2.1 Multi-valued Ns

In this section I discuss Nominal RNR as a case of multi-valued Ns. Right Node Raising constructions (RNR) are cases where the conjuncts share the rightmost portion of the structure. In (6a) for example, the object apples is shared by the two conjoined sentences.¹

Nominal RNR refers to cases where two DPs share one noun. The intended interpretation of (7a) is in (7b) and student is shared by the two DPs. I will label the shared element the pivot and the pivot will be in bold throughout the paper.

Although the conjoined DPs refer to two individuals when both of the DPs are singular, the pivot must be singular in English. The plural pivot in (8) is unacceptable.

This is true for different kinds of DPs in (9). Note that the presence of the number marking in the remnant in the DPs is not necessary for the pivot to be singular. In (9d–e), John’s tall, Mary’s short, his tall and her short are not overtly marked as singular. Yet when the conjoined DPs refer to two individuals, only the singular pivot is possible. The intended reading is controlled by the use of the predicate are a couple.

Note also that strings like John’s tall and Mary’s short students themselves are acceptable in (10) when referring to more than two individuals. Since the focus on the current paper is the noun which is valued by multiple singular features, I will leave the reading in (10) aside.

2.2 Multi-valued Ts

Having discussed multi-valued Ns, we turn to another multi-valued target: T heads. Like Nominal RNR, the first case of multi-valued Ts involves Right Node Raising. Postal (1998); Yatabe (2003); Grosz (2009); Kluck (2009); Grosz (2015) observe that in the Right Node Raising constructions in (24), the verb have agrees with both singular subjects Bill and John and can show plural agreement, i.e. summative agreement.

Grosz (2015) observes that summative agreement on the T is seen in English, Western Armenian, Standard Gujarati, Hebrew, Italian, and Czech. On the other hand, Serbo-Croatian, Dutch, and Greek categorically ban plural agreement in these cases, allowing only singular agreement (see Kluck 2009 for experimental data from Dutch). (25) is an example of summative agreement in Italian and (26) shows an example of singular marked T in Slovenian.⁷

Grosz (2015) argues for a multi-dominance analysis for summative agreement in (27) where the T merges with both PerfPs and agrees with both the embedded subjects. To distinguish this structure from Nominal RNR, I will label this construction as TP RNR. In (27), Grosz (2015) assumes an analysis where multiple elements are multi-dominated. What’s important for the current purpose is that in this structure the T is shared and agrees with both the embedded subjects, thus multi-valued. As we have seen, the multi-valued Ts in English can be spelled out as plural.

As is noted in (24) and (25), singular marking on the T head is optionally available in English and Italian. For the singular marking observed in TP RNR, Grosz (2015) suggests two possibilities. First, it could be the case that while summative agreement results from multi-dominance, the singular marking results from ellipsis as in (28). The sentence starts out as two full conjoined sentences and the T’ of the first conjunct gets elided. The consequence of this approach is that languages like English and Italian allow both multi-dominance and ellipsis (see Barros & Vicente 2011), whereas languages like Slovenian and Serbo-Croatian that only allow singular marking in TP RNR do not allow multi-dominance. In other words, only summative agreement in TP RNR involves multi-valuation. As two reviewers point out, one question for this approach is what decides whether a language allows multi-dominance or not.

The second option is to assume that TP RNR in every language is a product of multi-dominance regardless of the agreement patterns. Different agreement patterns do not involve different structures of RNR but different agreement mechanisms. The implication of this approach for multi-valuation is that both the singular marking and summative agreement in TP RNR involve multi-valued Ts. The point of variation is how languages resolve multi-valued Ts with two singular values. Languages like English resolve the multi-valuation with summative agreement or distributive agreement, whereas languages like Serbo-Croatian resolve it only with distributive agreement.

