Toward anaphora resolution via underspecified types in Dependent Type Semantics

Abstract

Dependent type theory has been used to formulate natural language semantics. Natural language semantics based on it provides several methods for natural language inference, making dependent type theory an attractive alternative in natural language semantics. Dependent Type Semantics (DTS) is a natural language semantics based on dependent type theory, and anaphora is one of major semantic phenomena that DTS can account for. Recently, underspecified types have been introduced in DTS. Underspecified types enable to treat anaphora resolution as proof search in dependent type theory, while a method of anaphora resolution is not implemented yet. We aim to implement the anaphora resolution process via underspecified types, by using the proof assistant Coq. We formulate this process by means of Coq's refine tactic. Furthermore, some examples of natural language inference involving anaphora resolution crucially are discussed: we prove these inferences as theorems in Coq.