On the Relationship Between Non-Horn Magic Sets and Relevancy Testing

Model-generation based theorem provers such as SATCHMO and MGTP suffer from a combinatorial explosion of the search space caused by clauses irrelevant to the goal (negative clause) to be solved. To avoid this, two typical methods have been proposed. One is relevancy testing implemented in SATCHMORE by Loveland et al., and the other is non-Horn magic sets that are the extension of Horn magic sets and used for MGTP. In this paper, we define the concept of weak relevancy testing, which somewhat relaxes the relevancy testing constraint. Then, we analyze the relationship between non-Horn magic sets and weak relevancy testing in detail, and prove that the total number of interpretations generated by MGTP employing non-Horn magic sets is always the same as that by SATCHMORE using weak relevancy testing. Thus, we find that non-Horn magic sets and weak relevancy testing, although they are completely different approaches, have the same power in pruning redundant branches of a proof tree.