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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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