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

Тип публикации: статья из журнала

Год издания: 1994

Идентификатор DOI: 10.1007/BF01054709

Аннотация: The main result of this paper is the following theorem: each modal logic extending K4 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 K4, K4.1, K4.2, K4.3, S4.1, S4.2, GL.2; to all smallest and greatest counterparts of intermediate Gabbay-De-Jong logics Dn; to all intermediate Gabbay-De-Jong logics Dn; to all finitely axiomatizable modal and intermediate logics of finite depth etc. Semantic criteria for recognizing admissibility for these logics are offered as well. © 1994 Kluwer Academic Publishers.

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Издание

Журнал: Studia Logica

Выпуск журнала: Vol. 53, Is. 2

Номера страниц: 203-225

ISSN журнала: 00393215

Авторы

  • Rybakov V.V. (Mathematics Department, Krasnoyarsk University, Pr. Svobodnyi 79, Krasnoyarsk, 660 062, Russian Federation)

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