Hybrid rules with well-founded semantics

A general framework is proposed for integration of rules and external first-order theories. It is based on the well-founded semantics of normal logic programs and inspired by ideas of Constraint Logic Programming (CLP) and constructive negation for logic programs. Hybrid rules are normal clauses extended with constraints in the bodies; constraints are certain formulae in the language of the external theory. A hybrid program consists of a set of hybrid rules and an external theory. Instances of the framework are obtained by specifying the class of external theories and the class of constraints. An example instance is integration of (non-disjunctive) Datalog with ontologies formalized in description logics. The paper defines a declarative semantics of hybrid programs and a goal-driven formal operational semantics. The latter can be seen as a generalization of SLS-resolution. It provides a basis for hybrid implementations combining Prolog with constraint solvers (such as ontology reasoners). Soundness of the operational semantics is proven. Sufficient conditions for decidability of the declarative semantics and for completeness of the operational semantics are given.