can be traced back to the absence of K, following the structure in (39), see subsection 5.3 for an extended discussion.Marušič et al. (2015) carry out experiments and confirm that the agreement pattern given in Table 3 also holds for Slovenian.Agreement in their system is a two-step process, in which first an Agree-Link is established in syntax between a probe and a suitable goal, a second step Agree-Copy then transfers φ values from goal to probe.Variation in terms of agreement strategies is accounted for by the relative timing of Agree-Copy, i.e. whether it happens in syntax or post-syntax.The participle first probes for the &P (or KP) via Agree-Link.Since the &P/KP has no features of its own, the probe continues searching inside the &P/KP.If Agree-Copy, as the next step, is established in syntax proper, the features of the first conjunct, i.e. the hierarchically closer goal, are copied onto the participle.If Agree-Copy is established in post-syntax, that is after linearisation, the last conjunct is the linearly closer goal agreeing with the participle.Below, ( 40) and ( 41) illustrate how this theory can account for the N-Agree/Q-Agree alternation in pre-verbal structures.
Note that topicalisation does not allow for N-Agree per se, as we have seen in the examples in (10b) and (15).Table 5 provides an overview of the agreement options available across syntactic configurations.
In order to account for (44b), Marušič et al. (2015) would have to take topicalisation to be a PF-operation and order it after Copy-Agree.As a consequence, topicalisation has to take place after linearisation.While there are word order inducing operations ordered after linearisation, such as e.g.Local Dislocation (Embick & Noyer 2001), it is worth pointing out that post-linearisation operations are generally understood to rely on adjacency, hence must be maximally local.
To sum up, although the distributed agreement model can explain the pre-verbal vs. post-verbal agreement alternations, it needs to make additional assumptions in order to account for the availability of N-Agree in pre-verbal topicalisation configurations.

Order of operations
A purely syntactic account for the conjunct agreement patterns shown in Table 3 is proposed by Murphy & Puškar (2018). 18,19It builds on the idea that syntactic operations can be ordered freely, if they are triggered by the same functional head (Müller 2009;Georgi 2014;Assmann et al. 2015).Agreement variation is achieved by allowing the & head in &P to agree with the first conjunct, the last conjunct, neither one of them, or both of them.20 After the φ-features of & have projected up to &P, the participle agrees with the entire &P.We adopt this model for QNP agreement, transferring the structure in (38) to the structure in (39).
The structure of KP is built using three basic operations: Merge, ↑Agree↑, and ↓Agree↓, with the addition of Move, whose application or non-application derives the pre-verbal or the post-verbal word order. 21The order of operations is here assumed to be free, however, once established, it has to be maintained throughout the derivation.This is ensured by Move -(Internal Merge) applies freely, but only if it has a (positive) effect on outcome (cf. Chomsky 2001: 60f. on Object Shift).c.
↓Agree↓ -('Downward' Head-Comp Agree) copies a feature value from a goal c-commanded by the probe d.
↑Agree↑ -('Upward' Spec-Head Agree) copies a feature values from a goal m-commanded by the probe Merge: With the order of operations on Part maintained, Move cannot feed Agree, as in (57), therefore it does not apply. (57) Move ≫ ↓Agree↓: With the KP remaining in Spec,v, ↓Agree↓ applies successfully and the features of the quantifier appear on the participle, which correctly predicts that Q-Agree is available post-verbally.This step is shown in (58).
(58) ↓Agree↓: The two orders of operations in which both ↓Agree↓ and ↑Agree↑ apply before Merge equally result in a derivation where the features on K remain unvalued.With respect to order #3, shown in (59), ↑Agree↑ precedes ↓Agree↓, and both apply vacuously since neither the complement nor the specifier have been merged yet, cf. ( 60)-( 61).Merging the arguments counter-feeds both Agree operations, and KP enters the next stage with both φ-slots unvalued, see ( 62). Merge: The derivation, however, does not crash, since probes can fail to agree.Move can feed Agree, so that when Part probes for φ-features, it peeks into KP, where the highest goal it finds is QP, shown in ( 63). Merge: In this scenario, however, Move would bleed Agree, since its application would destroy the context for ↓Agree↓ to apply, see (68). (68) Move ≫ ↓Agree↓: Thus, Move does not apply.The subject KP stays in Spec,vP, as shown in (69).Again, Part peeks into KP, in which the highest goal is QP, and agrees with it.
(69) ↓Agree↓: The four orders discussed so far give the following results: order #1 derives pre-verbal N-Agree, while the other three orders result in Q-Agree, order #3 pre-verbally, and orders #2 and #4 post-verbally.There is no order of operations in this system that predicts N-Agree post-verbally.
Reversing the order of the two Agree operations, see (74), produces the same result.Since Merge has applied first, the K head agrees with both QP and NP, so that it projects two sets of φ-features, see ( 75)-( 77). (74) Merge ≫ ↑Agree↑ ≫ ↓Agree↓ In contrast to Marušič et al. (2015), Murphy & Puškar (2018) derive m.pl via an optimality-theoretic constraint interaction (Prince & Smolensky 1993/2004) in post-syntax, giving rise to Resolved Agreement. 25The system of resolution is based on the Markedness Hierarchy of Gender (Stankiewicz 1986;Andrews 1990), where m is unmarked.In post-syntax every other gender value is deleted, and masc arises as an Emergence of the Unmarked effect (McCarthy & Prince 1994).
For QNP agreement, there is no m.plresolution in agreement, instead we observe n.sg default agreement.We propose that the OT resolution is not available for QNPs.The reason might lie in the different nature of the agreeing heads.While the & head only agrees with its conjuncts, the K head also assigns genitive case to its complement.Moreover, & and K differ in their semantics, in that only the former requires the conjuncts to form a plurality and thus arguably need φ-feature values to resolve.We argue that unresolved feature clashes lead to spell-out dilemmas which result in insertion of the default value n.sg. 26This step provides an explanation as to why two different feature values can be triggered by the same feature set-up, that is why two different mechanisms can be employed to resolve the same feature conflict.

