protoalgebraic

The use of generalized matrices and abstract logics as models for logic systems has proved very useful for the study of selfextensional logics in general and more in particular for the study of the non-protoalgebraic and selfextensional logics such as the logics in Section 12.

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

As we will see, some interesting logics are not protoalgebraic.

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

L is protoalgebraic if and only if for every full model there is an

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

Due to the monotonicity property of the Leibniz operator, for any protoalgebraic logic

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

There are selfextensional and non-selfextensional logics in any of the classes of the Leibniz hierarchy and also in the class of non-protoalgebraic 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

For example it is known (see (Czelakowski, 2001)) that for every finitary protoalgebraic logic

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

The label ˜protoalgebraic logic™ is due to these last authors.

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

An important characterization of protoalgebraic logics is via the behaviour of the Leibniz operator.

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

(finitr or not) of formulas are called protoalgebraic.

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006