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The syntax-semantics interface of ‘respective’ predication: a unified analysis in Hybrid Type-Logical Categorial Grammar

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Abstract

This paper proposes a unified analysis of the ‘respective’ readings of plural and conjoined expressions, the internal readings of symmetrical predicates such as same and different, and the summative readings of expressions such as a total of $10000. These expressions pose significant challenges to compositional semantics, and have been studied extensively in the literature. However, almost all previous studies focus exclusively on one of these phenomena, and the close parallels and interactions that they exhibit have been mostly overlooked to date. We point out two key properties common to these phenomena: (i) they target all types of coordination, including nonconstituent coordination such as Right-Node Raising and Dependent Cluster Coordination; (ii) the three phenomena all exhibit multiple dependency, both by themselves and with respect to each other. These two parallels suggest that one and the same mechanism is at the core of their semantics. Building on this intuition, we propose a unified analysis of these phenomena, in which the meanings of expressions involving coordination are formally modelled as multisets, that is, sets that allow for duplicate occurrences of identical elements. The analysis is couched in Hybrid Type-Logical Categorial Grammar. The flexible syntax-semantics interface of this framework enables an analysis of ‘respective’ readings and related phenomena which, for the first time in the literature, yields a simple and principled solution for both the interactions with nonconstituent coordination and the multiple dependency noted above.

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Notes

  1. It has been noted by Postal (1998), Kehler (2002) and Chaves (2012) that ‘respective’ readings interact with extraction, as exemplified by the following data (called ‘interwoven dependency’ by Postal 1998):

    figure d

    It is possible to construct parallel examples involving summative predicates (symmetrical predicates seem to be uncomfortable in fronted wh or topicalized positions, and we weren’t able to construct relevant examples):

    figure e

    The analysis we propose in Sect. 3 is in principle compatible with these data. However, since the analysis of ATB extraction in Hybrid TLCG is still under development (due to the fact that this type of extraction constitutes an (apparent) exception to the linearity of the calculus underlying TLCG in general, including our own version), we will not attempt to formulate an explicit analysis of these interactions in this paper.

  2. One might be inclined to think that the adjective respective in examples like the following should be given a parallel treatment:

    figure g

    However, as convincingly argued by Okada (1999) and Gawron and Kehler (2002), the properties of the adjective respective is significantly different from those of the respectively sentences in (4). In particular, contrasts such as the following suggest that the adjective respective takes scope strictly within the NP in which it occurs:

    figure h

    We thus set aside the adjective respective in the rest of this paper. See Gawron and Kehler (2002) for an analysis of respective that captures its strictly local scope correctly.

  3. Other expressions whose interpretations are similarly sensitive to the order of mention include successively, progressively and increasingly:

    figure i

  4. At the final stage of revising this paper, we became aware of Schmitt (2013), which proposes to generalize the mechanism of cumulativity beyond this conventional assumption. Whether this approach generalizes to interactions between ‘respective’ readings and related phenomena with NCC of the sort discussed in the present paper is an open question.

  5. An event-based analysis (along the lines, e.g., of Lasersohn 1992) is conceivable for examples like (4b). See Sect. 4.1 for a brief comment on event-based approaches.

  6. Kratzer (2007) attributes the contrast between (21a) and Every copy editor caught 500 mistakes in the manuscript (which does not induce the relevant summative reading) to differences in grammatical relations. However, see Champollion (2010) for a discussion that grammatical relation is not the relevant factor.

  7. But note that linear order cannot be the sole determining factor. The following example induces the ‘respective’ reading with a universal quantifier, despite the fact that the quantifier linearly precedes the plural (it is also anomalous in involving disjunction rather than conjunction; for disjunction’s (apparently surprising) ability to license ‘respective’ readings, see Gawron and Kehler 2004):

    figure v

    Here, the PP containing the quantifier is fronted, which arguably affects processing, and so it isn’t too surprising that this example differs from simpler examples like those in (20) in its possible interpretation. That said, the exact licensing condition for ‘respective’ readings for quantifiers is still quite elusive.

  8. A reviewer notes that this leaves open a possibility that the ordering that a symmetrical predicate refers to happens to be identical to the contextually established one. This would be difficult with same, which involves only a single fixed entity (for which ordering is irrelevant), but seems indeed possible with different in the right kind of context, such as the following one provided by the reviewer. Suppose John and Bill travelled to Africa and East Asia, respectively, in which two particular types of hepatitises (types A and B, respectively) are widespread. In this context, the following sentence, with the definite article the crucially invoking reference to the contextually understood set of hepatitises (together with the contextually understood ordering/linking), seems quite unexceptional:

    figure x

    We want to acknowledge here however that, as it stands, the formal analysis we present below does not take into account the possible role of the definite article the in examples like (i). We believe that our analysis is not incompatible with a refinement that takes into account such further subtleties. This is left for future work.

