Bisequent Calculi for Neutral Free Logic with Definite Descriptions

TL;DR

This paper introduces a new bisequent calculus for neutral free logic with definite descriptions, extending previous work to include identity and proving the admissibility of cut.

Contribution

It develops a novel bisequent calculus for the minimal theory of definite descriptions in neutral free logic, including identity, with proven cut admissibility.

Findings

Extended the calculus to include identity and definite descriptions

Proved the admissibility of cut in the extended system

Built on and extended prior approaches by Pavlović and Gratzl

Abstract

We present a bisequent calculus (BSC) for the minimal theory of definite descriptions (DD) in the setting of neutral free logic, where formulae with non-denoting terms have no truth value. The treatment of quantifiers, atomic formulae and simple terms is based on the approach developed by Pavlovi\'{c} and Gratzl. We extend their results to the version with identity and definite descriptions. In particular, the admissibility of cut is proven for this extended system.