We introduce the system K4De. It is obtained by weakening the reflexivity axiom to the density axiom in the standard axiom set for S4. We analyze K4De both from the semantic and the proof theoretic side, giving in particular a cut-free system of rules for it.
The logic of transitive and dense frames : from the step-frame analysis to full cut-elimination / S. Ghilardi, G. Mints. - In: LOGIC JOURNAL OF THE IGPL. - ISSN 1367-0751. - 22:4(2014 Aug), pp. 585-596.
The logic of transitive and dense frames : from the step-frame analysis to full cut-elimination
S. GhilardiPrimo
;
2014
Abstract
We introduce the system K4De. It is obtained by weakening the reflexivity axiom to the density axiom in the standard axiom set for S4. We analyze K4De both from the semantic and the proof theoretic side, giving in particular a cut-free system of rules for it.
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