Studia Logica

, Volume 85, Issue 2, pp 251–260

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

Article

DOI: 10.1007/s11225-007-9030-4

Cite this article as:
Wen, X. Stud Logica (2007) 85: 251. doi:10.1007/s11225-007-9030-4

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.

Keywords

relative identitycontextparadox of analysishyperintensional logic

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Institute of Logic and CognitionSun Yat-sen UniversityGuangzhouP. R. China
  2. 2.Department of HumanitiesNational University of Defence TechnologyChangshaP. R. China