A New Hyperparamodulation Strategy for the Equality Relation

Equality is an Important re lat ion and many theorems can be easily symbolized through i t ' s use. A proposed Inference rule called HL-resolution Is intended to have the benefits of hyper steps while control l ing the application of paramodulation. It generates a resolvent by building a paramodulation and demodulation l ink between two terms using a pre pro ceased plan as a guide. The rule Is complete for E-unsatisfiable Horn sets. The l ink ing process makes use of an equality graph which is constructed once at the beginning of the run. Once a pair of candidate terms for HL-resolutlon is chosen in the search, potential linkages can be found and tested for compatibil i ty e f f i c ien t l y by looking at the paths in the graph. The method was implemented on an exist ing theorem-proving system. A number of experiments were conducted on problems in abstract algebra and a comparison with set-of-support paramodulation was made.