algebraizable

Blok and Pigozzi defined the notion of algebraizable logic only for finitary logics.

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

Today we say that an algebraizable logic is finitely algebraizable if the sets of equivalence formulas

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

L is finitely algebraizable if and only if for every algebra A and every

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

A different but related characterization of algebraizable logics is this:

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

L be a finitary and finitely algebraizable logic with the deduction-detachment property.

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

The algebraizable logics are purported to be the logics with the strongest possible link with their natural class of algebras.

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

The researchers in AAL are somehow surprised by the fact that several finitary and finitely algebraizable logics have a variety as its equivalent algebraic semantics, when the theory of algebraizable logics allows us in general to prove only that the equivalent algebraic semantics of a finitary and finitely algebraizable logic is a quasivariety.

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

We need some notational conventions before engaging in the definition of algebraizable logic.

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

Using (2) it gives the isomorphism theorem for finitary and finitely algebraizable logics.

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

Nonetheless, for many logics L, in particular for the algebraizable ones and the protoalgebraic ones to be discussed in the next sections, and also when

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006