Rigid Hypertableaux

This paper extends a calculus for rst-order logic that combines the inference mechanism of hyperresolution with the more informative structure of analytic tableaux and that has been introduced as hyper tableaux by Baumgartner et al. (1996). This clausal tableau calculus is proof connuent, but suuers from the need of partial ground instantia-tions. I will develop an improvement of hyper tableaux which avoids this by using full uniication with rigid variables, but keeps desirable features like proof connuence and a partially universal treatment of variables in a clausal tableau. The resulting calculus can be seen as a reened hyper-resolution calculus that deals properly with an arbitrary literal selection function without loss of completeness. For this calculus, I have implemented and evaluated a proof procedure which takes advantage of proof connuence and addresses the fairness problem of tableau caluli with a redundancy criterion based upon literal subsumption.