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Canonical formulas for \(\mathbf K\mathbf 4\). III: The finite model property. (English) Zbl 0893.03006
[For Parts I and II see ibid. 57, No. 4, 1377-1402 (1992; Zbl 0774.03005) and ibid. 61, No. 2, 421-449 (1996; Zbl 0884.03014), respectively.]
The paper presents two methods of proving the finite model property of normal modal logics containing K4. The methods are oriented mainly to logics represented by their canonical axioms and yield for such axiomatizations several sufficient conditions for the finite model property. They are used for proving that all normal extensions of K4 with modal reduction principles and all normal extensions of S4 with a formula in one variable have the finite model property.

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