Order-Sorted Congruence Closure

In this paper, an algorithm for testing the unsatisfiability of a set of ground order-sorted equational Horn clauses (for coherent signatures) is presented. This result follows from the fact that the concept of congruence closure extends to finite sets of ground order-sorted equational Horn clauses. We show how to compute the order-sorted congruence closure and obtain an algorithm running in O(η2)

HORNLOG: A graph-based interpreter for general Horn clauses

AbstractThis paper presents hornlog, a general Horn-clause proof procedure that can be used to interpret logic programs. The system is based on a form of graph rewriting, and on the linear-time algorithm for testing the unsatisfiability of propositional Horn formulae given by Dowling and Gallier [8]. hornlog applies to a class of logic programs which is a proper superset of the class of logic programs handled by PROLOG systems. In particular, negative Horn clauses used as assertions and queries consisting of disjunctions of negations of Horn clauses are allowed. This class of logic programs admits answers which are indefinite, in the sense that an answer can consist of a disjunction of substitutions. The method does not use the negation-by- failure semantics [6] in handling these extensions and appears to have an immediate parallel interpretation