We consider the problem of finding, in the ambit of modal logic, a minimal characterization for finite Kripke frames, i.e., a formula which, given a frame, axiomatizes its theory employing the lowest possible number of variables and implies the other axiomatizations. We show that every finite transitive frame admits a minimal characterization over K4, and that this result can not be extended to K.
Bellissima, F., Cittadini, S. (1997). Minimal Axiomatization in Modal Logic. MATHEMATICAL LOGIC QUARTERLY, 43(1), 92-102 [10.1002/malq.19970430112].
Minimal Axiomatization in Modal Logic
BELLISSIMA, FABIO;
1997-01-01
Abstract
We consider the problem of finding, in the ambit of modal logic, a minimal characterization for finite Kripke frames, i.e., a formula which, given a frame, axiomatizes its theory employing the lowest possible number of variables and implies the other axiomatizations. We show that every finite transitive frame admits a minimal characterization over K4, and that this result can not be extended to K.
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https://hdl.handle.net/11365/20443
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