Well-Founded Semantics for Hybrid Rules

Abstract

The problem of integration of rules and ontologies is addressed in a general framework based on the well-founded semantics of normal logic programs and inspired by the ideas of Constraint Logic Programming (CLP). Hybrid rules are defined as normal clauses extended with constraints in the bodies. The constraints are formulae in a language of a first order theory defined by a set T of axioms. Instances of the framework are obtained by specifying a language of constraints and providing T. A hybrid program is a pair (P, T) where P is a finite set of hybrid rules. Thus integration of (non-disjunctive) Datalog with ontologies formalized in a Description Logic is covered as a special case. The paper defines a declarative semantics of hybrid programs and a formal operational semantics. The latter can be seen as an extension of SLS-resolution and provides a basis for hybrid implementations combining Prolog with constraint solvers. In the restricted case of positive rules, hybrid programs are formulae of FOL. In that case the declarative semantics reduces to the standard notion of logical consequence. The operational semantics is sound and it is complete for a restricted class of hybrid programs.