Predictions and open questions
As the previous section has shown, N-Agree is only possible if QNPs precede participles.Since the only order of operations which allows for N-Agree (order #1) is an order which triggers move to a pre-verbal position, the lack of N-Agree in post-verbal position is 25 The reason for Marušič et al. (2015) to analyse m.pl as default and not resolved agreement in Slovenian comes from observations considering matching gender coordination where m.pl seems to be an option, even if neither of the conjuncts encodes masc.Willer-Gold et al. (2016: 204) Since n.sg is analysed as Q-Agree for uninflecting quantifiers, a new correlation between genitive case assignment and Q-Agree/default emerges: Q-Agree/default becomes an option in case genitive case is assigned.Post-verbally, N-Agree is unavailable.The data set is summarised in Table 6.

Conclusion and outlook
The current study provides an extensive exploration into the plurality of agreement patterns, observable with QNP subjects in Serbo-Croatian.Contrary to previous reports, the data we contribute show that agreement with QNPs, pre-verbally, can vary between Q-Agree, N-Agree, and default (neuter singular) agreement; but post-verbally only Q-Agree and default are available options.This asymmetry is consistent with what has been recently reported for conjunct agreement for South Slavic languages: first conjunct agreement and resolved agreement are available both pre-and post-verbally; last conjunct agreement is available only in the pre-verbal case.
Existing approaches to QNP agreement encounter difficulties in accounting for the full set of variation presented here.A rule ordering account, along the lines of Müller (2009); Georgi (2014); Assmann et al. (2015); Murphy & Puškar (2018), seems to offer the most promising solution.The variation in agreement is derived by recourse to different orders of syntactic operations.The derivational account we have argued for is superior to previous accounts because it correctly predicts all attested patterns of pre-verbal and post-verbal agreement in Serbo-Croatian, and excludes the possibility of post-verbal N-Agree, judged by the speakers as unacceptable.An additional advantage of this account is demonstrated by the right predictions it makes for more marked word orders such as topicalisation, without any further assumptions.

