A Feature Constraint System for Logic Programming with Entailment

We introduce a constraint system called FT. This system offers a theoretical and practical alternative to the usual Herbrand system of constraints over constructor trees. Like Herbrand, FT provides a universal data structure based on trees. However, the trees of FT (called feature trees) are more general than the constructor trees of Herbrand, and the constraints of FT are of finer grain and of different expressiveness. The essential novelty of FT is provided by functional attributes called features which allow representing data as extensible records, a more flexible way than that offered by Herbrand’s fixed arity constructors. The feature tree structure determines an algebraic semantics for FT. We establish a logical semantics thanks to three axiom schemes presenting the first-order theory FT. We propose using FT as a constraint system for logic programming. We provide a test for constraint unsatisfiability, and a test for constraint entailment. The former corresponds to unification and the latter to matching. The combination of the two is needed for advanced control mechanisms. We use the concept of relative simplification of constraints, a normalization process that decides entailment and unsatisfiability simultaneously. The two major technical contributions of this work are: (1) an incremental system performing relative simplification for FT that we prove to be sound and complete; and (2) a proof showing that FT satisfies independence of negative constraints, the property that conjoined negative constraints may be handled independently.