Grosz (2015) supports the second approach on two grounds: 1. in Serbo-Croatian, a language that only allows singular marking on T, multi-dominance has been independently argued for (see Gračanin-Yuksek 2007). If ellipsis is the source for singular marking and multi-dominance is the source for summative agreement, then languages like Serbo-Croatian should at least allow summative agreement, contrary to fact. The absence of summative agreement in Serbo-Croatian can be accounted for if multi-dominance can also generate singular agreement, like distributive agreement in Nominal RNR. 2. This option assumes a unified multi-dominance treatment of the TP RNR. One can assume that multi-dominance is available universally without having to worry about what conditions whether a language allows multi-dominance.

In addition to these arguments, I provide another piece of evidence for the unified multi-dominance analysis of TP RNR. The kind of ellipsis that TP RNR would involve in (28) is called Stripping where an entire clause except one constituent (the subject in (28)) is elided. Stripping has been observed and discussed since the 70s (Hankamer & Sag 1976; Lobeck 1995; Merchant 2003; Wurmbrand 2017b). Previous literatures observe that Stripping is allowed in matrix clauses but not in subordinate clauses as shown in (29). From my survey, Stripping in the embedded clauses is banned across languages as found in Greek, Dutch, Serbo-Croatian, Slovenian, Italian, Icelandic, German, and Hungarian among others. I refer readers to Wurmbrand (2017b) for accounts for such restrictions on Stripping. It suffices for our purpose to show that the ellipsis required in TP RNR is banned in general.

Sentences in (29) involves forward Stripping, i.e. ellipsis in the second conjunct. Larson (2012) shows that Stripping is also banned in backward ellipsis. Barros & Vicente (2011); Larson (2012) use morphological mismatch and sloppy interpretation as diagnostics for ellipsis. For example in the VP ellipsis in (30), under the intended sloppy reading where Alice has negotiated Alice’s salary and Bob is about to negotiate Bob’s salary, the elided VP in the first conjunct contains the past form of the verb negotiated and the feminine possessive pronoun her. The antecedent in the second conjunct contains the infinitival form of the verb negotiate and masculine possessive pronoun his. The mismatching elements and the reference of the possessive pronouns Alice and Bob are in bold. Despite the mismatch between the antecedent and the elided material, the VP ellipsis is grammatical. Multi-dominance on the other hand has a hard time deriving the mismatch.

Larson (2012) observes that in TP RNR, the same kind of mismatch is not available. Under the sloppy reading in (31), the elided T’ contains the feminine possessive pronoun her referring to Iris. The possessive pronoun in the antecedent in the second conjunct is his referring to Daniel. If (31) could involve ellipsis, i.e. backward Stripping were possible in TP RNR, (31) is predicted to be grammatical like (30), contrary to fact. Note that (31) does not involve overt agreement on the pivot verb. The ban on Stripping in TP RNR is independent from agreement on the pivot.

Consequently, the shared T in English, be it singular or plural, results from a multi-dominance structure and involves multi-valuation.⁸

Before ending this section, I want to point out that multi-valued Ts do not only exist in RNR constructions. Gluckman (2016) observes that in Nocte the verb agrees with both the subject and the object and the two agreement relations are realized as one morpheme on the verb (portmanteau). Interestingly, when the subject is 1st person singular and the object is 2nd person singular, the verb shows 1st person plural agreement. (32) shows that -e is 1st person plural marker. (33) shows that the 1st person plural marker is used on the verb in a sentence with no 1st plural argument but two singular arguments. The same pattern is found in Karuk (Hokan), Yimas (Papuan), Wayampi (Tupí-Guaraní), Mapudungun (S.A. isolate), Bolinao (Austronesian), Tongva (Uto-Aztecan), Anindilyakwa (Australian), Colloquial Ainu (Ishikari dialect). The agreement pattern is in (34).

