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

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 $10,000. 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.

Further evidence for an HPSG-based theory of the semantics of different and the same

“…Example (44) involves RNR out of non-coordinate structure, and the account described above is the only currently available account of the apparent internal reading that this sentence has. The theory advocated in Kubota and Levine (2016) and Kubota and Levine (2020) does not contain a mechanism that licenses non-coordinate RNR, and is therefore incapable of handling the apparent internal reading of a sentence like this.…”

“…The example in (44) below, discussed in Kubota and Levine (2016) and Kubota and Levine (2020), could be taken to be circumstantial evidence for such an account, because the acceptability of a sentence like this is expected in a theory based on the view that the apparent internal readings of the sentences under discussion are resulting from LNR and RNR, but unexpected in other theories, such as Kubota and Levine's, according to which apparent internal readings are always licensed by the presence of some sort of conjunction or plurality in the same sentence.…”

Respectively interpretation and Binding Conditions A and B

“…The second theory that I would like to compare our theory to is the one proposed in Kubota & Levine (2016). This theory is an extension of the theory presented in Gawron & Kehler (2004) using Categorial Grammar mechanisms.…”

Neg-raising with belief predicates as a scaleless implicature

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It has been proposed that the part structures of denotations of plurals 'project' to the denotations of expressions including those plurals (e.g., Gawron & Kehler 2004, Kubota & Levine 2016, Schmitt 2019/2020). If such a plural projection is possible, not only plural DPs but also expressions including those plural DPs denote pluralities (e.g., saw the two recipes denotes a plurality {SAW(recipe1),SAW(recipe2)} instead of a singularity {SAW({recipe1,recipe2})}).

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