Experiments with discrimination-tree indexing and path indexing for term retrieval

This article addresses the problem of indexing and retrieving first-order predicate calculus terms in the context of automated deduction programs. The four retrieval operations of concern are to find variants, generalizations, instances, and terms that unify with a given term. Discrimination-tree indexing is reviewed, and several variations are presented. The path-indexing method is also reviewed. Experiments were conducted on large sets of terms to determine how the properties of the terms affect the performance of the two indexing methods. Results of the experiments are presented.

[1]  Ross A. Overbeek,et al.  Formula databases for high-performance resolution/paramodulation systems , 2004, Journal of Automated Reasoning.

[2]  Ross A. Overbeek,et al.  Complexity and related enhancements for automated theorem-proving programs , 1976 .

[3]  Jim Christian,et al.  Flatterms, discrimination nets, and fast term rewriting , 1993, Journal of Automated Reasoning.

[4]  Jim Christian,et al.  Fast Knuth-Bendix Completion: Summary , 1989, International Conference on Rewriting Techniques and Applications.

[5]  Kotagiri Ramamohanarao,et al.  A Superimposed Codeword Indexing Scheme for Very Large Prolog Databases , 1986, ICLP.

[6]  William McCune,et al.  Logic Machine Architecture: Kernel Funtions , 1982, CADE.

[7]  Mark E. Stickel The Path-Indexing Method for Indexing Terms , 1989 .

[8]  William McCune,et al.  Paths to High-Performance Automated Theorem Proving , 1986, CADE.

[9]  Lawrence J. Henschen,et al.  An Improved Filter for Literal Indexing in Resolution Systems , 1981, IJCAI.

[10]  Eugene Charniak,et al.  Artificial Intelligence Programming , 1987 .

[11]  Carl Hewitt,et al.  Description and Theoretical Analysis (Using Schemata) of Planner: A Language for Proving Theorems and Manipulating Models in a Robot , 1972 .

[12]  Dallas Lankford,et al.  High-performance permutative completion , 1989 .

[13]  Ewing L. Lusk,et al.  Data Structures and Control Architectures for Implementation of Theorem-Proving Programs , 1980, CADE.

[14]  Ewing L. Lusk,et al.  Parallelizing the Closure Computation in Automated Deduction , 1990, CADE.

[15]  Ross A. Overbeek A New Class of Automated Theorem-Proving Algorithms , 1974, JACM.

[16]  David M. W. Powers,et al.  Indexing Prolog Clauses via Superimposed Code Words and Filed Encoded Words , 1984, SLP.

[17]  William McCune,et al.  OTTER 1.0 Users' Guide , 1990 .

[18]  S Winker Absorption and idempotency criteria for a problem in near-Boolean algebras , 1992 .

[19]  Steven Greenbaum Input transformations and resolution implementation techniques for theorem proving in first-order logic (clause form, discrimination networks, heuristic search, locking resolution) , 1986 .

[20]  R. Overbeek,et al.  A tutorial on the construction of high-performance resolution/paramodulation systems , 1990 .