Gluckman proposes that the plural marking in (33) is a composed plural by two singular arguments. The T head probes both the object and the subject, getting two singular values, i.e. multi-valuation. The multi-valued T in Nocte is spelled out as plural, i.e. summative agreement. The detailed derivation can be found in Gluckman (2016). What’s relevant here is that the Nocte agreement pattern offers a non-RNR case of multi-valuation, which shows that multi-valuation is not restricted to Right Node Raising constructions but constitutes a more general phenomena. See Citko (2018) for summative agreement patterns with coordinated subjects in Polish.

In this section, I have shown that multi-valuation can also target T heads in TP RNR and composed plurality in Nocte, and that ellipsis is not a valid predictor of multi-dominance/valuation. Like the multi-valued Ns, T heads valued by multiple singular features can show distributive and summative agreement depending on the particular language and idiolect.

3.1 Type 1: Distributive agreement on multi-valued Ns and Ts

The first type of language shows distributive agreement on multi-valued Ns and Ts, modular cases where neither singular nor plural marking is possible on one of the agreement targets. This type of language includes Slovenian, Serbo-Croatian, Polish, Slovak, Icelandic, Dutch, Hindi, Romanian, Brazilian Portuguese, Spanish, Greek, Finnish, Hungarian, and Spanish. Below are examples from Slovenian and Icelandic.

Slovenian

Icelandic

3.2 Type 2: Summative agreement on multi-valued Ns and Ts

The second language type allows summative agreement on multi-valued Ns and Ts. Russian is one example of this type. Both distributive agreement and summative agreement is allowed on multi-valued Ns while only summative agreement is allowed on multi-valued Ts.

Russian

Hebrew

Hebrew is another example of this language type. One speaker I consulted accepted both distributive agreement and summative agreement on both multi-valued Ns and Ts. The other Hebrew speaker only accepted distributive agreement on both multi-valued Ns and Ts. Although this individual variation is observed, it is shown that summative agreement is allowed on both multi-valued Ns and Ts for at least some speakers.

3.3 Type 3: Distributive agreement on multi-valued Ns, summative agreement on multi-valued Ts

The third type of languages show distributive agreement on multi-valued Ns and summative agreement on Multi-valued Ts. English, Slovak, German, and Italian are included in this type. Examples from English and Slovak are shown below.

English

Slovak

3.4 Type 4: Summative agreement on multi-valued Ns, distributive agreement on multi-valued Ts

This last type of language is not attested in the sampled languages.

As is indicated in Table 3, out of the four logically possible patterns crossing two agreement targets and two agreement patterns in multi-valuation, only three are attested, i.e. a 3/4 pattern. As far as I am aware, this typological observation is novel. In the next section, I discuss a longstanding observation of another 3/4 pattern in hybrid noun agreement and propose that the typological observation in multi-valuation is a subcase of the Agreement Hierarchy.

A brief remark on the sampling of languages. The claim that Type 4 languages do not exist is made based the relatively small pool of 17 languages. This might cause some concern regarding the robustness of the claim. Proving a negative universal like a typological gap can be tricky if possible at all. Ideally one would need to go through all the languages (dead, living, and emerging). Practically, one should test as many languages as possible.

On the other hand, the nature of multi-valuation restricts the pool of candidate languages to a small subset. First, the candidate languages need to show number marking on nouns and verbs. This rules out languages like Chinese, Japanese, Korean among many others. Second, the candidate languages need to allow Nominal RNR and/or TP RNR. Languages that have agreement but do not allow Nominal RNR or TP RNR have to be excluded. On a practical level, since Nominal RNR and TP RNR constructions are generally not included in traditional grammars, native speakers have to be consulted with. According to WALS, apart from the 17 languages reported here, most of the languages that show both nominal and verbal number markings are indigenous languages spoken in Africa, Oceania, or North and South America. We were not able to contact the speakers of these languages. The 17 languages reported in the survey are a result of these limitations. They include all eligible languages that the author have access to native speakers of. For now, we will proceed with the available evidence while keeping in mind that more languages should be surveyed.

In the next section, I argue for a link between the patterns discussed in this section and the Agreement Hierarchy, a long-standing set of generalization observed for hybrid noun agreement. I propose that summative/distributive agreement dichotomy is a subcase of morphological/semantic agreement.

