Behavioral Algebraization ofLogics

摘要

We introduce and study a new approach to the theory of abstract algebraiclogic (AAL) that explores the use of many-sorted behavioral logic in the role traditionallyplayed by unsorted equational logic. Our aim is to extend the range of applicability ofAAL toward providing a meaningful algebraic counterpart also to logics with a many-sorted language, and possibly including non-truth-functional connectives. 'the proposedbehavioral approach covers logics which are not algebraizable according to the standardapproach, while also bringing a new algebraic perspective to logics which are algebraizableusing the standard tools of AAL. Furthermore, we pave the way toward a robust behavioraltheory of AAL, namely by providing a behavioral version of the Leibniz operator whichallows us to generalize the traditional Leibniz hierarchy, as well as several well-knowncharacterization results. A number of meaningful examples will be used to illustrate thenovelties and advantages of the approach.