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Logics containing K4. II. (English) Zbl 0574.03008
[For Part I see ibid. 39, 31-42 (1974; Zbl 0287.02010).]
Fine defines a class of modal logics containing K4, called sub-frame logics. These are all proved to be complete by the method of eliminating certain points from the canonical model of the system in question and showing that any finite sub-frame of the resulting model is a frame for the logic. Each sub-frame logic has the finite model property, and since the sub-frame logics turn out to be precisely those complete for a condition that is closed under sub-frames, it follows that every logic complete for a condition closed under sub-frames has the finite model property. Fine also proves that a sub-frame logic is compact iff its axioms express an elementary condition.
Reviewer: M.J.Cresswell

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