Categorical abstract algebraic logic: The categorical Suszko operator

Voutsadakis, George

doi:10.1002/malq.200710020

Cited by 2 publications

(2 citation statements)

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“…Its introduction followed the work of Blok and Pigozzi [6] that introduced the Leibniz operator for the first time to characterize algebraizable logics. The categorical Suszko operator was introduced in [60], taking after the work of Czelakowski [18], who introduced the Suszko operator with the goal of lifting some of the methods of abstract algebraic logic that are applicable to the class of protoalgebraic deductive systems to arbitrary logics.…”

Section: Leibniz and Suszko Operatorsmentioning

confidence: 99%

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Categorical Abstract Algebraic Logic: Truth-Equational π-Institutions

Voutsadakis¹

2015

Notre Dame J. Formal Logic

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Finitely algebraizable deductive systems were introduced by Blok and Pigozzi to capture the essential properties of those deductive systems that are very tightly connected to quasivarieties of universal algebras. They include the equivalential logics of Czelakowski. Based on Blok and Pigozzi's work, Herrmann defined algebraizable deductive systems. These are the equivalential deductive systems that are also truth-equational, in the sense that the truth predicate of the class of their reduced matrix models is explicitly definable by some set of unary equations. Raftery undertook the task of characterizing the property of truth-equationality for arbitrary deductive systems. In this paper, following Raftery, we extend the notion of truth-equationality for logics formalized as πinstitutions and abstract several of the results that hold for deductive systems in this more general categorical context.

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Section: Leibniz and Suszko Operatorsmentioning

confidence: 99%

“…To provide more details, recall from Section 6 of [58] (see also [60]) that given a π-institution I = Sign, SEN,C , with N a category of natural transformations on SEN, and a theory family T = {T Σ } Σ∈|Sign| of I , the family of binary relations Ω…”

Section: Sometimes the Relation In The Conclusion Of Lemma 4 Is Denomentioning

confidence: 99%