algebraization

In this entry we concentrate on the general theory of the algebraization of propositional logics taken as consequence relations.

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

L-filters of an algebra A plays a crucial role in the theory of the algebraization of logic systems.

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

The Lindenbaum-Tarski method contributed in two respects to the elaboration of important notions in the theory of the algebraization of logics.

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

RMatr (L) plays a prominent role in the theory of the algebraization of logics and it is denoted by

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

In the next section we will expound the semantics of abstract logics and generalized matrices that serves to develop a really general theory of the algebraization of logic systems.

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

From the algebraic study of specific logics a general theory of the algebraization of logics slowly emerged during the last century with the aim, more or less explicitly stated during the process, of obtaining general and informative results relating the properties a logic may have with the algebraic properties the class of algebras (or algebra related structures) associated with it might posses.

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

The concept of Leibniz congruence plays a fundamental role in the general theory of the algebraization of the logic systems developed during the 1980's by Blok and Pigozzi.

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

The generalized matrix models that have naturally attacted most the attention in the research on the algebraization of logics are the generalized matrices of the form where FiLA is the set of all the

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

Fermat, who as we said had discovered a similar algebraization of geometry, objected to trivial points.

Euclid’s Window Leonard Mlodinow 2001

Fermat, who as we said had discovered a similar algebraization of geometry, objected to trivial points.

Euclid’s Window Leonard Mlodinow 2001