Unification in commutative idempotent monoids
Theoretical Computer Science
ACM Transactions on Programming Languages and Systems (TOPLAS)
RTA '00 Proceedings of the 11th International Conference on Rewriting Techniques and Applications
Deriving Focused Calculi for Transitive Relations
RTA '01 Proceedings of the 12th International Conference on Rewriting Techniques and Applications
Str+ve-Subset: The Str+ve-based Subset Prover
Proceedings of the 10th International Conference on Automated Deduction
AMAST'06 Proceedings of the 11th international conference on Algebraic Methodology and Software Technology
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We derive rewrite-based ordered resolution calculi for semilattices,distributive lattices and boolean lattices. Using ordered resolution as a metaprocedure, theory axioms are first transformed into independent bases. Focused inference rules are then extracted from inference patterns in refutations. The derivation is guided by mathematical and procedural background knowledge, in particular by ordered chaining calculi for quasiorderings (forgetting the lattice structure), by ordered resolution (forgetting the clause structure) and by Knuth-Bendix completion for non-symmetric transitive relations (forgetting both structures). Conversely, all three calculi are derived and proven complete in a transparent and generic way as special cases of the lattice calculi.