The heuristics and experimental results of a new hyperparamodulation: HL-resolution

Abstract

Equality is an important relation and many theorems can be easily symbolized through it’s use. But it presents special strategic problems, both theoretical and practical, for theorem proving programs. A proposed inference rule in [6] called HL-resolution is intended to have the benefits of hyper steps while controlling the application of paramodulation. The rule is complete for E-unsatisfiable Horn sets. Here we try to find an efficient procedure for finding all k-pd links between two terms and try to find useful heuristics by making some experiments on ring theory. The linking 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-resolution is chosen in the search, potential linkages can be found and tested for compatibility efficiently by looking at the paths in the graph. Further we try to find heuristics to prevent redundant k-pd links from being used to generate HL-resolvents. The method has been implemented on an existing theorem- proving system. A number of experiments were conducted on problems in abstract algebra and a comparison with set-of-support paramodulation was made.