Using matings for pruning connection tableaux

Abstract

Tableau calculi and the connection method are generally considered as related paradigms in automated deduction. However, in their essence, the frameworks are based on different concepts, and there is a large potential for cross-fertilization which is by far not exploited. In this paper, we demonstrate how the matings concept, which is central to the connection method framework, can be used to identify significant redundancies in the search for connection tableau proofs. The redundancies we discuss arise from the fact that different tableaux may encode the same mating. We concentrate on certain permutations of connection tableaux that occur when so-called reduction steps are performed in the tableau construction. Those permutations can be avoided without having to store the corresponding matings, which would be expensive. Instead the input formula is augmented with a literal ordering which is used in the connection tableau calculus to prune certain reduction steps. With this technique a significant reduction of the search space for almost every non-Horn formula can be achieved. Furthermore, the method can be implemented very easily and has almost no run-time overhead.