Interpolation in Non-Classical Logics

Abstract

This chapter surveys some of the main results on interpolation in several of the most prominent families of non-classical logics. Special attention is given to the distinction between the two most commonly studied variants of interpolation--namely, Craig interpolation and deductive interpolation. Our discussion focuses primarily on how these properties present in families of logical systems taken as a whole, particularly those comprising all axiomatic extensions of any of several notable non-classical logics. We consider a range of important examples: superintuitionistic and modal logics, fuzzy logics, paraconsistent logics, relevant logics, and substructural logics.

This is a chapter of the forthcoming book "Theory and Applications of Craig Interpolation", edited by Balder ten Cate, Jean Christoph Jung, Patrick Koopmann, Christoph Wernhard and Frank Wolter