Undecidable properties of extensions of provability logic. II
type: Item
instance of: scholarly article
title: Undecidable properties of extensions of provability logic. II
zbMATH Open document ID: 0729.03009
DOI: 10.1007/BF02215288
published in: Algebra and Logic
publication date: 1990-01-01T00:00:00Z
review text: [For part I see Algebra Logika 29, No.3, 350-367 (1990; Zbl 0723.03005).] The aim of this paper is to study questions of effective recognition of properties of modal logics which extend the Gödel-Löb system GL. Using some uniform emulation method for the working of a Minski maschine in modal propositional logic, the author shows that the following properties: a) to be Kripke-complete, b) to be the modal counterpart of Int, c) to be closed with respect to the Gödel normalization rule, d) to be Halldén-complete, are undecidable. By the way, some interesting results of other kinds are obtained. For instance that there are \(2^{\omega}\) maximal logics among the modal counterparts of Int extending the logic S.
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03F40
Mathematics Subject Classification ID: 03D35
Mathematics Subject Classification ID: 03B25
zbMATH DE Number: 4204314
zbMATH Keywords: modal logics which extend the Gödel-Löb system GL
zbMATH Keywords: Minski maschine
author: Alexander Vasil'evich Chagrov
reviewed by: Vladimir Rybakov
MaRDI profile type: Publication
cites work: Undecidable properties of extensions of the logic of provability
cites work: Q4198476
cites work: Varieties of logical matrices
cites work: Post Completeness and Free Algebras
cites work: On systems of modal logic with provability interpretations
cites work: Q3784045
full work available at URL: https://doi.org/10.1007/bf02215288
OpenAlex ID: W2054049955
description: scientific article; zbMATH DE number 4204314