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MGTP: A model generation theorem prover — Its advanced features and applications —

Invited Lectures

Part of the Lecture Notes in Computer Science book series (LNAI,volume 1227)

Abstract

This paper outlines a parallel model-generation based theorem-proving system MGTP that we have been developing, focusing on the recent developments including novel techniques for efficient proof-search and successful applications.

We have developed CMGTP (Constraint MGTP) to deal with constraint satisfaction problems. By attaining the constraint propagation with negative atoms, CMGTP makes it possible to reduce search spaces by orders of magnitude compared to the original MGTP.

To enhance the ability to prune search spaces, we have developed a new method called non-Horn magic sets (NHM) and incorporated its relevancy testing function into the folding-up (FU) method proposed by Letz. The NHM method suppresses useless model generation with clauses irrelevant to the goal. The FU method avoids generating duplicated subproofs after case-splitting. With these methods we can eliminate two major kinds of redundancies in model-generation based theorem provers. We have studied several applications in AI such as negation as failure, abductive reasoning and modal logic systems, through extensive use of MGTP. These studies share a basic common idea, that is, to use MGTP as a meta-programming system. We can build various reasoning systems on MGTP by writing the specific inference rules for each system in MGTP input clauses.

Furthermore, we are now working on other applications such as machine learning with MGTP and heuristic proof-search based on the genetic algorithm.

Keywords

  • Model Candidate
  • Theorem Prover
  • Constraint Satisfaction Problem
  • Horn Clause
  • Modal Formula

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. J. Akahani, K. Inoue, and R. Hasegawa. Bottom-Up Modal Theorem Proving Based on Modal Clause Transformation. J. IPS Japan, 36(4):822–831, April 1995. (in Japanese).

    Google Scholar 

  2. F. Bancilhon, D. Maier, Y. Sagiv, and J.D. Ullman. Magic sets and other strange ways to implement logic programs. In Proc. 5th ACM SIGMOD-SIGACT Symp. on Principles of Database Systems, pages 1–15, 1986.

    Google Scholar 

  3. F. Bennett. Quasigroup Identities and Mendelsohn Designs. Canadian Journal of Mathematics, 41:341–368, 1989.

    Google Scholar 

  4. F. Bry. Query evaluation in recursive databases: bottom-up and top-down reconciled. Data & Knowledge Engineering, 5:289–312, 1990.

    Google Scholar 

  5. M. Fitting. First-Order Modal Tableaux. In J. Automated Reasoning, volume 4, pages 191–213, 1988.

    Google Scholar 

  6. T. Fujise, T. Chikayama, K. Rokusawa, and A. Nakase. KLIC: A Portable Implementation of KL1. In Proc. Int. Symp. on Fifth Generation Computer Systems, December 1994.

    Google Scholar 

  7. H. Fujita, N. Yagi, T. Ozaki, and K. Furukawa. A New Design and Implementation of PROGOL by Bottom-up Computation. In Proc. of the 6th International Workshop on Inductive Logic Programming, 1996.

    Google Scholar 

  8. M. Fujita, J. Slaney, and F. Bennett. Automatic Generation of Some Results in Finite Algebra. In Proc. IJCAI-93, 1993.

    Google Scholar 

  9. R. Hasegawa and M. Koshimura. An AND Parallelization Method for MGTP and Its Evaluation. In Proc. First Int. Symp. on Parallel Symbolic Computation, pages 194–203, Linz, 1994.

    Google Scholar 

  10. R. Hasegawa, Y. Ohta, and K. Inoue. Non-Horn Magic Sets and Their Relation to Relevancy Testing. Technical Report 834, ICOT, 1993. Dagstuhl Seminor on Deduction in Germany, 1993 Workshop on Finite Domain Theorem Proving, 1994.

    Google Scholar 

  11. R. Hasegawa and Y. Shirai. Constraint Propagation of CP and CMGTP: Experiments on Quasigroup Problems. In Proc. Workshop 1C (Automated Reasoning in Algebra), CADE-12, Nancy, France, 1994.

    Google Scholar 

  12. K. Inoue, M. Koshimura, and R. Hasegawa. Embedding Negation as Failure into a Model Generation Theorem Prover. In Proc. 11th Int. Conf. on Automated Deduction, pages 400–415. Springer-Verlag, 1992. LNAI 607.

    Google Scholar 

  13. K. Inoue, Y. Ohta, R. Hasegawa, and M. Nakashima. Bottom-Up Abduction by Model Generation. In Proc. IJCAI-93, 1993. ICOT TR-816.

    Google Scholar 

  14. M. Koshimura and R. Hasegawa. Modal Propositional Tableaux in a Model Generation Theorem Prover. In Proc. Third Workshop on Theorem Proving with Analytic Tableaux and Related Methods, pages 145–151, UK, 1994. also in ICOT TR-860.

    Google Scholar 

  15. R. Letz, K. Mayr, and C. Goller. Controlled integration of the cut rule into connection tableau calculi. J. Automated Reasoning, 13:297–337, 1994.

    Google Scholar 

  16. D. W. Loveland, D. W. Reed, and D. S. Wilson. SATCHMORE: SATCHMO with RElevancy. Technical report, Department of Computer Science, Duke University, Durham, North Carolina, 1993. CS-1993-06.

    Google Scholar 

  17. R. Manthey and F. Bry. SATCHMO: a theorem prover implemented in Prolog. In Proc. 9th Int. Conf. on Automated Deduction, Argonne, Illinois, 1988.

    Google Scholar 

  18. W. W. McCune and L. Wos. Experiments in Automated Deduction with Condensed Detachment. In Proc. 11th Int. Conf. on Automated Deduction, pages 209–223, Saratoga Springs, NY, 1992.

    Google Scholar 

  19. S. Muggleton. Inverse Entailment and Progol. New Generation Computing, 13:245–286, 1995.

    Google Scholar 

  20. H. J. Ohlbach. A resolution calculus for modal logics. In Proc. 9th Int. Conf. on Automated Deduction, pages 500–516, 1988.

    Google Scholar 

  21. J. Rohmer, R. Lescoeur, and J.M. Kerisit. The alexander method — a technique for the processing of recursive axioms in deductive databases. New Generation Computing, 4:273–285, 1986.

    Google Scholar 

  22. Y. Shirai and R. Hasegawa. Two Approaches for Finite-Domain Constraint Satisfaction Problem — CP and MGTP-. In L. Sterling, editor, Proc. 12th Int. Conf. on Logic Programming, pages 249–263. MIT Press, June 1995. Tokyo.

    Google Scholar 

  23. G. Sutcliffe, C. Suttner, and T. Yemenis. The tptp problem library. In Proc. 12th Int. Conf. on Automated Deduction, pages 252–266, 1994.

    Google Scholar 

  24. K. Ueda and T. Chikayama. Design of the Kernel Language for the Parallel Inference Machine. Computer J., 33:494–555, December 1990.

    Google Scholar 

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© 1997 Springer-Verlag Berlin Heidelberg

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Hasegawa, R., Fujita, H., Koshimura, M. (1997). MGTP: A model generation theorem prover — Its advanced features and applications —. In: Galmiche, D. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 1997. Lecture Notes in Computer Science, vol 1227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0027401

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  • DOI: https://doi.org/10.1007/BFb0027401

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