Substitution tree indexing

Abstract

Sophisticated maintenance and retrieval of first-order predicate calculus terms is a major key to efficient automated reasoning. We present a new indexing technique, which accelerates the speed of the basic retrieval operations such as finding complementary literals in resolution theorem proving or finding critical pairs during completion. Subsumption and reduction are also supported. Moreover, the new technique not only provides maintenance and efficient retrieval of terms but also of idem-potent substitutions. Substitution trees achieve maximal search speed paired with minimal memory requirements in various experiments and outperform traditional techniques such as path indexing, discrimination tree indexing, and abstraction trees by combining their advantages and adding some new features.