Fast algorithms for testing unsatisfiability of ground horn clauses with equations

Authors:
Jean H. Gallier
Affiliations:
Department of Computer and Information Science, University of Pennsylvania, Philadelphia, PA 19104, U.S.A.
Venue:
Journal of Symbolic Computation
Year:
1987

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Abstract

This paper presents two fast algorithms for testing the unsatisfiability of a set of ground Horn clauses with or without equational atomic formulae. If the length of the set H of Horn clauses (viewed as the string obtained by concatenating the clauses in H) is n, it is possible to design an algorithm running in time O(n log(n)). These algorithms are obtained by generalising the concept of congruence closure to ground Horn clauses. The basic idea behind these algorithms is that the congruence closure induced by a set of ground Horn clauses can be obtained by interleaving steps in which an equational congruence closure is computed, and steps in which an implicational type of closure is computed.