Completeness of Pruning Methods for Consequence Finding Procedure Sol ?

In this paper, we study the completeness of several types of pruning methods for the logical consequence nding procedure SOL-resolution. The consequence nd-ing problem is a generalization of the refutation nding problem. The SOL-resolution is a Model-Elimination-like calculus with Skip operation, and is one of the most signiicant calculi for consequence nding. The concept \completeness" of consequence-nding cal-culi diiers from the one of refutation nding calculi, hence the pruning methods that are complete for refutation nding tasks may not be complete for consequence nding problems. In this paper, we rst reformulate SOL-resolution within connection tableaux and properly strengthen one of structural conditions, the regularity for skipped literals, which reduces a great amount of the redundancies in the search space. Next we investigate various types of pruning methods, such as order-preserving reduction, lemma matching, merge, unit subsumption, etc, and show the completeness theorems of each pruning method for consequence nding. Finally we show Skip operation itself has a signiicantly important future as a new local failure pruning method in consequence nding.