A temporal semantics for basic logic
type: Item
instance of: scholarly article
title: A temporal semantics for basic logic
zbMATH Open document ID: 1186.03052
author: Stefano Aguzzoli
author: Matteo Bianchi
author: Vincenzo Marra
published in: Studia Logica
publication date: 2009-11-16T00:00:00Z
review text: In this paper, the authors give a temporal semantics of Basic Fuzzy Logic, the many-valued logic of continuous t-norms [see \textit{P. Hájek}, Metamathematics of fuzzy logic. Dordrecht: Kluwer Academic Publishers (1998; Zbl 0937.03030)]. The algebraic counterparts of Basic Fuzzy Logic are the BL-algebras. Any linearly ordered BL-algebra can be decomposed as the ordinal sum of linearly ordered MV-algebras (that are the algebraic counterpart of Łukasiewicz logic). Using this decomposition and the completeness theorem of Basic Logic with respect to linearly ordered BL-algebras, a temporal semantics is given for Basic Logic in such a way that the logic of each instant is Łukasiewicz logic with a finite or infinite number of truth values. The main result of the paper is the soundness with respect to flows of time that do not branch in the future and completeness with respect to all finite linear flows of time.
reviewed by: Brunella Gerla
Mathematics Subject Classification ID: 03B52
Mathematics Subject Classification ID: 03B50
Mathematics Subject Classification ID: 03G25
zbMATH DE Number: 5633557
zbMATH Keywords: many-valued logics
zbMATH Keywords: basic logic
zbMATH Keywords: Łukasiewicz logic
zbMATH Keywords: modal logics
zbMATH Keywords: temporal logics
zbMATH Keywords: temporal semantics
MaRDI profile type: Publication
Wikidata QID: Q59321747
full work available at URL: s11225-009-9192-3
OpenAlex ID: W1991780340
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cites work: Metamathematics of fuzzy logic
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DOI: 10.1007/S11225-009-9192-3
description: scientific article; zbMATH DE number 5633557