Semantics and expressiveness of disjunctive ordered logic

Abstract

The paper proposes a knowledge representation language which extends logic programming with disjunction, inheritance, true negation and modularization. The resulting language is called Disjunctive Ordered Logic (\mathcal{DOL} for short). A modeldtheoretic semantics for \mathcal{DOL} is given, and it is shown to extend the stable model semantics of disjunctive logic programs. A number of examples show the suitability of \mathcal{DOL} for knowledge representation and commonsense reasoning. Among other things, the proposed language appears to be a powerful tool for the description of diagnostic processes which are based on stepwise refinements. The complexity and the expressiveness of the language are carefully analyzed. The analysis pays particular attention to the relative power and complexity of inheritance, negation and disjunction. An interesting result in this course concerns the role played by inheritance. Indeed, our results show that inheritance does not increase at all the complexity of any fragment of the language, while it does increase the expressive power of some \mathcal{DOL} fragments.