Mathematical Logic Quarterly 45 (4):505-520 (1999)

Our investigation is concerned with the finite model property with respect to admissible rules. We establish general sufficient conditions for absence of fmp w. r. t. admissibility which are applicable to modal logics containing K4: Theorem 3.1 says that no logic λ containing K4 with the co-cover property and of width > 2 has fmp w. r. t. admissibility. Surprisingly many, if not to say all, important modal logics of width > 2 are within the scope of this theorem–K4 itself, S4, GL, K4.1, K4.2, S4.1, S4.2, GL.2, etc. Thus the situation is completely opposite to the case of the ordinary fmp–the absolute majority of important logics have fmp, but not with respect to admissibility. As regards logics of width ≤ 2, there exists a zone for fmp w. r. t. admissibility. It is shown that all modal logics A of width ≤ 2 extending S4 which are not sub-logics of three special tabular logics have fmp w.r.t. admissibility
Keywords Finite model property  Inference rule  Modal logic  Admissible rule
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DOI 10.1002/malq.19990450409
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References found in this work BETA

Modal Logic.Alexander Chagrov - 1997 - Oxford, England: Oxford University Press.
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Modal Logics Between S 4 and S 5.M. A. E. Dummett & E. J. Lemmon - 1959 - Mathematical Logic Quarterly 5 (14‐24):250-264.

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Logics with the Universal Modality and Admissible Consecutions.Rybakov Vladimir - 2007 - Journal of Applied Non-Classical Logics 17 (3):383-396.

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