A Note on the Completeness of Certain Refinements of Resolution
Résumé
Resolution and many refinements thereof have now been known for a long time. Completeness is usually proved by semantic means (e.g., semantic trees, Bachmair-Ganzinger forcing), or by syntactic tricks (Bledsoe's excess literal technique). The purpose of this paper is to note that there is a completely proof-theoretic way of proving completeness for several refinements of resolution, resembling Gentzen's method of cut-elimination. While this technique has a number of shortcomings compared to the semantic arguments cited above, it is valuable in that the completeness proofs for different refinements are the same. We have found this proof technique to be effective in teaching the ins and outs of refinements of resolution to masters level students. This can also be used to extract propositional proofs in one resolution format from resolution proofs in some other format automatically; in the first-order case, the same technique allows one to extract ordered resolution or hyperresolution proofs from proofs in any other resolution format mechanically.
Domaines
Logique en informatique [cs.LO]
Origine : Fichiers produits par l'(les) auteur(s)