A Presuppositional Analysis of Definite Descriptions in Proof Theory
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 ε-calculus introduced in Carlström  and on constructive type theory [11,12]. Based on the idea in , we use the ε-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.
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