A Binary Quantifier for Definite Descriptions for Cut Free Free Logics

DOI10.1007/S11225-021-09958-XarXiv2108.09777MaRDI QIDQ6375775

Nils Kürbis

Publication date: 22 August 2021

Abstract: This paper presents rules in sequent calculus for a binary quantifier $I$ to formalise definite descriptions: $Ix[F,G]$ means `The $F$ is $G$'. The rules are suitable to be added to a system of positive free logic. The paper extends the proof of a cut elimination theorem for this system by Indrzejczak by proving the cases for the rules of $I$. There are also brief comparisons of the present approach to the more common one that formalises definite descriptions with a term forming operator. In the final section rules for $I$ for negative free and classical logic are also mentioned.

Mathematics Subject Classification ID

Mathematical logic and foundations (03-XX)

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