Horn Clauses and Feature-Structure Logic: Principles and Unification Algorithms

The desirability of Horn clauses in logical deductive systems has long been recognized. The reasons are at least threefold. Firstly, while inference algorithms for full logics of any reasonable extent are typically intractable, for systems restricted to Horn clauses the picture is much better. (For example, in ordinary propositional logic, while the full satisfiability problem is NP-complete, a linear-time algorithm exists for Horn clauses.) Secondly, the knowledge-representation capabilities of Horn clauses, while weaker than those of the full logic, remain remarkably rich; indeed, far richer than that of simple conjunctive logic alone. Thirdly, Horn clauses define the maximal subset of a full logic which has the property of admitting generic models, which roughly means that for any set of Horn clauses, there is a least model of the clauses in that set. It is the purpose of this paper to initiate an investigation of Horn clause logic for an extended class of feature structures. After laying the groundwork for this context, we provide two key results. In the first, we show how the property of admitting generic models can be extended to feature structure logic, and demonstrate the importance of this property in generalizing the use of ordinary feature structures in unification-based formalisms. Our second contribution is a tractable unification algorithm for extended feature structures constrained by Horn clauses. This algorithm is an integration of the traditional unification algorithm for feature structures and the linear-time inference algorithm for propositional logic. †Current address: Department of Computer Science and Electrical Engineering, Votey Building, University of Vermont, Burlington, VT 05405, USA; Internet: [email protected].