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

Peter Milne


We refine the interpolation property of classical propositional logic, showing that if \phi is not a contradiction, \psi is not a tautology, and \phi |= \psi then there is an interpolant \chi, constructed
using at most atomic formulas occurring in both \phi and \psi and negation, conjunction and disjunction, such that (i) \phi entails \chi in Kleene’s strong threevalued logic and (ii) \chi entails \psi in Priest’s Logic of Paradox.


Kleene, Stephen C. (1952), Introduction to Metamathematics, Amsterdam/Groningen/New York: North-Holland/P. Noordhoff/D. van Nostrand.

Priest, Graham (1979), ‘The Logic of Paradox’, Journal of Philosophical Logic, 8(1), 219–41.


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