The computational value of joint consistency

Abstract

In this paper we investigate the complexity of some recent reconstructions of Reiter's Default Logic using graph-theoretical structures. It turns out that requiring joint consistency of the justification of the applied rules has serious effects on the computational features of default reasoning. Namely, many of the intractability problems of Reiter's original approach, in some cases disappear in the new frameworks. However, interesting problems remain intractable. We also present a propositional semantics for those approaches, stemming from the translation of the graph structures into propositional logic. Finally, the constraint stable model semantics is introduced, and proved to be related to the notion of joint consistency. © 1994, Springer Verlag. All rights reserved.