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On finite model property for admissible rules. (English) Zbl 0938.03033
The finite model property (f.m.p.) is important not only for helping to investigate the decidability problem, but also for providing a much more precise semantic description of logics under consideration. This paper is concerned with a technique for verifying the f.m.p. with respect to admissible rules. The authors present a general sufficient condition for the absence of the f.m.p. with respect to admissibility and find that no modal logic extending <span class=”textbf”>K</span>4 <span class=”textrm”>w</span>ith the co-cover property and of width $$>2$$ has the f.m.p. with respect to admissibility. A surprising number of important modal logics of width $$>2$$ are within the scope of this result: K4, S4, GL, K4.1, K4.2, S4.1, S4.2, GL.2, etc. Consequently, the situation is quite opposite to the case of the ordinary f.m.p. where the absolute majority of the important modal logics have the f.m.p. (but not with respect to admissibility). On the other hand, it is shown that all modal logics of width $$\leq 2$$ containing S4 and being not subsystems of three special tabular logics, have the f.m.p. with respect to admissibility.

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