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

摘要

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.