2025/12/01 by Fussner, Wesley
#03B22 (Secondary) #03C40 (Primary) #FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO) #Logic in Computer Science (cs.LO)
paper · doi:10.48550/arxiv.2512.01600
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.