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Abstract

This article addresses the problem of maintaining and retrieving first-order
predicate calculus terms in context of automatic reasoning. A new indexing
technique that accelerates the speed of the basic retrieval operations, such as
finding complementary literals in resolution theorem proving or finding
critical pairs during completion is presented. Subsumption and reduction are
also supported. Moreover, the new index not only provides maintenance and
efficient retrieval of terms but also of idempotent 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.