15-815 Automated Theorem Proving
Lecture 22: Indexing

We postpone further discussion of equality in order to introduce techniques for subsumption. Subsumption is extremely important in saturation based theorem provers in order to control the size of the data base of derived clauses (= sequents, in the intuitionistic case).

We present two basic techniques: discrimination trees (most suitable for unit forward subsumption) and path indexing (most suitable for backward subsumption). We also presents Tammet's hierarchical filters which provide an additional technique to perform subsumption checking.

[T98] Tanel Tammet.
Towards Efficient Subsumption.
Proceedings of the 15th International Conference on Automated Deduction, C.Kircher and H.Kirchner, eds., pp.427-441, Springer-Verlag LNAI 1421, 1998.
[RSV01] I.V. Ramakrishnan, R. Sekar, and Andrei Voronkov.
Term Indexing.
Handbook of Automated Reasoning, Vol.2, pp 1853-1965, Elsevier Science and MIT Press, 2001.

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