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

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.