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• W2535894220 abstract "Blok and Pigozzi introduced the Leibniz operator, mapping filters of an algebra to congruences of the algebra, in order to provide a characterization of algebraizable deductive systems, i.e., those deductive systems whose entailment relation is very closely connected to the algebraic consequence operation associated with a quasi-variety of universal algebras. Font and Jansana generalized the Leibniz operator to the Tarski operator, that maps closure systems on a given algebra to congruences of the algebra. In previous work by the author, Tarski congruence systems were introduced as a generalization of the Tarski operator in order to cover logical systems formalized as π-institutions. Tarski congruence systems consist, roughly speaking, of a system of equivalence relations, one for each set of sentences, of the given πinstitution, that are preserved both by the signature morphisms and by given collections of natural transformations from tuples of sentences to sentences. In this paper, Tarski congruence systems are generalized so as to accommodate also equivalences at the signature level. In the main result of the paper a characterization of these generalized Tarski congruence systems is obtained, which abstracts the known characterization of Tarski congruence systems." @default.
• W2535894220 created "2016-10-28" @default.
• W2535894220 creator A5084446669 @default.
• W2535894220 date "2011-01-01" @default.
• W2535894220 modified "2023-09-27" @default.
• W2535894220 title "Categorical Abstract Algebraic Logic" @default.
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