Generalized default logic: minimal knowledge, autoepistemic and default reasoning reconciled

Abstract

Logical approaches to nonmonotonic reasoning have been developed within different technical settings, thus making it difficult to establish correspondences among them and to identify common underlying principles. In this paper we argue that the most well-known nonmonotonic reasoning formalisms are actually characterized by two closure assumptions: a minimal knowledge assumption and an autoepistemic assumption. We justify this thesis by introducing generalized default logic (GDL), obtained through a simple and natural generalization of Reiter’s default logic, which fully captures both closure assumptions. We then analyze the relationship between GDL and nonmonotonic modal logics, in particular Moore’s autoepistemic logic and Lifschitz’s logic of minimal knowledge and negation as failure, showing the existence of a full correspondence between these modal formalisms and GDL. Such a correspondence gives us a unified reading of nonmonotonic reasoning formalisms in terms of the above two assumptions; in particular, it clarifies the relationship between default and autoepistemic logic.