# SATCHMOREBID: SATCHMO(RE) with BIDirectional relevancy

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## Abstract

SATCHMORE was introduced as a mechanism to integrate relevancy testing with the model-generation theorem prover SATCHMO. This made it possible to avoid invoking some clauses that appear in no refutation, which was a major drawback of the SATCHMO approach. SATCHMORE relevancy, however, is driven by the entire set of negative clauses and no distinction is accorded to the query negation. Under unfavorable circumstances, such as in the presence of large amounts of negative data, this can reduce the efficiency of SATCHMORE. In this paper we introduce a further refinement of SATCHMO called SATCHMOREBID: SATCHMORE with BIDirectional relevancy. SATCHMOREBID uses only the negation of the query for relevancy determination at the start. Other negative clauses are introduced on demand and only if a refutation is not possible using the current set of negative clauses. The search for the relevant negative clauses is performed in a forward chaining mode as opposed to relevancy propagation in SATCHMORE which is based on backward chaining. SATCHMOREBID is shown to be refutationally sound and complete. Experiments on a prototype SATCHMOREBID implementation point to its potential to enhance the efficiency of the query answering process in disjunctive databases.

## Keywords

Disjunctive Deductive Databases Query Answering Bidirectional Search Model Generation Theorem Proving Relevancy## Preview

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## References

- 1).Bancilhon, F., Sagiv, Y. and Ullman, J., “Magic Sets and Other Strange Ways to Implement Logic Programs,” in
*Proc. of the Fifth ACM SIGMOD-SIGART Symposium on Principles of Database Systems (PODS)*, pp. 1–15, 1986.Google Scholar - 2).Bry, F. and Yahya, A., “Minimal Model Generation with Positive Unit Hyper-Resolution tableaux,”
*Journal of Automated Reasoning, 25, 1*, pp. 35–82, 2000.MATHCrossRefMathSciNetGoogle Scholar - 3).Bry, F., “Query Evaluation in Recursive Databases: Bottom-up and Top-down Reconciled,”
*Data and Knowledge Engineering, 5*, pp. 289–312, 1990.CrossRefGoogle Scholar - 4).Chang, C. L. and Lee, K. C.,
*Symbolic Logic and Mechanical Theorem Proving*, Academic Press, New York, 1973.MATHGoogle Scholar - 5).Demolombe, R., “An Efficient Strategy for Non-horn Deductive Databases,”
*Theoretical Computer Science, 78*, pp. 245–259, 1991.MATHCrossRefMathSciNetGoogle Scholar - 6).Eiter, T. and Gottlob, G., “Complexity Aspects of Various Semantics for Disjunctive Databases,” in
*Proc. of the Twelfth ACM SIGACT SIGMOD-SIGART Symposium on Principles of Database Systems (PODS-93)*, pp. 158–167, 1993.Google Scholar - 7).Hasegawa, R., Inoue, K., Ohta, Y. and Koshimura, M., “Nonhorn Magic Sets to Incorporate Top-down Inference into Bottom-up Theorem Proving,” in
*Proc. of the seventeenth Conference on automated deduction (CADE097)*, pp. 176–190, 1997.Google Scholar - 8).He, L., “I-SATCHMO: An Improvement of SATCHMO,”
*Journal of Automated Reasoning, 27, 3*, pp. 313–322, 2001.MATHCrossRefMathSciNetGoogle Scholar - 9).He, L., “UNSEARCHMO: Eliminating Redundant Search Space on Backtracking for Forward Chaining Theorem Proving,” in
*Proc. of the International Joint Conference on Artificial Intelligence (IJCAI-2001)*, pp. 618–623, 2001.Google Scholar - 10).He, L., Chao, Y., Shimajiri, T., Seki, H. and Itoh, H., “A-SATCHMORE: SATCHMORE with Availability Checking,”
*New Generation Computing, 16, 1*, pp. 55–74, 1998.CrossRefGoogle Scholar - 11).He, L., Chao, Y., Nakamura, T. and Itoh, H., “An Improvement of Theorem Prover A-SATCHMORE,”
*Journal of the Japanese Society for Artificial Intelligence, 15, 6*, pp. 1125–1129, 2000.Google Scholar - 12).Johnson, C. A., “Top-down Deduction in Indefinite Deductive Databases,”
*Journees Bases de Donnees Avances*, pp. 119–138, 1993.Google Scholar - 13).Lloyd, J.,
*Foundations of Logic Programming*(2nd Ed.), Springer Verlag, 1987.Google Scholar - 14).Lobo, J., Minker, J. and Rajasekar, A.,
*Foundations of Disjunctive Logic Programming*, MIT Press, 1992.Google Scholar - 15).Loveland, D. W., “Near-Horn Prolog,” in
*Proc. of the 4th International Conference on Logic Programming*, MIT Press, pp. 456–469, 1987.Google Scholar - 16).Loveland, D. W., Reed, D. and Wilson, D., “SATCHMORE: SATCHMO with RElevancy,”
*Journal of Automated Reasoning, 14*, pp. 325–351, July 1995.MATHCrossRefMathSciNetGoogle Scholar - 17).Manthey, R. and Bry, F., “SATCHMO: a Theorem Prover Implemented in Prolog,” in
*Proc. of the 9*^{th}Conference on Automated DEduction (CADE-9), Springer Verlag, pp. 415–434, 1988.Google Scholar - 18).Ohta, Y., Inoue, K. and Hasegawa, R., “On the Relationship Between Non-Horn Magic Sets and Relevancy Testing,” in
*Proc. of the Fifteenth International Conference on Automated Deduction (CADE-15)*, Springer Verlag, pp. 333–348, 1998.Google Scholar - 19).Plaisted, D., “An Efficient Relevance Criterion for Mechanical Theorem Proving,”
*Proceedings of the First National Conference on Artificial Intelligence (AAAI-1980)*, pp. 79–83, 1980.Google Scholar - 20).Plaisted, D. and Yahya, A. “A Relevance Restriction Strategy for Automated Deduction,” in
*Artificial Intelligence, 144, 1–2*, pp. 59–93, 2003.Google Scholar - 21).Rajasekar, A. and Yusuf, H., “Dwam—A WAM Model Extension for Disjunctive Logic Programming,”
*Annals of Mathematics and Artificial Intelligence, 14*, pp. 275–308, 1995.CrossRefMathSciNetGoogle Scholar - 22).Ramakrishnan, R. and Sudarshan, S., “Top-down vs. Bottom-up Revisited,” in
*Proc. of the International Symposium on Logic Programming (ISLP’91)*, 1991.Google Scholar - 23).Ramsay, A., “Generating Relevant Models,”
*Journal of Automated Reasoning, 7*, pp. 359–368, 1991.MATHCrossRefMathSciNetGoogle Scholar - 24).Stickel, M., “Upside-down Meta-Interpretation of the Model Elimination Theorem Proving Procedure for Deduction and Abduction,”
*Journal of Automated Reasoning, 13, 3*, pp. 349–363, 1994.MathSciNetGoogle Scholar - 25).Yahya, A., “Duality for Goal-Driven Query Processing in Disjunctive Deductive Databases,”
*Journal of Automated Reasoning, 28, 1*, pp. 1–34, 2002.MATHCrossRefMathSciNetGoogle Scholar