Definitional equivalence and algebraizability of generalized logical systems
type: Item
instance of: scholarly article
title: Definitional equivalence and algebraizability of generalized logical systems
zbMATH Open document ID: 0948.03007
DOI: 10.1016/S0168-0072(98)00058-X
author: A. P. Pyn'ko
published in: Annals of Pure and Applied Logic
publication date: 2000-03-09T00:00:00Z
review text: The author introduces and studies a concept of algebraizable sequential logic, a generalized notion of a logical system that covers, on a uniform basis, sequential systems and the quasi-equational theories of quasivarieties in Mal'tsev's sense. The author defines a concept of equivalence between generalized logics so that a logic is considered to be algebraizable whenever it is equivalent to the quasi-equational theory of a quasivariety. The author presents also a general algebraic approach to a rather wide class of sentential logics containing all intermediate logics and many interesting non-algebraizable logics.
Mathematics Subject Classification ID: 03B22
Mathematics Subject Classification ID: 03G99
Mathematics Subject Classification ID: 03B60
Mathematics Subject Classification ID: 08B05
Mathematics Subject Classification ID: 03B55
Mathematics Subject Classification ID: 08C15
zbMATH DE Number: 1340808
zbMATH Keywords: consequence operation
zbMATH Keywords: equational theory
zbMATH Keywords: sequential system
zbMATH Keywords: sentential logic
zbMATH Keywords: algebraizable logic
zbMATH Keywords: quasivariety
zbMATH Keywords: conjunctive logic
zbMATH Keywords: quasi-equational theories
reviewed by: Leo Esakia
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1340808