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Issue No. 05 - September/October (2000 vol. 12)
ISSN: 1041-4347
pp: 845-860
<p><b>Abstract</b>—This paper presents an extension of Disjunctive Datalog (<tmath>${\rm{DATALOG}}^{\vee,}{^\neg}$</tmath>) by integrity constraints. These are of two types: <it>strong</it>, that is, classical integrity constraints and <it>weak</it>, that is, constraints that are satisfied <it>if possible</it>. 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, <tmath>${\rm{DATALOG}}^{\vee,}{^{\neg,}}{^c}$</tmath>) 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 <tmath>${\rm{DATALOG}}^{\vee,}{^{\neg,}}{^c}$</tmath> is defined in a general way that allows us to put constraints on top of any existing (model-theoretic) semantics for <tmath>${\rm{DATALOG}}^{\vee,}{^\neg}$</tmath> programs. Knowledge representation issues are then addressed and the complexity of reasoning on <tmath>${\rm{DATALOG}}^{\vee,}{^{\neg,}}{^c}$</tmath> programs is carefully determined. An in-depth discussion on complexity and expressiveness of <tmath>${\rm{DATALOG}}^{\vee,}{^{\neg,}}{^c}$</tmath> is finally reported. The discussion contrasts <tmath>${\rm{DATALOG}}^{\vee,}{^{\neg,}}{^c}$</tmath> to <tmath>${\rm{DATALOG}}^{\vee,}{^\neg}$</tmath> and highlights the significant increase in knowledge modeling ability carried out by constraints.</p>
Nonmonotonic reasoning, knowledge representation, deductive databases, disjunctive datalog, computational complexity.

P. Rullo, F. Buccafurri and N. Leone, "Enhancing Disjunctive Datalog by Constraints," in IEEE Transactions on Knowledge & Data Engineering, vol. 12, no. , pp. 845-860, 2000.
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