Skip to main content
SpringerLink
Log in

A Model Generation Based Theorem Prover MGTP for First-Order Logic

  • Chapter
  • First Online:
Computational Logic: Logic Programming and Beyond

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2408))

Abstract

This paper describes the major results on research and development of a model generation theorem prover MGTP. It exploits OR parallelism for non-Horn problems and AND parallelism for Horn problems achieving more than a 200-fold speedup on a parallel inference machine PIM with 256 processing elements. With MGTP, we succeeded in proving difficult mathematical problems that cannot be proven on sequential systems, including several open problems in finite algebra.

To enhance the pruning ability of MGTP, several new features are added to it. These include: CMGTP and IV-MGTP to deal with constraint satisfaction problems, enabling negative and interval constraint propagation, respectively, non-Horn magic set to suppress the generation of useless model candidates caused by irrelevant clauses, a proof simplification method to eliminate duplicated subproofs, and MM-MGTP for minimal model generation.

We studied several techniques necessary for the development of applications, such as negation as failure, abductive reasoning and modal logic systems, on MGTP. These techniques share a basic idea, which is to use MGTP as a meta-programming system for each application.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Franz Baader and Bernhard Hollunder. How to prefer more specific defaults in terminological default logic. In Proc. International Joint Conference on Artificial Intelligence, pages 669–674, 1993.

    Google Scholar 

  2. Peter Baumgartner, Ulrich Furbach, and Ilkka Niemelä. Hyper Tableaux. In José Júlio Alferes, Luís Moniz Pereira, and Ewa OrJlowska, editors, Proc. European Workshop: Logics in Artificial Intelligence, JELIA, volume 1126 of Lecture Notes in Artificial Intelligence, pages 1–17. Springer-Verlag, 1996.

    Google Scholar 

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

    Google Scholar 

  4. Gerhard Brewka. Preferred subtheories: An extended logical framework for default reasoning. In Proc. International Joint Conference on Artificial Intelligence, pages 1043–1048, Detroit, MI,USA, 1989.

    Google Scholar 

  5. Gerhard Brewka. Adding priorities and specificity to default logic. In Proc. JELIA 94, pages 247–260, 1994.

    Google Scholar 

  6. Gerhard Brewka. Reasoning about priorities in default logic. In Proc. AAAI 94, pages 940–945, 1994.

    Google Scholar 

  7. Gerhard Brewka. Well-founded semantics for extended logic programs with dynamic preference. Journal of Artificial Intelligence Research, 4:19–36, 1996.

    MATH  MathSciNet  Google Scholar 

  8. Gerhard Brewka and Thomas F. Gordon. How to Buy a Porsche: An Approach to defeasible decision making. In Proc. AAA94 workshop on Computational Dialectics, 1994.

    Google Scholar 

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

    Article  Google Scholar 

  10. François Bry and Adnan Yahya. Minimal Model Generation with Positive Unit Hyper-Resolution Tableaux. In Proc. 5th International Workshop, TABLEAUX’96, volume 1071 of Lecture Notes in Artificial Intelligence, pages 143–159, Terrasini, Palermo, Italy, May 1996. Springer-Verlag.

    Google Scholar 

  11. Hiroshi Fujita and Ryuzo Hasegawa. A Model-Generation Theorem Prover in KL1 Using Ramified Stack Algorithm. In Proc. 8th International Conference on Logic Programming, pages 535–548. The MIT Press, 1991.

    Google Scholar 

  12. Masayuki Fujita, Ryuzo Hasegawa, Miyuki Koshimura, and Hiroshi Fujita. Model Generation Theorem Provers on a Parallel Inference Machine. In Proc. International Conference on Fifth Generation Computer Systems, volume 1, pages 357–375, Tokyo, Japan, June 1992.

    Google Scholar 

  13. Masayuki Fujita, John Slaney, and Frank Bennett. Automatic Generation of Some Results in Finite Algebra. In Proc. International Joint Conference on Artificial Intelligence, 1993.

    Google Scholar 

  14. Tetsuro Fujita, Takashi Chikayama, Kazuaki Rokuwasa, and Akihiko Nakase. KLIC: A Portable Implementation of KL1. In Proc. International Conference on Fifth Generation Computer Systems, pages 66–79, Tokyo, Japan, December 1994.

    Google Scholar 

  15. Michael Gelfond and Vladimir Lifschitz. The Stable Model Semantics for Logic Programming. In Proc. 5th International Conference and Symposium on Logic Programming, pages 1070–1080. MIT Press, 1988.

    Google Scholar 

  16. Michael Gelfond and Vladimir Lifschitz. Classical Negation in Logic Programs and Disjunctive Databases. New Generation Computing, 9:365–385, 1991.

    Article  Google Scholar 

  17. Benjamin Grosof. Generalization Prioritization. In Proc. 2nd Conference on Knowledge Representation and Reasoning, pages 289–300, 1991.

    Google Scholar 

  18. Reiner Hähnle. Tableaux and related methods. In Alan Robinson and Andrei Voronkov, editors, Handbook of Automated Reasoning, volume I. North-Holland, 2001.

    Google Scholar 

  19. Reiner Hähnle, Ryuzo Hasegawa, and Yasuyuki Shirai. Model Generation Theorem Proving with Finite Interval Constraints. In Proc. First International Conference on Computational Logic (CL2000), 2000.

