The Semantics of Respective Readings, Conjunction, and Filler-Gap Dependencies

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

“…Building on related ideas explored by previous authors, in particular, Gawron and Kehler (2004) and Barker (2007), we argue precisely for such an approach in this paper. In fact, in the case of conjoined NPs, which are standardly taken to denote sums (or, more correctly, joins in a semilattice, as a reviewer reminds us, since sums are constructs in the translation language, not the model-but we'll stick to the informal locution of plurals 'denoting' sums for convenience), the issue of compositionality is already moot since the denotation itself (j ⊕ b) retains the internal structure of the conjunction that can be accessed by other operators such as the distributivity operator commonly assumed in the semantics literature (compare this situation to the generalized conjunction of the lifted versions of the individual terms λP.P (j)∧ P (b), for which the individual parts are no longer directly accessible).…”

“…So far as we are aware, there is no explicit analysis of these respectively/NCC interactions in the literature. In particular, it is worth noting that the proposals by Gawron and Kehler (2004) and Chaves (2012) that we review below both fail to extend to these NCC cases since they assume phrase structure-based syntax for formulating their analyses (although to be fair, the semantic analysis that Gawron and Kehler (2004) propose does not depend in any crucial way on the syntactic assumptions they make).…”

“…2 The meanings of 'respective', symmetrical and summative predicates 2.1 The empirical parallel between 'respective', symmetrical and summative predicates 'Respective' readings of plural and conjoined expressions (cf., e.g., Kay 1989;McCawley 1998;Gawron and Kehler 2004;Winter 1995;Bekki 2006;Chaves 2012) and the semantics of symmetrical predicates such as same and different (cf., e.g., Carlson 1987;Moltmann 1992;Beck 2000;Barker 2007;Brasoveanu 2011) have been known to poses major challenges to theories of compositional semantics. Each of these two constructions alone present a set of quite complex problems of its own, and previous authors have thus mostly focused on studying the properties of one or the other.…”

“…In fact, in the case of conjoined NPs, which are standardly taken to denote sums (or, more correctly, joins in a semilattice, as a reviewer reminds us, since sums are constructs in the translation language, not the model-but we'll stick to the informal locution of plurals 'denoting' sums for convenience), the issue of compositionality is already moot since the denotation itself (j ⊕ b) retains the internal structure of the conjunction that can be accessed by other operators such as the distributivity operator commonly assumed in the semantics literature (compare this situation to the generalized conjunction of the lifted versions of the individual terms λP.P (j)∧ P (b), for which the individual parts are no longer directly accessible). As shown in detail for 'respective' readings by Gawron and Kehler (2004), by generalizing this approach to non-NP-type meanings, the complex semantics that 'respective' readings and related phenomena exhibit can be uniformly handled by modelling the meanings of expressions involving plurals or conjunction by a structured object-either (generalized) sums (Gawron and Kehler 2004), tuples (Winter 1995;Bekki 2006), or multisets, as we propose in this paper.…”

“…The present paper extends this approach to the other two empirical phenomena (symmetrical and summative predicates), as well as embedding the analysis in a flexible syntax-semantics interface. As will become clear below, our choice of multisets over sums for the underlying data structuredeparting, in this respect, from Gawron and Kehler (2004)-is primarily motivated by the need to generalize the analysis to the other two phenomena (see Sect. 4 for discussion).…”