Factivity and presupposition in Dependent Type Semantics

Dependent Type Semantics (DTS, Bekki [3]) is a framework of natural language semantics based on dependent type theory (Martin-Löf [19]). In contrast to traditional model-theoretic semantics, DTS is a proof-theoretic semantics, where entailment relations are characterized as provability relations between semantic representations. One of the distinctive features of DTS, as compared to other type-theoretical frameworks, is that it is augmented with underspecified terms so as to provide a unified analysis of entailment, anaphora and presupposition from an inferential/computational perspective. In contrast to previous work on anaphora in dependent type theory (cf. Ranta [22]), DTS gives a fully compositional account of inferences involving anaphora (Bekki [3]). It is also extended to the analysis of modal subordination (Tanaka et al. [25]). In this paper, we provide the framework of DTS with a mechanism to handle entailment and presupposition associated with factive verbs such as know. Although there are numerous studies on factive verbs in natural language semantics, they are usually based on model-theoretic approaches; it seems fair to say that there has been little attempt to formalize inferences with factivity from a computational and proof-theoretical perspective. On the other hand, various proof systems for knowledge and belief have been studied in the context of epistemic logic (cf. Meyer and van der Hoek [20]). However, such systems are mainly concerned with knowledge and belief themselves, not with how they are expressed in natural languages, nor with linguistic phenomena such as factivity presuppositions. Our study aims to fill this gap by providing a framework that explains entailments and presuppositions with factive verbs in dependent type theory.