The management of heuristic search in boolean experiments with RUE resolution

• Authors: Vincent J. Digricoli
• Venue: IJCAI'85 Proceedings of the 9th international joint conference on Artificial intelligence - Volume 2
• Year: 1985

In assessing the power of a theorem prover, we should select a theorem difficult to prove, compare the quality of proof with the published work of mathematicians, and most important determine whether cpu time used to find the proof is economically acceptable. In this paper we apply the above criteria to RUE resolution, equality-based binary resolution which incorporates the axioms of equality into the definition of resolution. We select a theorem in Boolean algebra, show the published proof of George and Garret Birkhoff side by side with the computer deduced proof achieved in less than 30 seconds of cpu time. The proof is quite long requiring the derivation of four lemmas and is proven by two RUE refutations of 16 and 18 steps respectively. The same refutations with the equality axioms and unification resolution are 38 and more than 40 steps. Hence, the power of RUE resolution is shown by the brevity of proof compared to using the equality axioms. The primary pragmatic issue in theorem proving is the effective management of heuristic search to find proofs in acceptable computer time. Whether an inference system supports or obstructs this objective is a crucial property and in this paper we explain in detail the heuristics applied to find proofs. These heuristics are RUE specific and dependent, and cannot be applied in the context of unification resolution.