Abstract
Dependent Type Semantics (DTS; Bekki and Mineshima, 2017) is a proof-theoretic compositional dynamic semantics based on Dependent Type Theory. The semantic representations for declarative sentences in DTS are types, based on the propositions-as-types paradigm. While type-theoretic semantics for natural language based on dependent type theory has been developed by many authors, how to assign semantic representations to interrogative sentences has been a non-trivial problem. In this study, we show how to provide the semantics of interrogative sentences in DTS. The basic idea is to assign the same type to both declarative sentences and interrogative sentences, partly building on the recent proposal in Inquisitive Semantics. We use Combinatory Categorial Grammar (CCG) as a syntactic component of DTS and implement our compositional semantics for interrogative sentences using ccg2lambda, a semantic parsing platform based on CCG. Based on the idea that the relationship between questions and answers can be formulated as the task of Recognizing Textual Entailment (RTE), we implement our inference system using proof assistant Coq and show that our system can deal with a wide range of question-answer relationships discussed in the formal semantics literature, including those with polar questions, alternative questions, and wh-questions.
Highlights
Dependent Type Semantics (DTS; Bekki and Mineshima (2017)) is a semantic framework that provides a unified analysis of presupposition and anaphora, based on dependent type theory (Martin-Lof, 1984)
We show how to provide the semantics of interrogative sentences in DTS
The basic idea is to assign the same type to both declarative sentences and interrogative sentences, partly building on the recent proposal in Inquisitive Semantics (Ciardelli et al, 2019), where interrogative and declarative sentences are treated as having the same type
Summary
Dependent Type Semantics (DTS; Bekki and Mineshima (2017)) is a semantic framework that provides a unified analysis of presupposition and anaphora, based on dependent type theory (Martin-Lof, 1984). While double negation is a key to make a distinction between assertion and question in Inquisitive Semantics, we do not make use of double negation for this purpose because it blocks anaphoric links in terms of Σ-types in DTS (see section 3.4 for the detail) Another difference is that DTS is based on the idea of proof-theoretic semantics where the meaning of a sentence is given in terms of inference rules. We extend the basic theory of DTS and present semantic representations for basic interrogative sentences We show that this extension preserves the analysis of anaphora in terms of Σ-types in DTS. We use the following four type constructors (in the DTS notation) which are used in the previous study on formal semantics based on dependent type theory (Ranta, 1994; Luo, 2012; Bekki and Mineshima, 2017). In our extension of DTS with interrogative semantics, this uniform treatment of anaphora and presupposition in terms of underspecification is preserved
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