Categorical Abstract Algebraic Logic: Syntactically Algebraizable pi-Institutions

• Autorzy: Voutsadakis G.
• Języki publikacji: EN

Abstrakty

EN

This paper has a two-fold purpose. On the one hand, it introduces the concept of a syntactically N-algebraizable pi-institution, which generalizes in the context of categorical abstract algebraic logic the notion of an algebraizable logic of Blok and Pigozzi. On the other hand, it has the purpose of comparing this important notion with the weaker ones of an N-protoalgebraic and of a syntactically N-equivalential pi-institution and with the stronger one of a regularly N-algebraizable pi-institution. N-protoalgebraic pi-institutions and syntactically N-equivalential pi-institutions were previously introduced by the author and abstract in the categorical framework the protoalgebraic logics of Blok and Pigozzi and the equivalential logics of Prucnal and Wroński and of Czelakowski. Regularly N-algebraizable pi-institutions are introduced in the present paper taking after work of Czelakowski and of Blok and Pigozzi in the sentential logic framework. On the way to defining syntactically N-algebraizable pi-institutions, the important notion of an equational pi-institution associated with a given quasivariety of N-algebraic systems is also introduced. It is based on the notion of an N-quasivariety imported recently from the theory of Universal Algebra to the categorical level by the author.

Słowa kluczowe

EN

quasi-varieties; equational logic; algebraizable logics; syntactically N-algebraizable pi-institutions; equivalential logics; N-equivalential pi-institutions; protoalgebraic logics; N-protoalgebraic pi-insitutions; Leibniz operator; Leibniz hierarchy; N-Leibniz operator; regularly algebraizable logics; relatively point-regular quasivarieties; deduction-detachment theorem

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2009
• Tom: Vol. 44
• Strony: 105--151
• Opis fizyczny: Bibliogr. 25 poz.

Twórcy

autor

Voutsadakis G.

• School of Mathematics and Computer Science, Lake Superior State University, Sault Sainte Marie, MI 49783, USA,,

Bibliografia

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• [21] G. Voutsadakis, Categorical Abstract Algebraic Logic: Closure Operators on Classes of PoFunctors, Submitted to Algebra Universalis, Preprint available at http://www.voutsadakis.com/RESEARCH/papers.html
• [22] G. Voutsadakis, Categorical Abstract Algebraic Logic: Equivalential #-Institutions, To appear in the Australasian Journal of Logic, Preprint available at http://www.voutsadakis.com/RESEARCH/papers.html
• [23] G. Voutsadakis, Categorical Abstract Algebraic Logic: Subdirect Representation of PoFunctors, Communications in Algebra 35, 1 (2007), pp. 1–10.
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• [25] G. Voutsadakis, Categorical Abstract Algebraic Logic: Selfextensional pi-Institutions with Implication, Submitted to Applied Categorical Structures, Preprint available at at http://www.voutsadakis.com/RESEARCH/papers.html