  9. The reviewer also notes that the following example however does not induce the summative reading:

    figure z

    This seems to be due to the fact that the ‘contrast’ discourse relation lexically invoked by whereas is inherently incompatible with the pragmatics of summative interpretation (in which the two clauses need to be construed to pertain to some common point, rather than being in contrast with one another).

  10. A reviewer notes that the following examples are acceptable:

    figure ac

    The native speakers we consulted uniformly rejected (ia) on the internal reading for same. For (ib), the judgment was not so clear; most of our informants reported that it was a borderline example. This latter fact makes sense given that the if A then B part in (ib) is not a conditional statement, but rather the then clause is a temporal adjunct clause inside the antecedent of a conditional. Thus, the A then B is a hidden conjunction with an additional temporal precedence information imposed on it (which presumably is a confounding factor in inducing the relevant internal reading).

  11. Note that, though Heim (1985) takes a parallel between comparatives and same and different as a starting point for her analysis of the latter two, she does not provide any explicit analysis of examples like (26a) in which the two phenomena interact with one another (nor is it obvious how her account could be extended to such examples).

  12. Though the nature of ‘covert movement’ is still considerably unclear and controversial (see, for example, Ruys and Winter 2010 for a recent review), this at least means that a movement-based analysis of these expressions (via QR) cannot be motivated in terms of island-sensitivity. On the other hand, if one takes island effects to be by-products of functional factors such as constraints on real-time processing and felicity conditions on discourse (Deane 1991; Kluender 1992, 1998; Kehler 2002; Hofmeister and Sag 2010), what the above data suggests is that the processing and discourse factors which come into play in filler-gap dependencies are not the same ones which govern the interpretation of ‘respective’ and symmetrical predicates. In the former case, island violation does result in reduced acceptability, but it can be ameliorated by manipulating various non-structural factors; in the latter case, island violation simply does not seem to arise to begin with, as evidenced by the near-perfect acceptability of the examples in (27) and (28).

  13. One might worry about potential overgeneration of the following kind. Suppose we hypothesize the same variable in the two conjuncts of a conjoined sentence and bind them at once after the conjoined sentence is formed:

    figure aq

    Then, by combining this sign with the quantifier everyone, we seem to obtain the following:

    figure ar

    In other words, we (apparently) incorrectly predict that Everyone is male or everyone is female has the reading ‘everyone is either male or female’.

    Such a derivation actually doesn’t go through. Recall from above that ↾ is linear, meaning that it can bind only one hypothesis at a time. This means that (i) can’t be derived as a well-formed sign in Hybrid TLCG. For this reason, the above problematic derivation is correctly ruled out.

    This of course raises the question of how to treat ATB extraction (see our analysis of ‘overt movement’ below):

    figure as

    This is an important open question for the family of approaches including ours (as well as Muskens 2003 and Mihaliček and Pollard 2012) in which the mode of implication (↾ in our calculus) used for overt movement is linear. Unfortunately, addressing this issue is beyond the scope of this paper, but see Morrill (2010) for some discussion about how multiple gaps (such as parasitic gaps) may be treated in a TLCG setup.

  14. As noted by a reviewer, another possible extension of our analysis of ‘respective’ readings is binominal each, exemplified by the following sentence:

    figure au

    The key problem that binominal each poses for compositional semantics is that even though each syntactically appears as a constituent attached to the NP designating the distributed share (three tables), it forces a distributive reading of the syntactically distant sorting key (the boys). By assuming that each takes a relation and two arguments corresponding to the sorting key and the distributive share as its syntactic arguments (this can be done by the same mechanism of double λ-abstraction in the syntax via the vertical slash that plays a key role in our analysis of ‘respective’ predication presented below), an analysis implementing Blaheta’s (2003) strategy described in Dotlačil (2012) is in fact straightforward.

  15. Another difference is that CCG directly posits rules like type raising and function composition (which are theorems in the Lambek calculus and Hybrid TLCG) as axioms.

