Results 31 to 40 of about 62 (49)

On the Algebraizability of the Implicational Fragment of Abelian Logic

Studia Logica, 2013
In this paper we consider the implicational fragment of Abelian logic A→. We show that although the Abelian groups provide an semantics for the set of theorems of A→ they do not for the associated consequence relation. We then show that the consequence relation is not algebraizable in the sense of Blok and Pigozzi (Mem Am Math Soc 77, 1989).
Butchart, Sam, Rogerson, Susan
openaire   +3 more sources

Characterizing Equivalential and Algebraizable Logics by the Leibniz Operator

Studia Logica, 1997
In this paper the author characterizes the hierarchy of protoalgebraic, equivalential, finitely equivalential, possibly infinitely algebraizable and finitely algebraizable logics by properties of the Leibniz operator. The author gives a new short proof of the main result of \textit{W. J. Blok} and \textit{D. Pigozzi} [Algebraizable logics, Mem.
openaire   +2 more sources

A Non-finitary Sentential Logic that is Elementarily Algebraizable

Journal of Logic and Computation, 2008
Summary: We exhibit a non-finitary sentential logic that is algebraized by a quasivariety -- in fact by a finitely based variety of finite type. The algebraization process requires infinitely many defining equations. The existence of such a logic settles a question posed by \textit{J. Czelakowski} [Protoalgebraic logics.
openaire   +2 more sources

Categorical Abstract Algebraic Logic: Algebraizable Institutions

Applied Categorical Structures, 2002
The framework developed by W. J. Blok and D. Pigozzi for the algebraizability of deductive systems is extended to the algebraizability of multisignature logics with quantifiers.
openaire   +1 more source

Regularly Algebraizable Logics

2001
A sentential logic (S, C) is regularly algebraizable (alias 1-algebraizable) if it possesses a non-empty system E(p, q) of equivalence sentences such that E(p, q) ⊆ C(p, q).
openaire   +1 more source

Duality for Lattice-Ordered Algebras and for Normal Algebraizable Logics

Studia Logica, 1997
This paper consists of three parts. In Part I, a new topological representation for general lattices is presented, and this representation is extended to a full duality. In Part II, the Jónsson and Tarski representation results for Boolean algebras with operators are extended for lattice-ordered algebras (lattices with additional operators).
openaire   +2 more sources

Algebraizable logics

Memoirs of the American Mathematical Society, 1989
W. J. Blok, Don Pigozzi
openaire   +1 more source

Applications to protoalgebraic and algebraizable logics

1996
Josep Maria Font, Ramon Jansana
openaire   +1 more source

Algebraizable Logics

2001
openaire   +1 more source

Categorical Abstract Algebraic Logic: Models of π-Institutions

Notre Dame Journal of Formal Logic, 2005
George Voutsadakis
exaly