Abstract
This paper presents an analysis of modal subordination in the framework of Dependent Type Semantics, a framework of natural language semantics based on dependent type theory. Dependent types provide powerful type structures that have been applied to various discourse phenomena in natural language, yet there has been little attempt to produce an account of modality and its interaction with anaphora from the perspective of dependent type theory. We extend the framework of Dependent Type Semantics with a mechanism of handling explicit quantification over possible worlds, and show how modal anaphora and subordination can be handled within this framework.
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Notes
- 1.
Geurts [8] (pages 72–79) admits the importance of inferences with world knowledge in resolving presuppositions, but provides no clues on how to incorporate additional inferential architectures into the framework of DRT.
- 2.
In dependent type theory, terms and types can be mutually dependent; thus, the terms defined here can serve as types as well.
- 3.
Kratzer (2012) derives accessibility relation from a modal base and an ordering source. Our analysis would be compatible with such a decomposition.
- 4.
In this section, might and would will be treated as propositional operators. A fully compositional analysis will be given in Sect. 6.
- 5.
Presuppositional contents can be independent from asserted contents. A classical example is too; for example, John \(_i\) is leaving, too \(_i\) is said to be presupposing that some (particular) person other than John is leaving. Such cases can be treated within the present framework by incorporating the mechanism developed in Bekki and McCready [3] to handle semantic contents independent of the asserted meaning. The aim of Bekki and McCready [3] is to analyze conventional implicature in the framework of DTS, but their analysis can be applied, with a suitable modification, to the analysis of presuppositions that are independent of asserted contents.
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Acknowledgments
This paper is a revised and expanded version of [18]. We thank the two reviewers of LENLS11 for helpful comments and suggestions on an earlier version of this paper. I also thank the audiences at LENLS11, in particular, Chris Barker and Matthew Stone, for helpful comments and discussion. Special thanks to Nicholas Asher, who gave constructive comments and advice, and to Antoine Venant, Fabio Del Prete, and Márta Abrusán for their feedback and discussions. This research was supported by JST, CREST.
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Tanaka, R., Mineshima, K., Bekki, D. (2015). Resolving Modal Anaphora in Dependent Type Semantics. In: Murata, T., Mineshima, K., Bekki, D. (eds) New Frontiers in Artificial Intelligence. JSAI-isAI 2014. Lecture Notes in Computer Science(), vol 9067. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48119-6_7
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