Type of quantifier concord genitive N-Agree
Agreement with QNPs in Slavic has received much attention in generative syntax, especially for Russian, where an alternation between singular and plural agreement is found.Proposals put forward (Pesetsky 1982;2013;Bošković 2003;2006;2010;Pereltsvaig 2006;Bailyn 2012) have tied these facts to case (nominative vs. non-nominative), sentence positions, and the presence vs. absence of a DP-layer, among other things.Krasovitsky et al. (2009b), a QNP corpus study, report on agreement patterns with QNPs in Russian that exhibit the singular-plural alternations pre-as well as post-verbally (37% singular, 63% plural).Thus, the restriction which holds for Serbo-Croatian, N-Agree being unavailable post-verbally, seems not to hold for the Russian corpus data.With respect to the current approach, the Russian QNP facts could be explained by desynchronising the order of operations between heads.This would ultimately allow for more agreement options, that is, post-verbal N-Agree would not be excluded.Different patterns are reported for conjunct agreement (Krasovitsky et al. 2009a).Alternations are only found if the closest conjunct is singular (pre-verbal singular = 6%, plural = 94%; post-verbal singular = 70%, plural = 30%).These results lead one to conclude that plural is the resolved value, available pre-and postverbally, whereas postverbal last conjunct agreement and preverbal first conjunct agreement are excluded.
According Marušič & Nevins (2010), QNPs in Slovenian do not show alternating agreement options, agreement only varies with the type of quantifier (N-Agree with numerals 1-4; default with numerals > 5 and other uninflecting quantifiers; Q-Agree with nominal numerals like 'milion').Conjunctions in Slovenian, however, do trigger agreement alternations (Marušič et al. 2015).Since we associate the parallel between coordinations and QNPs agreement patterns with a parallel in structure, see ( 38) and ( 39), Slovenian might diverge from this picture in this respect.
Polish Conjunct agreement is the mirror image of Serbo-Croatian.While Polish manifests resolved agreement both pre-and post-verbally, only the last conjunct agrees in preverbal subjects.Agreement with either conjunct is always acceptable when the subject is post-verbal, but the availability of pre-verbal last conjunct agreement is dependent on the type of noun, i.e. it is only available with abstract nouns (Citko 2004;Willim 2012).φ-agreement with QNP subjects, however, does not alternate: numerals 1-4 combine with nouns in the nominative, allowing predicates to agree only with N. With nominal quantifiers, Q-Agree is the only option, except for cases where the quantifier (nominal or paucal) bears accusative case, then only default n.sg is available.The same restriction holds for higher numerals, which, as argued by Przepiórkowski & Patejuk (2012); Miechowicz-Mathiasen (2014); Witkoś & Dziubała-Szrejbrowska (2016), are accusative by default, and for which, thus, default is the only option.Polish does, however, show agreement alternations in case.Participial and adjectival predicates can agree either with the numeral or the noun, where the predicative may bear accusative or genitive, respectively.For Polish, thus, case assignment seems to play a crucial role and needs to be closer looked into.The present account, so far, does not consider case assignment as an operation that is ordered with respect to other operations.
Judging from the data given by Danon (2013), we can conclude that QNP agreement in Modern Hebrew can optionally alternate between Q-Agree and N-Agree in the pre-verbal position, but it is unclear what restricts the availability of these options in examples like (3).To the best of our knowledge, it is not reported whether the same holds for postverbal cases.Doron (2000), however, reports that agreement with conjoined noun phrases alternates only post-verbally, and pre-verbal subjects trigger resolved agreement.A more thorough look into Hebrew is required in order to give a solution to the puzzle.
Hungarian and Finnish are some of the languages reported by Kiss (2012) and Crone (2016) to have a pre-verbal/post-verbal agreement asymmetry with conjoined noun phrases.In Hungarian, pre-verbal agreement can alternate between singular and plural, but post-verbally only singular is available.In Finnish, agreement alternations with conjoined noun phrases are available post-verbally (singular or plural), but pre-verbally only plural agreement is available.Swahili exhibits the same pattern, as Marten (2005) reports.Conjoined noun phrases in Modern Greek trigger a large variety of agreement alternations, sensitive to the hierarchy of genders, with a preference for first conjunct agreement in post-verbal cases (Kazana 2011).In contrast to these languages, in Albanian the adjectival participle must agree with the closest conjunct, which is the final one (Peterson 1986).Depending on whether QNPs can trigger agreement alternations, 28  potential further evidence can be found for the current theory.
Needless to say, more extensive empirical studies are required in order to give a full account of the cross-linguistic variation, a goal that lies beyond the scope of this paper.The empirical generalisations on the parallels of QNP agreement and conjunct agreement, identified in this paper for Serbo-Croatian, thus remain to be further examined.

(
, ends up with two unvalued feature slots if the order of Agree operations is reversed, as the order in (64) requires.Again, Merge counter-feeds both ↓Agree↓ and ↑Agree↑, see (65)-(67).
5.2.4 Orders #5,#6: Multiple valuation (= Default)If Merge is ordered before both ↓Agree↓ and ↑Agree↑, required by the order in (70), both Agree operations succeed, shown in This will lead to a clash of features in the post-syntactic component.

Table 1 :
Agree, concord and genitive with QNPs (to be revised) (the exclamation point indicates new observations).

Table 2
provides an overview for the exponents on quantifiers, nouns and participles.Of the paucal-triggering quantifiers, only only 'two' and 'both' inflect: -e for f and -a for m and n.
Murphy & Puškar (2018)ion for Serbo-Croatian.Murphy & Puškar (2018)account for this observation by proposing two kinds of &, one that is pre-specified for masc and one that is not, i.e. & ɣ:m,□,□ vs. & ɣ:□,□ .The former is used for m.pl agreement strategy only.It seems then for QNP agreement alternations that there is only K ɣ:□,□ .26Anothercontext that creates a need for this default to get inserted is in impersonal sentences with dative subjects like (i), where arguably no agreement is taking place and a different kind of spell-out dilemma needs to be resolved.