Efficient Computation of Solutions for Contradictory Time Interval Networks

The model elimination calculus is a linear, refutationally complete calculus for first order clause logic. We show how to extend this calculus with aframeworkfor theory reasoning. Theory reasoning m~ans to separate the knowledge of a given domain or theory and treat it by special purpose inference rules. We present two versions of theory model elimination: the one is called total theory model elimination (which allows e.g. to treat equality in a rigid E-resolution style), and the other is called partial theory model elimination (which allows e.g. to treat equality in a paramodulation style).