Proof-Theory and Semantics for a Theory of Definite Descriptions

08/09/2021

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by   Nils Kürbis, et al.

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This paper presents a sequent calculus and a dual domain semantics for a theory of definite descriptions in which these expressions are formalised in the context of complete sentences by a binary quantifier I. I forms a formula from two formulas. Ix[F, G] means `The F is G'. This approach has the advantage of incorporating scope distinctions directly into the notation. Cut elimination is proved for a system of classical positive free logic with I and it is shown to be sound and complete for the semantics. The system has a number of novel features and is briefly compared to the usual approach of formalising `the F' by a term forming operator. It does not coincide with Hintikka's and Lambert's preferred theories, but the divergence is well-motivated and attractive.