Coherence in Modal Logic

A variety is said to be coherent if the finitely generated subalgebras of its finitely presented members are also finitely presented. In a recent paper by the authors it was shown that coherence forms a key ingredient of the uniform deductive interpolation property for equational consequence in a variety, and a general criterion was given for the failure of coherence (and hence uniform deductive interpolation) in varieties of algebras with a term-definable semilattice reduct. In this paper, a more general criterion is obtained and used to prove the failure of coherence and uniform deductive interpolation for a broad family of modal logics, including K, KT, K4, and S4

Uniform interpolation, bisimulation quantifiers and fixed points

In this paper we consider some basic questions regarding the extensions of modal logics with bisimulation quantifiers. In particular, we consider the relation between bisimualtion quantifiers and uniform interpolation for modal logic and the \u3bc-calculus. We first consider these questions over the whole class of frames, and then we restrict to specific classes, where we see that the results obtained before can be easily falsified. Finally, we introduce classes of frames where we found the same good behaviour than in the whole class of frames. The results presented in this paper have been obtained in collaboration with other authors during the last years; in alphabetical order: Tim French, Marco Hollenberg, and Giacomo Lenzi