Towards a Type-Theoretical Account of Lexical Semantics

Computing the Semantics of Plurals and Massive Entities Using Many-Sorted Types

“…Detailed in [2,14], it has been constantly upgraded and aggregates many different phenomena such as deverbals ( [29]) or the narrative of travel ( [27,10]). See [30] for a recent, complete, open-access synthesis.…”

Category theory, logic and formal linguistics: Some connections, old and new

“…Issues such as selectional restriction have been much discussed in type theoretical framework e.g. in [13,3,5,2,28].…”

An Account of Natural Language Coordination in Type Theory with Coercive Subtyping

“…One of the most important 4 See also [3] for a critique of the flaws in the various formalizations of dot-types in their original formulation as well as in much of the later work based on that. 5 Plastic [5] is a proof assistant, an implementation of the modern types theory UTT [15] on the computer for formalised proof development.…”

“…However, a number of central issues as regards NL coordination have not been clarified yet. In this paper we depart from single-sorted versions of type theory found in Montague's work (as well as in most of the subsequent work within the same tradition) and employ a many-sorted modern type theory (MTT) 3 , as proposed and studied for NL semantics in [30,17,18], to deal with two central issues in NL coordination. These issues concern the notion of conjoinable types, in effect the question of which NL elements can be coordinated, and non-Boolean conjunction, where a collective rather than the expected Boolean distributive reading of and arises.…”

“…Given that the dot-types of the coordinated phrases are different and assuming that the NL coordination operate on the same types, we will have to explain how coordination is possible in these cases. The problem that arises in examples like (3) and (4) is that the individual NPs of the conjunction (e.g. the book and my lunch in (3) have different types (Phy • Info for book and Event • Phy for lunch).…”