Simultaneous Construction of Refutations and Models for Propositional Formulas

Methodology is developed to attempt to construct simultaneously either a refutation or a model for a propositional formula in conjunctive normal form. The method exploits the concept of \autarky", which was introduced by Monien and Speckenmeyer. Informally, an autarky is a \self-suucient" model for some clauses, but which does not aaect the remaining clauses of the formula. Whereas their work was oriented toward nding a model, our method has as its primary goal to nd a refutation in the style of model elimination. It also nds a model if it fails to nd a refutation, essentially by combining autarkies. However, the autarky-related processing is integrated with the refutation search, and can greatly improve the eeciency of that search even when a refutation does exist. Unlike the pruning strategies of most reenements of resolution, autarky-related pruning does not prune any successful refutation; it only prunes attempts that ultimately will be unsuccessful; consequently, it will not force the underlying search to nd an unnecessarily long refutation. A game characterization of refutation search is introduced, which demonstrates some symmetries in the search for a refutation and the search for a model. Limited experience with a prototype implementation is reported, and indicates the possibility of developing high-performance refutation methods that are competitive with recently reported model-searching methods. Considerations for rst-order refutation methods are discussed brieey.