Logic knowledge bases with two default rules

Logic knowledge based systems (LKBS) containing at most one form of default negation and explicit (or “classical”) negation have been studied in the literature. In this paper we describe a class of LKBS containing multiple forms of default negation in addition to explicit negation. We define a semantics for these systems in terms of the well‐founded semantics defined by Van Gelder et al. (1988) and the stable semantics introduced by Gelfond and Lifschitz (1988) and later extended to the 3‐valued case by Przymusinski (1991). We investigate properties of the new combined semantics and calculate the computational complexity of three main reasoning tasks for this semantics, namely existence of models, skeptical and credulous reasoning. An effective procedure to construct the collection of models characterizing the semantics of such a system is given. Applications to knowledge representation and knowledge base merging are presented. This revised version was published online in June 2006 with corrections to the Cover Date.