Existence, uniqueness, and construction of rewrite systems
SIAM Journal on Computing
Handbook of theoretical computer science (vol. B)
On rewrite programs: semantics and relationship with Prolog
Journal of Logic Programming
Equational inference, canonical proofs, and proof orderings
Journal of the ACM (JACM)
Towards a foundation of completion procedures as semidecision procedures
Theoretical Computer Science
Exact Kanowledge Compilation in Predicate Calculus: The Partial Achievement Case
CADE-14 Proceedings of the 14th International Conference on Automated Deduction
ACM Transactions on Computational Logic (TOCL)
Searching while keeping a trace: the evolution from satisfiability to knowledge compilation
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
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Completionis a general paradigm for applying inferences to generate a canonical presentation of a logical theory, or to semi-decide the validity of theorems, or to answer queries. We investigate what canonicitymeans for implicational systemsthat are axiomatizations of Moore families--- or, equivalently, of propositional Horn theories. We build a correspondence between implicational systems and associative-commutative rewrite systems, give deduction mechanisms for both, and show how their respective inferences correspond. Thus, we exhibit completion procedures designed to generate canonical systems that are "optimal" for forward chaining, to compute minimal models, and to generate canonical systems that are rewrite-optimal. Rewrite-optimality is a new notion of "optimality" for implicational systems, one that takes contraction by simplification into account.