Towards an Operational Semantics of Rules in Knowledge Systems

We develop a general closure semantics for deduction rules in knowledge bases, using the concept of a (deductive) knowledge system proposed in [Wag94a] where rules are interpreted as update functions operating on knowledge bases. We first present four important examples of basic knowledge systems: relational databases, (defeasible) factbases, temporal databases, and epistemic states. We then define the notion of a supported closure, and we show that every ampliative deductive knowledge base has a supported closure. Choosing those supported closures which satisfy a certain stability condition as the preferred (or intended) ones we obtain the stable closure semantics for deductive knowledge bases (including normal, extended, disjunctive, and other logic programming and rule-based systems). Contents 1 Introduction 2 2 Basic Concepts 3 2.1 Knowledge Systems : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 2.2 Regular Knowledge Systems : : : : : : : : : : : : : : : ..