A Binary Quantifier for Definite Descriptions in Intuitionist Negative Free Logic: Natural Deduction and Normalisation

Abstract: This paper presents a way of formalising definite descriptions with a binary quantifier $\iota$, where $\iota x[F, G]$ is read as `The $F$ is $G$'. Introduction and elimination rules for $\iota$ in a system of intuitionist negative free logic are formulated. Procedures for removing maximal formulas of the form $\iota x[F, G]$ are given, and it is shown that deductions in the system can be brought into normal form.