4.1 Multi-valuation as a subcase of the Agreement Hierarchy

The 3/4 pattern observed on multi-valued Ns and Ts is also seen in other agreement phenomena. A series of work by Corbett (1979; 2000; 2006) observe a general implication relation among agreement targets when agreeing with hybrid nouns. Hybrid nouns can control both morphological agreement and semantic agreement. In (48) and (49), the hybrid noun committee in British English among other varieties can control singular or plural agreement on the verb and the personal pronoun. Note that (48b) and (49b) involve mismatches on different agreement targets: the demonstratives show morphological/singular agreement while the verb and personal pronoun show semantic/plural agreement.

This effect is also observed in gender agreement in languages like German and Russian (Corbett 1979). In Russian, vrač ‘doctor’ is morphologically masculine but can refer to a female individual, i.e. semantically feminine. (50a–b) show that it is possible for the adjective and the verb to both show either masculine agreement or feminine agreement when referring to a female doctor. However, mismatch between the two targets can only be in one direction: it is possible for the adjective to be masculine and the verb to be feminine in (50c), but not the other way around in (50d).

Table 4 shows the general scheme between two targets: when the verb shows morphological agreement, the attributive element cannot show semantic agreement. For examples from other languages, see Corbett (2006).

The same pattern is observed on other agreement targets. Although verbs in English can show either morphological or semantic agreement, personal pronouns tend to show more semantic agreement than the verbs. In (51c), the auxiliary has is singular while the personal pronoun shows plural marking, both of which are controlled by the government. Mismatch in the opposite direction is impossible as is shown in (51d) where the auxiliary is plural and the personal pronoun is singular. The 3/4 pattern between the verb and the personal pronouns is summarized in Table 5.

With evidence from a variety of constructions and languages in addition to the 3/4 patterns shown above, Corbett (1979) proposes the Agreement Hierarchy in (52).

Empirical work has shown that the Hierarchy effect holds for at least 3 levels: 1. the corpus level: the positions to the right of the Hierarchy are more likely to show semantic agreement and the positions to the left of the Hierarchy are more likely to show morphological agreement; 2. the sentence level: if a position shows morphological agreement, no positions to its left on the Hierarchy can show semantic agreement in the same sentence; 3. the language level: no languages show morphological agreement on a position X exclusively and semantic agreement on positions left to X.

Various work has been addressing different aspects of the Agreement Hierarchy effect. Corbett (1979; 2006) among others focuses mainly on the corpus level. Recent work by Smith (2015); Landau (2016) address the Hierarchy effects observed within one sentence. The language level of the Hierarchy is the least talked about, but see Wechsler & Zlatić (2003); Puškar (2017).

Now we can come back to multi-valuation and its relation with the Agreement Hierarchy. The Hierarchy is motivated by the 3/4 patterns in hybrid noun agreement shown in Tables 4 and 5. These pattens are homogeneous to the 3/4 pattern in Table 3 observed in multi-valuation: there is a monotonicity regarding two agreement patterns between two agreement targets. For hybrid noun agreement, the agreement patterns involved are morphological and semantic agreement. For multi-valuation, they are distributive and summative agreement. Although it is possible for both targets to show either agreement pattern across languages, the mismatch only goes one way. No language that shows morphological/distributive agreement on position X exclusively and semantic/summative agreement on positions left to X (i.e. the distributive agreement generalization (35)).

Thus I propose that multi-valuation, like hybrid noun agreement, is a case of the Agreement Hierarchy effect. If we align distributive agreement in multi-valuation with morphological agreement and summative agreement with semantic agreement, and add the N heads to the Agreement Hierarchy as in (53), the typological gap in multi-valuation in Table 3 is predicted: no language shows morphological agreement on multi-valued Ts and semantic agreement on multi-valued Ns, given that Ns are on the left of Ts in (53).