  16. This analysis predicts that the contribution of respectively is truth-conditional. This seems to be the correct result. Note that the relevant content can be directly negated (similarly, examples can be readily constructed to show that the meaning contribution of respectively scopes under standard presupposition/CI holes such as conditionals and modals).

    figure ay

  17. See also Krifka (1990) for some discussion about the relationship between boolean and non-boolean and.

  18. There is a close connection between the lexical entries for the internal readings posited in (67) and those for the external readings. The lexical entries in (67) essentially establish (non-)identity among each element of a multiset, and in this sense, it can be thought of as involving a reflexive anaphoric reference. By replacing this reflexive anaphoric reference with an anaphoric reference to some external object and stating the (non-)identity conditions to pertain to the object identified by the symmetrical term and the anaphorically invoked external object, we obtain a suitable lexical meaning for the external readings for same and different. Thus, while it may not be possible to unify the lexical entries for the two readings completely, we believe that our approach provides a basis for understanding the close relationship between the two readings. In fact, whether a unified analysis of internal and external readings is desirable seems still controversial. See Brasoveanu (2011) and Bumford and Barker (2013) for some recent discussion.

  19. There is a certain awkwardness to (72). But again, we believe that this arises from a Gricean implicature. Had the speaker known that (72) were the case, s/he could have instead more cooperatively said John and Bill read some of the same books, but some different ones too, or something equivalent. Thus, we take (72) to be only awkward, but crucially, not contradictory.

  20. As noted at the end of Sect. 3.2.1, we take distributive readings to be derived by the resp operator we posit in our system, following a proposal by Bekki (2006). Our assumption here is in the same spirit as G&K’s suggestion of unifying the distributive and ‘respective’ operators in their system.

  21. Dotlačil (2010) questions this assumption by noting the infelicity of the following (the judgments are his):

    figure br

    But the awkwardness of these examples seems to be due to the redundant marking of distributivity by the same word (albeit perhaps in distinct uses of it; compare, for example, the sentences in (i) with ??All boys all went swimming, which is degraded for precisely the same reason of redundancy). Thus, we do not take these data to provide a convincing counterevidence to the family of ‘universal as sum’ type approach.

  22. One issue that remains is why the NP containing different is singular if the licensor is a distributive quantifier rather than a plural NP. In order to get our compositional mechanism yield the right result, we need to assume that a different book in (80) denotes a multiset just like different books. We suspect that the singular marking here is a matter of morphological agreement with the licensor, but leave a detailed investigation of this matter for a future study.

  23. Note, however, that this by no means means that (81a) and (81b) are truth conditionally equivalent to the non-negative versions of each other. Rather, the relation between them is that the truth conditions of these sentences, when augmented with typical (but cancelable) implicatures they are associated with (that is, the maximality implicature that the books in question are the only ones that John and Bill respectively read), effectively amount to the same as the truth conditions of the non-negative versions of each other plus their implicatures.

  24. For the sake of exposition, we give here an analysis of an example in which the argument of a total of is countable rather than mass. Extending the analysis to mass terms is straightforward (it merely involves replacing the counting function # in (84) with some suitable measure function), once we introduce sums as the domain for the denotations of uncountable objects.

  25. Since Brasoveanu’s approach and our own primarily focus on different sets of issues pertaining to the semantics of symmetrical predicates, a direct comparison does not seem to be very meaningful, but we would nevertheless like to note that it is unclear whether Brasoveanu’s DRT-based system extends in any straightforward way to the interactions of symmetrical predicates (and related phenomena) and NCC.

  26. Another potential issue with event-based approaches is that ‘respective’ predication and alternately sentences are found with non-eventive predicates as well (see also Barker 2007, 418 for essentially the same point in connection to a similar example with same):

    figure bx

    It is of course conceivable to extend the notion of event to non-dynamic ones (and it is indeed tempting to think that in an example like (ib), a metaphorical extension of the notion of ‘path’ from a temporal/spatial domain to an atemporal/aspatial domain is involved), but even with such an extension, it is still considerably unclear how the proper ‘events’ can be individuated and distinguished from each other to derive the correct truth conditions for sentences such as those in (i).

  27. There is an additional technical problem in G&K’s proposal. Their analysis, in which ‘respective’ readings are analyzed via a series of successive applications of the distributive and ‘respective’ operators, turns out to be rather unwieldy in cases such as the following ((ib) is the same example as (53) above):

    figure by

    The problem essentially is that the distributive operator that G&K posit (which is identical in all relevant respects to the distributive operator standardly assumed in the formal semantics literature) can only distribute a functor over the components of a sum of argument objects, not vice versa. But the analysis of (ia) requires distributing the object argument to the conjoined functor read and reviewed. See Kubota and Levine (2014d) for a more detailed discussion of this problem and possible solutions for it (the most straightforward of which is to extend the phrase structure-based setup of G&K to an architecture like our own which recognizes hypothetical reasoning fully generally).

