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

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## Abstract

The main result of this paper is the following theorem: each modal logic extending*K*4 having the branching property below*m* 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 below*m* 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 logics*K*4,*K*4.1,*K*4.2,*K*4.3,*S*4.1,*S*4.2,*GL*.2; to all smallest and greatest counterparts of intermediate Gabbay-De-Jong logics*D*_{n}; to all intermediate Gabbay-De-Jong logics*D*_{n}; to all finitely axiomatizable modal and intermediate logics of finite depth etc. Semantic criteria for recognizing admissibility for these logics are offered as well.

## Keywords

Mathematical Logic Modal Logic Inference Rule Computational Linguistic Intuitionistic Logic## Preview

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