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Quasi-characteristic inference rules for modal logics. (English) Zbl 0887.03014
Adian, S. (ed.) et al., Logical foundations of computer science. 4th international symposium, LFCS ’97, Yaroslavl, Russia, July 6–12, 1997. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 1234, 333-341 (1997).
Summary: The aim of this paper is to develop techniques characterizing quasi-characteristic inference rules for modal logics. We describe a necessary and sufficient condition for a quasi-characteristic rule to be valid on an algebra and obtain basic properties concerning derivability of quasi-characteristic rules. Using this approach, we characterize all structurally complete logics with the finite model property. The main results of this paper characterize admissible quasi-characteristic inference rules for the modal logics S4 and K4. We also show that the set of all quasi-characteristic inference rules admissible in the logic S4 have a finite basis consisting of three special rules which are precisely described.
For the entire collection see [Zbl 0865.00035].

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