Abstract

In this thesis we are concerned with two major issues in knowledge representation: semantics of negation in knowledge representation languages, and combining knowledge bases. ;We take two different approaches to characterize the semantics of negation in knowledge representation languages. The first approach is based on an iterated fixpoint computation of the semantics. We present a uniform framework for iterated fixpoint semantics of logic programs. Based on this framework we study three particular instances in detail: Generalized Well-founded Semantics , $WF\sp3$ semantics, and Disjunctive Well-founded Semantics . For WF$\sp3$ semantics we present an equivalent procedural characterization and for GWFS and WF$\sp3$ semantics we present equivalent model theoretic characterizations. The second approach is based on extending the traditional way to characterize default theories and auto-epistemic theories. We introduce the concept of "classes" to be able to characterize the class of all theories when they are represented as normal logic programs, default theories, auto-epistemic theories and non-monotonic modal theories. We study various aspects of the "class" semantics and show that the concept of classes can also be used to give a simple specification of the well-founded semantics. ;We study the problem of combining knowledge bases with respect to three knowledge representation languages: logic programs, first-order theories and default theories. We formalize the various properties that the combined knowledge base should satisfy; mainly consistency with respect to the integrity constraints, and maximality and correctness with respect to the union of the knowledge bases. To satisfy the maximality criterion the combined knowledge base of a set of Horn programs may have to be a disjunctive logic program. Unlike normal and disjunctive logic programs, the union of a set of first-order theories and union of a set of default theories may be inconsistent. We present methods that consider these aspects and construct the combined knowledge base of a set of knowledge bases. We compare combining knowledge bases with the problem of updating a knowledge base