Studia Logica

, Volume 53, Issue 2, pp 203–225 | Cite as

Criteria for admissibility of inference rules. Modal and intermediate logics with the branching property

  • Vladimir V. Rybakov


The main result of this paper is the following theorem: each modal logic extendingK4 having the branching property belowm and the effective m-drop point property is decidable with respect to admissibility. A similar result is obtained for intermediate intuitionistic logics with the branching property belowm and the strong effective m-drop point property. Thus, general algorithmic criteria which allow to recognize the admissibility of inference rules for modal and intermediate logics of the above kind are found. These criteria are applicable to most modal logics for which decidability with respect to admissibility is known and to many others, for instance, to the modal logicsK4,K4.1,K4.2,K4.3,S4.1,S4.2,GL.2; to all smallest and greatest counterparts of intermediate Gabbay-De-Jong logicsDn; to all intermediate Gabbay-De-Jong logicsDn; to all finitely axiomatizable modal and intermediate logics of finite depth etc. Semantic criteria for recognizing admissibility for these logics are offered as well.


Mathematical Logic Modal Logic Inference Rule Computational Linguistic Intuitionistic Logic 
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Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Vladimir V. Rybakov
    • 1
  1. 1.Mathematics DepartmentKrasnoyarsk UniversityKrasnoyarskRussia

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