  28. Gawron and Kehler (2004, 174) claim that this assumption explains the ill-formedness of the following:

    figure bz

    Our analysis does not rule out (i) via the combinatoric mechanism for licensing ‘respective’ readings alone. But note that the awkwardness of (i) (whose truth conditional content could be expressed much more perspicuously by Sue and Bob like Fred) derives from the fact that the same expression with identical reference is conjoined, without any good reason. This is independently bad regardless of whether the ‘respective’ reading is involved (cf., e.g., ??Fred and Fred smiled).

  29. Barker (2012) partially addresses the multiple symmetrical predicate issue by revising the translation for same in Barker (2007) slightly, removing the distributive operator from the meaning of same (and instead assuming that it is implicit in the lexical meaning of the verb). However, this approach does not seem to work for the case of different (within the set of assumptions that Barker 2007, 2012 makes), and Barker (2012) remains silent about cases like (91).

  30. Similar difficulties arise in an only slightly less striking fashion in John and Bill put the same object in different boxes, where Barker’s analysis predicts that on the inverse scoping of the two symmetrical predicates it is impossible for John to have put any object in a box that Bill put some other, distinct object in. While the surface scope (same > different) does yield the correct interpretation for this example, the picture changes when the subject is singular rather than plural: in the case of John put the same object in different boxes, the surface scoping yields a tautology predicting that the sentence is true in all conceivable circumstances.

  31. Given the parallel semantic action of symmetrical predicates on the one hand and ‘respective’ readings on the other, it is worth observing that Kubota’s (2015) extension of Barker’s (2007) analysis of same to ‘respective’ readings fails to generalize to multiple ‘respective’ readings. The problem in these cases is the same type mismatch dilemma blocking recursive application of operators: after the first application of the ‘respective’ operator, the result is a boolean conjunction whose parts are no longer accessible as sum components, making further application of the same operator in principle impossible.

  32. Chaves (2012) extensively relies on the ellipsis strategy even in cases like the following that do not involve nonconstituent coordination:

    figure cd

    According to Chaves (2012), the ‘respective’ reading of (i) is obtained from the underlying structure in (ii):

    figure ce

  33. Note that we model plural individuals in terms of multisets alone, eliminating sums altogether from the ontology of plurality. This still leaves room for sums as the possible denotations of mass objects. Since there is a functional mapping from multisets modelling plural entities in the present approach to the corresponding Linkean sums (it just involves eliminating nesting and duplication of identical elements), representing plurals by multisets does not mean that we lose the robust empirical generalization between nominal and verbal domains noted extensively in the mereological literature (Bach 1986; Krifka 1989, 1992, among many others).

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Acknowledgements

Our first thanks go once again to Louise McNally, our handling editor at NLLT. Thanks to her marvelous editorial handling of our manuscript (which always kept us on track and made us focus on the most crucial issues), the revision process was intellectually quite stimulating this time too. The critical but constructive comments from the two NLLT reviewers were also very helpful in this respect. In addition, we would like to thank the following people for comments and discussions: Daisuke Bekki, Koji Mineshima, Shuichi Yatabe, Carl Pollard and Richard Moot. We have presented earlier versions of this work and related research at various venues, including ESSLLI 2013, Formal Grammar 2014 and WCCFL 33. We would like to thank the audiences at these venues for their feedback. The first author was supported by the Japan Society for the Promotion of Science (JSPS; PD 2010–2013 and Postdoctoral Fellowship for Research Abroad 2013–2014) when he worked on this paper, and would like to thank JSPS for its financial support. In addition, he would like to thank the Institute for Comparative Research at the University of Tsukuba for research leave to visit OSU (2014–2016), which enabled us to bring the paper to completion in a timely manner in the last revision cycle. The second author thanks the Department of Linguistics and College of Arts and Sciences at OSU for grant support during the course of the research for this paper over the past four years.

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Authors and Affiliations

  1. Institute for Comparative Research in Human and Social Sciences, University of Tsukuba, 1-1-1 Tennoudai, Tsukuba Ibaraki, 305-8571, Japan

    Yusuke Kubota

  2. Department of Linguistics, Ohio State University, 222 Oxley Hall, 1712 Neil Avenue, Columbus, OH, 43210-1298, USA

    Robert Levine

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  1. Yusuke Kubota
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Correspondence to Yusuke Kubota.

Appendix: Ancillary derivations

Appendix: Ancillary derivations

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figure cs
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    figure ct
figure cu
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    figure cv
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    figure cw
figure cx

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Kubota, Y., Levine, R. The syntax-semantics interface of ‘respective’ predication: a unified analysis in Hybrid Type-Logical Categorial Grammar. Nat Lang Linguist Theory 34, 911–973 (2016). https://doi.org/10.1007/s11049-015-9315-7

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