Nonmonotonic logics and their algebraic foundations

The goal of this note is to provide a background and references for the invited lecture presented at Computer Science Logic 2006. We briefly discuss motivations that led to the emergence of nonmonotonic logics and introduce two major nonmonotonic formalisms, default and autoepistemic logics. We then point out to algebraic principles behind the two logics and present an abstract algebraic theory that unifies them and provides an effective framework to study properties of nonmonotonic reasoning. We conclude with comments on other major research directions in nonmonotonic logics.