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Completeness of logics with the transitive closure modality and related logics
Stanislav Kikot, Ilya Shapirovsky, Evgeny Zolin
We give a sufficient condition for Kripke completeness of modal logics enriched with the transitive closure modality. More precisely, we show that if a logic admits what we call de…
Modal logics of finite direct powers of have the finite model property
Ilya Shapirovsky
Let be the direct power of instances of , natural numbers with the standard ordering, the direct power of instances of . We s…
Glivenko's theorem, finite height, and local tabularity
Ilya B. Shapirovsky
Glivenko's theorem states that a formula is derivable in classical propositional logic iff under the double negation it is derivable in intuitionistic propositional l…
On modal logics of model-theoretic relations
Denis I. Saveliev, Ilya B. Shapirovsky
Given a class of models, a binary relation between models, and a model-theoretic language , we consider the modal logic and the modal algebra of the…