An outline of type-theoretical approaches to lexical semantics

We take the opportunity of the publication of some of the papers of the ESSLLI workshop  TYTLES (TYpes Theory and LExical Semantics, ESSLLI 2015, Barcelona) to provide an overview of the possibilities that type theory offer to model lexical semantics, especially the type theoretical frameworks that properly model compositional semantics

Factivity and presupposition in Dependent Type Semantics

Dependent type theory has been applied to natural language semantics to provide a formally precise and computationally adequate account of dynamic aspects of meaning. One of the frameworks of natural language semantics based on dependent type theory is Dependent Type Semantics (DTS), which focuses on the compositional interpretations of anaphoric expressions. In this paper, we extend the framework of DTS with a mechanism to handle logical entailment and presupposition associated with factive verbs such as know. Using the notion of proof objects as first-class objects, we provide a compositional account of presuppositional inferences triggered by factive verbs. The proposal also gives a formal reconstruction of the type-distinction between propositions and facts, and thereby accounts for the lexical semantic differences between factive and non-factive verbs in a typetheoretical setting