Bisequent Calculi for Neutral Free Logic with Definite Descriptions

2024/12/02 by Andrzej Indrzejczak, Indrzejczak, Andrzej, Yaroslav Petrukhin +1 · 1 citation
Computer Science · #Advanced Algebra and Logic #Logic, Reasoning, and Knowledge #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2412.01712

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 Pavlović 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.

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• Description Logics with Two Types of Definite Descriptions: Complexity, Expressiveness, and Automated Deduction

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