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Modal sequents and definability. (English) Zbl 0641.03014
The usual approach to propositional modal logic is extended by the introduction of sequents. A sequent \(\Gamma\) /\(\Delta\) is defined to be valid on a Kripke-frame \(<W,R>\) if every model on \(<W,R>\) that verifies all formulas in \(\Gamma\) verifies at least one formula in \(\Delta\). It appears that this notion of sequent validity is much more powerful than the notion of formula-validity: many classes of frames for which no characteristic set of modal formulas exists, turn out to be characterizable by a set of sequents. Through the use of modal algebras and general frames, a study of the properties of such sequent axiomatic classes of frames is begun.
Reviewer: F.Veltman

MSC:
03B45 Modal logic (including the logic of norms)
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