Behavioral algebraization
by
Ricardo Gonçalves
Dep. Mathematics, IST-TU Lisbon
Coauthors: Carlos Caleiro

The theory of Abstract Algebraic Logic (AAL) aims at drawing a strong bridge between logic and algebra. It can be seen as a generalization of the well known Lindenbaum-Tarski method. Although the enormous success of the theory we can point out some drawbacks. An evident one is the inability of the theory to deal with logics with a many-sorted language. Even if one restricts to the study of propositional based logics, there are some logics that simply fall out of the scope of this theory. One paradigmatic example is the case of the so-called non-truth-functional logics that lack of congruence of some of its connectives, a key ingredient in the algebraization process.

The quest for a more general framework to the deal with these kinds of logics is the subject of our work.

In this talk we will present a generalization of AAL obtained by substituting the role of unsorted equational logic with (many-sorted) behavioral logic. The incorporation of behavioral reasoning in the algebraization process will allow to amenably deal with connectives that are not congruent, while the many sorted framework will allow to reflect the many sorted character of a given logic to its algebraic counterpart.

We illustrate theses ideas by exploring some examples, namely, paraconsistent logic C1 of da Costa and Exogenous Global and Probabilistic Propositional Logic.

PDF

Date received: April 24, 2007