On Well-Founded Set-Inductions and Locally Monotone Operators

Abstract

In the past, compelling arguments in favour of the well-founded semantics for autoepistemic logic have been presented. In this article, we show that for certain classes of theories, this semantics fails to identify the unique intended model. We solve this problem by refining the well-founded semantics. We develop our work in approximation fixpoint theory, an abstract algebraical study of semantics of nonmonotonic logics. As such, our results also apply to logic programming, default logic, Dung’s argumentation frameworks, and abstract dialectical frameworks.