This proposal makes three additions to the Agreement Hierarchy in (52). First it adds multi-valuation as a subcase of the Hierarchy effect on top of hybrid noun agreement. As far as the author is aware, the discussion on the Agreement Hierarchy has been exclusively on hybrid noun agreement. The second addition is to add N heads as a position on the Hierarchy. When the Agreement Hierarchy was originally proposed, N was treated as the source of the gender and number features. Subsequent work has revealed that the NUM head and the small n are sources of number features (Ritter 1991; Kramer 2016; Landau 2016). Thus treating the noun head as one of the agreement targets is a natural move. The third aspect of the proposal is the alignment of distributive agreement with morphological agreement as well as summative agreement with semantic agreement.

4.2 Summative agreement = semantic agreement; distributive agreement = morphological agreement

This section argues for the connection between summative agreement and semantic agreement as well as that between distributive agreement and morphological agreement. Empirically, mismatches in distributive agreement are resolved as closest conjunct agreement (CCA) which is associated with morphological agreement, mismatches in summative agreement are taken care of by resolved agreement which is associated with semantic agreement.

Linking distributive agreement in multi-valuation with morphological agreement in the Agreement Hierarchy is a natural move. Morphological agreement in Corbett’s sense involves a shared morphological number marking. In (54a) the demonstrative this involve morphological agreement with the noun committee because they are both marked as singular (as opposed to the plural verb have). In (54b), the multi-valued noun student also shows the same singular marking with this and that, despite the plural reference of the whole DP.

Empirically, Corbett (1979) proposes that closest conjunct agreement (CCA) is a resolution of mismatch in morphological agreement. This is parallel to the CCA observed in mismatch cases in multi-valuation in (55) (observed by Shen 2016). When two DPs are of different number values, the pivot shows the same marking as the closest conjunct.

For languages that only allow distributive agreement in multi-valued Ts, the prediction is that CCA is also observed when the embedded subjects in two conjuncts mismatch in number. This prediction is borne out. To investigate agreement in RNR constructions in Dutch, Kluck (2009) did an acceptability judgment experiment with 28 native speakers of Dutch in a 5-point likert scale acceptability judgment task (1 being bad and 5 being good). The results show that closest conjunct agreement is used in mismatching cases. Although some of her examples involve relative clauses which are not the focus of the current paper, Kluck (2009) included the sentences in the survey in the appendix, which makes it possible to check the sentences relevant to our purpose. Sentences (10), (19), and (22) in her survey involve mismatching subjects and closest conjunct agreement on the T. The average ratings for these items are 3.6, 3.5, and 2.9 (on a scale of 1–5). I repeat her (19) below as (56). Her (3) and (18) involve mismatching subjects and a plural multi-valued T, and the average ratings for these two sentences are 2 and 2.6. I repeat her (3) below as (57). I follow Kluck’s conclusion that CCA is used in mismatch cases of multi-valued Ts in Dutch, as is expected from the current proposal.

Linking summative agreement in multi-valuation with semantic agreement in the Agreement Hierarchy is also justified conceptually. Semantic agreement with hybrid nouns reflects not the morphological marking of the noun but the semantic reference. In accounting for summative agreement on multi-valued Ts, Grosz (2015) proposes that the reference feature on each embedded subject gets copied onto T as in (58a). If both embedded subjects have the same reference as in (58b), the plural agreement on T is ruled out. In other words, summative agreement in multi-valuation is linked to semantic reference.

Data from mismatch cases support this connection as well. Semantic agreement resolves mismatches by resolved agreement. This is indeed what we found in TP RNR in English, when the two embedded subjects are of different number values in (59), the shared T can show plural marking regardless of the order of the two subjects.

