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).

As previously mentioned, there is a subgroup of quantifiers which consists of only four members, numerals 2–4 and ‘both’.3 Due to their special behaviour, we classify them as a separate group, between fully-agreeing adjectival and non-agreeing nominal quantifiers.

As shown by the examples in (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.4 Additionally, ‘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 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).

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).

Uninflecting quantifiers are thus the only group of quantifiers in Serbo-Croatian for which agreement alternates only between the default N.SG and plural N-Agree, as shown in (7a) and (7b).

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.

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).

Since N-Agree tracks gender features in (9), also (5a) and (7a), an analysis based on semantic agreement is untenable. Grammatical gender information has to be transferred onto the participle by a syntactic mechanism and cannot be the result of QNP interpretation.

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.67

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.8 Under 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.

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 subject–predicate 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.

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.

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

Additional evidence for movement comes from observations considering syntactic islands such as relative clauses and coordinations. Compare (18) to (19), where topicalisation seems to be blocked if moved out of a a complex noun phrase. Note that split topics are not clause-bound per se, as (20) shows.

Extraction out of conjuncts is equally degraded, compare (21) to (22).13

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 feature-triggered 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.14 This 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.

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).

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.

In post-verbal configurations, the both hierarchically and linearly closest goal is the first conjunct. Structures (42) and (43) show how this reasoning translates into QNP configurations, modelled after (29) and (30):

Marušič et al. (2015) draw an additional distinction between a Peeking and a No-Peeking Grammar. Resolved agreement results from the latter option in that an agreement probe is not allowed to probe further than the maximal projection of the conjunction (or KP in this case). Since &P/KP is not valued for gender, a default value, M.PL, gets inserted.17

The two-step Agree account can cover both agreement patterns, presented in Tables 3 and 4. Without any further assumptions, the theory makes an important prediction: since N-Agree is the result of post-syntactic Agree-Copy, it should be sensitive to additional syntactic displacement operations such as NP-topicalisation. As (44) shows, this prediction is not borne out. N-Agree is possible, despite NP not being the linearly closest goal. (45) provides the structure for (44b).

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.

A purely syntactic account for the conjunct agreement patterns shown in Table 3 is proposed by Murphy & Puškar (2018).1819 It 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.21 The order of operations is here assumed to be free, however, once established, it has to be maintained throughout the derivation. This is ensured by the Uniform Order of Operations constraint, see (46), motivated by a similar idea from Assmann et al. (2015).

Two crucial assumption concern the status of MOVE: (i) it is not feature-driven and can only apply, if it feeds AGREE, and (ii) if it applies, its position is fixed, i.e. it is always the first operation that applies.22 Probes can fail to agree (Preminger 2014) which will become important in orders #3 and #4, shown in (47).

Given the three elementary operations, MERGE, ↑AGREE↑ and ↓AGREE↓, the factorial typology derives the following six patterns for QNP agreement:

Case assignment is ignored here because the operation does not have any impact on the output other than it being required to be fed by MERGE.23 In the rest of this section, we will show how the system can derive the agreement patterns given in Table 4.

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 accounted for. Q-Agree can be achieved either in pre-verbal or in post-verbal position. The former results from order #3 and the latter is a consequence of orders #2 or #4. Default agree is possible pre- and post-verbally as well, the former is derived by #6 and the latter by #5.

A crucial advantage of this system over the distributed account, presented in subsection 5.1, is its locality restriction, leaving the agreement pattern unaffected by further movement operations which are not relevant in the local environment. Note that the topicalisation data presented in (10), which disallow N-Agree, are cases of post-verbal agreement, while topicalisation in the pre-verbal structure in (44) allows for N-Agree. Since NP extraction happens at an arguably late stage of the syntactic derivation, all that counts for the availability of N-Agree is whether KP precedes or follows the participle. Hence, the (non-)availability of N-Agree under topicalisation is derived without any further assumptions.

The current system systematically predicts the behaviour of nominal quantifiers which alternate between N-Agree, Q-Agree, and default. In order to capture the alternation of uninflecting quantifiers between N-Agree and default, the ϕ-features of Q have to be specified for N.SG, following one of the options Danon (2013: 29) suggests for Serbo-Croatian. Adjectival quantifiers do not embed nouns with genitive case, thus they lack the case assigning head. Below, we make two suggestions for the internal structure of adjectival quantifiers, both of which predict only N-Agree as an option, as well as concord with NP.27

The picture becomes slightly more complex with paucal quantifiers, as ‘two’ and ‘both’ do not enter the derivation with their ϕ-features completely valued and can, at least in one order (#2), only agree with the participle via the K head. They receive their gender value via concord with the embedded noun, while the number feature is intrinsically valued. As soon as MERGE applies, both QP and NP are in a configuration where they can perform concord, following Pesetsky’s (1989) Earliness principle. For the orders #3 and #4, the participle directly agrees with QP, see (63) and (69), respectively. KP-internal concord, therefore, applies after QP and NP have merged in &P. For the order #2, an interesting constellation occurs, which is given in (80). Concord in gender between QP and NP on the one hand and ↑Agree↑ between K and QP on the other hand have to happen simultaneously after MERGE has applied.

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.