Programming in Martin-Lo¨f's type theory: an introduction
Programming in Martin-Lo¨f's type theory: an introduction
Type-theoretical grammar
Toward the formulation of presupposition by illative combinatory logic
LACL'12 Proceedings of the 7th international conference on Logical Aspects of Computational Linguistics
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In this paper we propose a proof-theoretic analysis of presuppositions in natural language, focusing on the interpretation of definite descriptions. Our proposal is based on the natural deduction system of Ɛ-calculus introduced in Carlström [2] and on constructive type theory [11,12]. Based on the idea in [2], we use the Ɛ-calculus as an intermediate language in the translation process from natural language into constructive type theory. Using this framework, we formulate the process of presupposition resolution as the process of searching for a derivation in a natural deduction system. In particular, we show how to treat presupposition projection and accommodation within our proof-theoretic framework.