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Categorical Abstract Algebraic Logic: Referential π-Institutions

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Voutsadakis G., School of Mathematics and Computer Science L. S. S. U., gvoutsad@lssu.edu

Bulletin of the Section of Logic

2015

tom 44

nr 1-2

Wójcicki introduced in the late 1970s the concept of a referential semantics for propositional logics. Referential semantics incorporate features of the Kripke possible world semantics for modal logics into the realm of algebraic and matrix semantics of arbitrary sentential logics. A well-known theorem of Wójcicki asserts that a logic has a referential semantics if and only if it is selfextensional. Referential semantics was subsequently studied in detail by Malinowski and the concept of selfextensionality has played, more recently, an important role in the field of abstract algebraic logic in connection with the operator approach to algebraizability. We introduce and review some of the basic definitions and results pertaining to the referential semantics of π-institutions, abstracting corresponding results from the realm of propositional logics.

Ograniczanie wyników

1 Bulletin of the Section of Logic

1 School of Mathematics and Computer Science L. S. S. U.

1 Voutsadakis G.

1 gvoutsad@lssu.edu

1 2015

Wyniki wyszukiwania

Categorical Abstract Algebraic Logic: Referential π-Institutions