, Volume 85, Issue 2, pp 251-260
Date: 04 Apr 2007

A Propositional Logic with Relative Identity Connective and a Partial Solution to the Paradox of Analysis

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Abstract

We construct a a system PLRI which is the classical propositional logic supplied with a ternary construction \({\alpha \equiv_{\gamma} \beta}\) , interpreted as the intensional identity of statements \({\alpha}\) and \({\beta}\) in the context \({\gamma}\) . PLRI is a refinement of Roman Suszko’s sentential calculus with identity (SCI) whose identity connective is a binary one. We provide a Hilbert-style axiomatization of this logic and prove its soundness and completeness with respect to some algebraic models. We also show that PLRI can be used to give a partial solution to the paradox of analysis.

Presented by Jacek Malinowski