Hybrid Reasoning with Non-monotonic Rules

This is an introduction to integrating logic programs with first order theories. The main motivation are the needs of Semantic Web to combine reasoning based on rule systems with that based on Description Logics (DL). We focus on approaches which are able to re-use existing reasoners (for DL and for rule systems). A central issue of this paper is non-monotonic reasoning, which is possibly the main feature of rule based reasoning absent in DL. We discuss the main approaches to non-monotonic reasoning in logic programming. Then we show and classify various ways of integrating them with first order theories. We argue that for practical purposes none of the approaches seems sufficient, and an approach combining the features of so-called tight and loose coupling is needed.