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Behavioral algebraization of logics

The general theory of abstract algebraic logic (AAL from now on) was ?rst introduced in a mathematical precise way by Blok and Pigozzi in 1989. It aims at extending the so-called Lindenbaum-Tarski method, as used for instance to establish the well-known relationship between classical propositional logic and Boolean algebras, to the systematic study of the connection between a given logic and a suitable equational theory. This connection enables one to use many of the powerful tools of universal algebra to study the metalogical properties of the logic being algebraized, namely with respect to axiomatizability, de?nability, the deduction theorem, or interpolation properties. Despite of its success, the scope of applicability of the current theory of AAL is still quite limited. To wit, logics with a many-sorted language or with non-truth-functional connectives simply fall out of its scope. In this talk we will give an overview of the theory of AAL and we propose a generalization of some of the main notions of AAL using a tool from computer science: behavioral equivalence.