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Stratified Resolution
, 2001
"... We introduce a calculus of stratified resolution, in which special attention is paid to clauses that "define" relations. If such clauses are discovered in the initial set of clauses, they are treated using the rule of definition unfolding, i.e. the rule that replaces defined relations by t ..."
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We introduce a calculus of stratified resolution, in which special attention is paid to clauses that "define" relations. If such clauses are discovered in the initial set of clauses, they are treated using the rule of definition unfolding, i.e. the rule that replaces defined relations by their definitions. Stratified resolution comes with a powerful notion of redundancy: a clause to which definition unfolding has been applied can be removed from the search space. To prove the completeness of stratified resolution with redundancies, we use a novel combination of Bachmair and Ganzinger's model construction technique and a hierarchical construction of orderings and least fixpoints.
Regular Derivations in Basic SuperpositionBased Calculi
"... Abstract. We prove the completeness of the regular strategy of derivations for superpositionbased calculi. The regular strategy was pioneered by Kanger in [Kan63], who proposed that all equality inferences take place before all other steps in the proof. We show that the strategy is complete with th ..."
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Abstract. We prove the completeness of the regular strategy of derivations for superpositionbased calculi. The regular strategy was pioneered by Kanger in [Kan63], who proposed that all equality inferences take place before all other steps in the proof. We show that the strategy is complete with the elimination of tautologies. The implication of our result is the completeness of nonstandard selection functions by which in nonrelational clauses only equality literals (and all of them) are selected. 1