ISALOG(¬): A Deductive Language with Negation for Complex-Object Databases with Hierarchies.

IsaLog(¬) is a research activity aimed at developing a framework that integrates deductive and object-oriented features. The data model has complex objects with classes, relations, and isa hierarchies, and the language is rule based. The main issue is the definition of the semantics of the language. For the (positive) IsaLog framework three different semantics are given and proven to be equivalent: a model-theoretic semantics, a fixpoint semantics, and a semantics based on a reduction to ordinary logic programming with functionasymbols. Then the semantics of the IsaLog¬ language is proposed. It presents novel features mostly due to the interaction of hierarchies with negation in the body of rules. Two semantics are presented for IsaLog¬ programs: a stratified semantics based on an original notion of stratification, which takes into account hierarchies, and a reduction to logic programming with function symbols. The two semantics are then shown to be equivalent. The solutions are based on the use of explicit Skolem functors, which represent a powerful tool for the management of object identifiers.