Furthermore, clear predictions are also made for Russian Nominal RNR, which allows both distributive and summative agreement in the context of mismatches. The summative/semantic agreement would generate plural pivots regardless of the order of the mismatching conjuncts. The distributive/morphological agreement generates the closest conjunct agreement pattern: singular pivots when the second conjunct is singular; plural pivots when the second conjunct is plural. Combining both types of agreement, it is predicted that the plural pivot is allowed in mismatches regardless of which conjunct is plural, and the singular pivot is allowed only when the second conjunct is singular. These predictions are borne out in (60).¹⁰

4.3 Formal representation of semantic/morphological agreement

So far I have argued that summative agreement in multi-valuation is a case of semantic agreement and distributive agreement a case of morphological agreement. In this subsection I lay out one way to formally represent these two sets of agreement in both hybrid noun agreement and multi-valuation.

Following recent work (Pollard & Sag 1994; Wechsler & Zlatić 2003; Smith 2015; Landau 2016; Wurmbrand 2017a), I assume that the two types of agreement result from agreeing with two types of features. One type is labeled as concord, uninterpretable, or morphological features (u[ ]), whereas the other is labeled as index, interpretable, or semantic features (i[ ]). Both types of features can co-exist on one element. A probe can agree with either type of features. Morphological agreement is the result of agreeing with the morphological features and semantic agreement is the result of agreeing with the semantic features.

Since the NUM head is the source of the phi features, it is the NUM head that start with two types of features.¹¹ I assume that subject-verb agreement results from Agree between the D head (the phase head of the DP) and the T head. Since it is possible for T to show either semantic or morphological agreement, the D head also has two types of features. The D head gets its values from the NUM head via DP internal agreement.

For common nouns like student, the morphological and semantic features on the NUM head share the same value as in (61a). The noun gets the value from the NUM. Since the morphological and semantic features share the same value on NUM, we cannot tell what type of agreement occurred. Similarly, the D head gets the values from NUM as in (61b). At that point the T head agrees with the D head and gets its feature valued in (61c). Features that are active in the relevant agreement relation are in bold.

Hybrid nouns are special in that their morphological feature and semantic feature have different values. For example in (62), the NUM head that selects the hybrid noun government has a singular morphological feature u[SG] and a plural semantic feature i[PL]. In (62b) the D head gets its values from the NUM head and the head noun agrees with the singular morphological feature of the NUM head.¹²

The T head, as before, agrees with the D head. In English it can either copy the singular morphological feature or the plural semantic feature from the D head. The former results in morphological agreement in (63) and the latter semantic agreement in (64). It is worth pointing out that the type of agreement depends on the type of feature on the goal in the Agree relation, not the probe. For example in (64), T shows semantic agreement because it is the semantic feature on D that gets copied. Whether T itself has morphological or semantic features is an independent issue. Here I follow the standard assumption that the phi features on T are morphological features.

Turning to multi-valuation, in Nominal RNR in (65), the pivot noun is shared by two DPs, thus agreeing with two NUM heads. As in the hybrid noun agreement, morphological agreement in multi-valuation results from copying the morphological features u[SG] from the two NUM heads onto the pivot noun in (66a). Semantic agreement results from copying the semantic features i[SG] as in (66b). Again the morphological and semantic agreement distinction depends on the relevant features on the goals, not the probe. Like the T head, I assume that the relevant feature on the head noun is morphological in both (66a) and (66b). As a result, no difference in interpretations between (66a) and (66b) is expected.

The difference between N_u[SG] in (66a) and N_{u[SG, SG]} in (66b) results from the feature arithmetic for morphological and semantic agreement in (67). In (67a) when two morphological features of the same value get copied onto one element, the result is the same as that value, e.g. when multiple singular morphological features get copied to a noun, the noun shows singular. In (67b) when multiple semantic features of the same value get copied onto one element, the result has to be calculated based on the values. For now I assume a simple addition operation where two or more instances of the singular value give out plural.

