Fixed points of modal schemes
type: Item
instance of: scholarly article
title: Fixed points of modal schemes
zbMATH Open document ID: 0795.03038
DOI: 10.1007/BF02259825
author: S. I. Mardaev
published in: Algebra and Logic
publication date: 1994-04-12T00:00:00Z
review text: The concepts of a \(\Sigma\)-formula and \(\Sigma\)-scheme are used in pedicate calculus [\textit{S. S. Goncharov} and \textit{D. I. Sviridenko}, Vychisl. Sist. 107, 3-29 (1985; Zbl 0628.03015)]. In this paper we transfer them to modal propositional logic, which holds a position between classical propositional and predicate logics. In our case, the use of schemes considerably, but not completely, simplifies the situation as compared to that in the predicate logic setting. We prove that a scheme over a transitive Kripke model arrives at its least fixed point in finitely many steps, and that this point is definable by suitable formulas.
Mathematics Subject Classification ID: 03B70
Mathematics Subject Classification ID: 03B45
zbMATH DE Number: 536676
zbMATH Keywords: propositional modal logic
zbMATH Keywords: \(\Sigma\)-formula
zbMATH Keywords: \(\Sigma\)-scheme
zbMATH Keywords: scheme over a transitive Kripke model
zbMATH Keywords: least fixed point
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 536676