Logical equations and admissible rules of inference with parameters in modal provability logics
type: Item
instance of: scholarly article
title: Logical equations and admissible rules of inference with parameters in modal provability logics
zbMATH Open document ID: 0729.03012
DOI: 10.1007/BF00935600
published in: Studia Logica
publication date: 1990-01-01T00:00:00Z
review text: The aim of this paper is to study admissible inference rules for the modal provability logics GL and S. It is proved that none of these logics has a basis for admissible rules in a finite number of variables, in particular, they do not have finite bases. It is proved that GL and S are decidable by admissibility, some algorithms are found which recognize admissibility of usual inference rules and inference rules in generalized form - inference rules with parameters (or metavariables). By using recognizability of admissibility of inference rules with parameters, we can recognize solvability of logical equations in GL and S and construct some of their solutions. Thus, the analogues of H. Friedman's problem for GL and S are affirmatively solved, the analogues of A. Kuznetsov's problem of finiteness of a basis for admissible rules for GL and S have negative solutions, and the problems of solvability of logical equations in GL and S have positive solutions.
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03F40
Mathematics Subject Classification ID: 03B25
zbMATH DE Number: 4204317
zbMATH Keywords: Gödel-Löb logic
zbMATH Keywords: admissible inference rules
zbMATH Keywords: modal provability logics
zbMATH Keywords: algorithms
zbMATH Keywords: solvability of logical equations
author: Vladimir Rybakov
reviewed by: Vladimir Rybakov
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00935600
OpenAlex ID: W1967787797
description: scientific article; zbMATH DE number 4204317