An explicit basis for the admissible inference rules of the modal logics extending $S4.1$ and $Grz$

V. V. Rimatskii

Institute of Urban Construction, Management and Regional Economics, Siberian Federal University, Krasnoyarsk

Abstract: We study bases for the admissible inference rules in a broad class of modal logics. We construct an explicit basis for all admissible rules in the logics $S4.1$, $Grz$, and their extensions whose number is at least countable. The resulting basis consists of an infinite sequence of rules in a concise and simple form. In the case of a logic of finite width a basis for all admissible rules consists of a finite sequence of rules.

Keywords: modal logic, Kripke frame and model, admissible inference rule, basis for admissible rules.

UDC: 510.643+517.11

Received: 05.03.2007

 English version: Siberian Mathematical Journal, 2009, 50:4, 692–699

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