Enhancing Disjunctive Datalog by constraints

This paper presents an extension of Disjunctive Datalog (DATALOG ^V,~) by integrity constraints. These are of two types: strong, that is, classical integrity constraints and weak, that is, constraints that are satisfied if possible. While strong constraints must be satisfied, weak constraints express desiderata, that is, they may be violated-actually, their semantics tends to minimize the number of violated instances of weak constraints. Weak constraints may be ordered according to their importance to express different priority levels. As a result, the proposed language (call it, DATALOG^V,~,c ) is well-suited to represent common sense reasoning and knowledge-based problems arising in different areas of computer science such as planning, graph theory optimizations, and abductive reasoning. The formal definition of the language is first given. The declarative semantics of DATALOG^V,~,c is defined in a general way that allows us to put constraints on top of any existing (model-theoretic) semantics for DATALOG^V,~ programs. Knowledge representation issues are then addressed and the complexity of reasoning on DATALOG^V,~,c programs is carefully determined. An in-depth discussion on complexity and expressiveness of DATALOG^V,~,c is finally reported. The discussion contrasts DATALOG^V,~,c to DATALOG^V,~ and highlights the significant increase in knowledge modeling ability carried out by constraints