In sum I propose that morphological/semantic agreement boils down to agreeing with morphological or semantic features in both hybrid noun agreement and multi-valuation. Different agreement patterns in multi-valuation result from distinct feature arithmetic when resolving multiple morphological/semantic agreement relations. The distributive agreement generalization in (35) thus can be rephrased as follows: if Ts in a language can only agree with morphological features, the Ns must also agree with morphological features and not semantic features. I will leave the sketch above as is for now, as it is beyond the scope of the current paper to hash out the detailed predictions stemming from this formalism.

4.4 More on the Agreement Hierarchy

It is worth noting that linking multi-valuation to the Agreement Hierarchy is not an explanation for the 3/4 pattern observed in multi-valuation. The Agreement Hierarchy in itself is a generalization of the cross-linguistic and cross-domain patterns observed in hybrid noun agreement, now also in multi-valuation. Given that hybrid noun agreement has been investigated in the context of the Agreement Hierarchy since the 70s, a natural move toward a formal account for the multi-valuation pattern is to borrow insights from the existing accounts for hybrid noun agreement. However, such previous accounts are concerned with the sentence level of the Hierarchy, and the multi-valuation Agreement Hierarchy operates on the language level.

To elaborate, the Agreement Hierarchy has at least three levels: the corpus level, the sentence level, and the language level. I will leave the corpus level aside in this paper (see Corbett 2006). The sentence level of the Hierarchy which holds within individual sentences is stated in (68).

The Hierarchy effect in hybrid noun agreement can be observed on the sentence level as in (69), because multiple agreement configurations (attributive-noun, noun-verb, etc.) can be packed in one sentence.

As is discussed above, multi-valuation on Ns require the Nominal RNR construction and multi-valuation on Ts require the TP RNR construction where the T agrees with two separate embedded subjects. These two constructions cannot be packed in one sentence in the relevant way. As a result, the multi-valuation aspect of the Agreement Hierarchy cannot be evaluated on the sentence level.

On the other hand, the language level of the Hierarchy is stated in (70). Unlike the sentence level, it does not require packing multiple agreement configurations in one sentence. Instead it holds across different sentences in a language.

Both hybrid noun agreement and multi-valuation can be evaluated on this level as is stated in (71) and (72), both of which predict a typological gap.

The accounts proposed for the sentence level of the Hierarchy do not extend to the language level in an obvious way. For example, coupled with assumptions such as late merge of adjectives, Smith (2015) proposes that semantic agreement precedes morphological agreement and at the derivational stage where morphological agreement is activated, semantic agreement is no longer available. Although this approach can account for the Hierarchy effect in one sentence, it does not apply to different sentences.

Landau (2016) proposes that the hybrid nouns like be’alim ‘owner’ in Hebrew are morphologically plural but semantically underspecified (decided by the context). The verbs must agree with the semantic features while the adjectives can agree with either semantic or morphological features (see also Wechsler & Zlatić 2003). Similar to Smith (2015), it is not clear how this approach would be extended to the language level of the Hierarchy. Furthermore it is not obvious how this approach carries over to multi-valuation, since the account depends on the special feature setup of hybrid nouns like be’alim. In multi-valuation, garden variety Ns and Ts suffice to demonstrate the Hierarchy effect.

Given the distinctions between the sentence level and the language level of the Hierarchy effects, the two levels may require distinct accounts. The language level of the Hierarchy has been rarely discussed in the previous literature. As far as I know, no formal approach has been proposed. The current paper frames the research question regarding the language level of the Hierarchy, leaving the formal account for future research.

To summarize, this section builds on the distribution of two agreement patterns in multi-valuation reported in Section 4 and previous empirical work on hybrid noun agreement and connects the two seemingly unrelated phenomena with the Agreement Hierarchy. I hope to have demonstrated that the alignment of summative agreement with semantic agreement and distributive agreement with morphological agreement are conceptually and empirically appealing. I propose that the Agreement Hierarchy, which has been discussed exclusively regarding hybrid noun agreement, also scopes over multi-valuation. I have also discussed different levels of the Agreement Hierarchy effects and whether existing accounts for hybrid noun agreement can be extended to multi-valuation.