Criteria for admissibility of inference rules. Modal and intermediate logics with the branching property
type: Item
instance of: scholarly article
title: Criteria for admissibility of inference rules. Modal and intermediate logics with the branching property
zbMATH Open document ID: 0807.03016
DOI: 10.1007/BF01054709
published in: Studia Logica
publication date: 1995-03-05T00:00:00Z
review text: This paper considers the class of normal modal logics containing K4 and intermediate logics having the finite model property and satisfying two rather complicated conditions (one of them is related to the possibility of constructing a frame for a logic L by adding a root to the disjoint union of finite frames for L, the other one to the possibility of effectively estimating the cardinality of finite frames separating a given formula from L). It is shown that the admissibility problem for logics in this class is decidable; more precisely, an inference rule with \(n\) variables is admissible in a logic L in this class iff it cannot be disproved in the \(n\)-universal frame for L, which can be checked effectively. This result covers a wide variety of modal and intermediate logics known in the literature (K4.1, K4.2, K4.3, GL2, etc.).
Mathematics Subject Classification ID: 03B55
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03B25
zbMATH DE Number: 590919
zbMATH Keywords: normal modal logics
zbMATH Keywords: intermediate logics
zbMATH Keywords: finite model property
zbMATH Keywords: frames
zbMATH Keywords: admissibility problem
author: Vladimir Rybakov
reviewed by: Michael Zakharyaschev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 590919