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

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.