A topological characterization of consistency of logic theories in propositional logic

✍ Scribed by Guo-Jun Wang; Yan-Hong She

• Publisher: John Wiley and Sons
• Year: 2006
• Tongue: English
• Weight: 116 KB
• Volume: 52
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.200610007

✦ Synopsis

Abstract

The main purpose of this note is to characterize consistency of logic theories in propositional logic by means of topological concept. Based on the concepts of truth degree of formulas and similarity degree between formulas the concept of logic metric space has been proposed by the first author. It is proved in this note that a closed logic theory Γ is consistent if and only if it contains no interior point in the logic metric space. Moreover the relationship between logic closedness and topological closedness of a logic theory Γ is discussed. Finally, the concept of full divergency is also characterized by means of the topological concept of density. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)