Canonical sets of Horn clauses
Proceedings of the 18th international colloquium on Automata, languages and programming
Handbook of theoretical computer science (vol. B)
Journal of the ACM (JACM)
Equational inference, canonical proofs, and proof orderings
Journal of the ACM (JACM)
Theorem proving with ordering and equality constrained clauses
Journal of Symbolic Computation
Information and Computation
Oriented equational logic programming is complete
Journal of Symbolic Computation
Decidability and complexity analysis by basic paramodulation
Information and Computation
Proving termination with multiset orderings
Communications of the ACM
Journal of Automated Reasoning
Complexity Analysis Based on Ordered Resolution
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Paramodulation with Non-Monotonic Orderings
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
On arbitrary selection strategies for basic superposition
JELIA'06 Proceedings of the 10th European conference on Logics in Artificial Intelligence
Regular derivations in basic superposition-based calculi
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
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A crucial way for reducing the search space in automated deduction are the so-called selection strategies: in each clause, the subset of selected literals are the only ones involved in inferences. For first-order Horn clauses without equality, resolution is complete with an arbitrary selection of one single literal in each clause [dN96]. For Horn clauses with built-in equality, i.e., paramodulation-based inference systems, the situation is far more complex. Here we show that if a paramodulation-based inference system is complete with eager selection of negative equations and, moreover, it is compatible with equality constraint inheritance, then it is complete with arbitrary selection strategies. A first important application of this result is the one for paramodulation wrt. non-monotonic orderings, which was left open in [BGNR99].