A non-classical refinement of the interpolation property for classical propositional logic

Citation

Milne P (2016) A non-classical refinement of the interpolation property for classical propositional logic. Logique et Analyse, 59 (235), pp. 273-281. http://virthost.vub.ac.be/lnaweb/ojs/index.php/LogiqueEtAnalyse/article/view/1856; https://doi.org/10.2143/LEA.235.0.3170109

Abstract
We refine the interpolation property of the {^, v, ¬}-fragment of classical propositional logic, showing that if /|= ¬Φ, and /|= Ψ then there is an interpolant Χ constructed using at most atomic formulas occurring in both Φ and Ψ and negation, conjunction and disjunction, such that (i) Φ   entails Χ in Kleene’s strong three-valued logic and (ii) Χ entails Ψ  in Priest’s Logic of Paradox.

Keywords
Interpolation theorem for classical propositional logic; Kleene’s strong 3-valued logic; Priest’s Logic of Paradox

Journal
Logique et Analyse: Volume 59, Issue 235

People

Professor Peter Milne

Emeritus Professor, Philosophy