    Google Scholar 

  20. Ryuzo Hasegawa and Hiroshi Fujita. Implementing a Model-Generation Based Theorem Prover MGTP in Java. Research Reports on Information Science and Electrical Engineering, 3(1):63–68, 1998.

    Google Scholar 

  21. Ryuzo Hasegawa and Hiroshi Fujita. A new Implementation Technique for a Model-Generation Theorem Prover to Solve Constraint Satisfaction Problems. Research Reports on Information Science and Electrical Engineering, 4(1):57–62, 1999.

    Google Scholar 

  22. Ryuzo Hasegawa, Hiroshi Fujita, and Miyuki Koshimura. MGTP: A Parallel Theorem-Proving System Based on Model Generation. In Proc. 11th International Conference on Applications of Prolog, pages 34–41, Tokyo, Japan, September 1998.

    Google Scholar 

  23. Ryuzo Hasegawa, Hiroshi Fujita, and Miyuki Koshimura. Efficient Minimal Model Generation Using Branching Lemmas. In Proc. 17th International Conference on Automated Deduction, volume 1831 of Lecture Notes in Artificial Intelligence, pages 184–199, Pittsburgh, Pennsylvania, USA, June 2000. Springer-Verlag.

    Google Scholar 

  24. Ryuzo Hasegawa, Katsumi Inoue, Yoshihiko Ohta, and Miyuki Koshimura. Non-Horn Magic Sets to Incorporate Top-down Inference into Bottom-up Theorem Proving. In Proc. 14th International Conference on Automated Deduction, volume 1249 of Lecture Notes in Artificial Intelligence, pages 176–190, Townsville, North Queensland, Australia, July 1997. Springer-Verlag.

    Google Scholar 

  25. Ryuzo Hasegawa and Miyuki Koshimura. An AND Parallelization Method for MGTP and Its Evaluation. In Proc. First International Symposium on Parallel Symbolic Computation, Lecture Notes Series on Computing, pages 194–203. World Scientific, September 1994.

    Google Scholar 

  26. Ryuzo Hasegawa, Miyuki Koshimura, and Hiroshi Fujita. Lazy Model Generation for Improving the Efficiency of Forward Reasoning Theorem Provers. In Proc. International Workshop on Automated Reasoning, pages 221–238, Beijing, China, July 1992.

    Google Scholar 

  27. Ryuzo Hasegawa, Katsumi Nitta, and Yasuyuki Shirai. The Development of an Argumentation Support System Using Theorem Proving Technologies. In Research Report on Advanced Software Enrichment Program 1997, pages 59–66. Information Promotion Agency, Japan, 1999. (in Japanese).

    Google Scholar 

  28. Ryuzo Hasegawa and Yasuyuki 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 

  29. Katsumi Inoue, Miyuki Koshimura, and Ryuzo Hasegawa. Embedding Negation as Failure into a Model Generation Theorem Prover. In Proc. 11th International Conference on Automated Deduction, volume 607 of Lecture Notes in Artificial Intelligence, pages 400–415, Saratoga Springs, NY, USA, 1992. Springer-Verlag.

    Google Scholar 

  30. Katsumi Inoue, Yoshihiko Ohta, Ryuzo Hasegawa, and Makoto Nakashima. Bottom-Up Abduction by Model Generation. In Proc. International Joint Conference on Artificial Intelligence, pages 102–108, 1993.

    Google Scholar 

  31. Miyuki Koshimura and Ryuzo Hasegawa. Modal Propositional Tableaux in a Model Generation Theorem Prover. In Proc. 3rd Workshop on Theorem Proving with Analytic Tableaux and Related Methods, pages 145–151, May 1994.

    Google Scholar 

  32. Miyuki Koshimura and Ryuzo Hasegawa. Proof Simplification for Model Generation and Its Applications. In Proc. 7th International Conference, LPAR 2000, volume 1955 of Lecture Notes in Artificial Intelligence, pages 96–113. Springer-Verlag, November 2000.

    Google Scholar 

  33. Robert A. Kowalski and Francesca Toni. Abstract Argumentation. Artificial Intelligence and Law Journal, 4:275–296, 1996.

    Article  Google Scholar 

  34. Reinhold Letz, Klaus Mayr, and Christoph Goller. Controlled Integration of the Cut Rule into Connection Tableau Calculi. Journal of Automated Reasoning, 13:297–337, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  35. Vladimir Lifschitz. Computing Circumscription. In Proc. International Joint Conference on Artificial Intelligence, pages 121–127, Los Angeles, CA, USA, 1985.

    Google Scholar 

  36. Donald W. Loveland, David W. Reed, and Debra S. Wilson. Satchmore: Satchmo with RElevancy. Journal of Automated Reasoning, 14(2):325–351, April 1995.

    Google Scholar 

  37. James J. Lu. Logic Programming with Signs and Annotations. Journal of Logic and Computation, 6(6):755–778, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  38. Rainer Manthey and Francoois Bry. SATCHMO: a theorem prover implemented in Prolog. In Proc. 9th International Conference on Automated Deduction, volume 310 of Lecture Notes in Computer Science, pages 415–434, Argonne, Illinois, USA, May 1988. Springer-Verlag.

    Chapter  Google Scholar 

  39. William McCune and Larry Wos. Experiments in Automated Deduction with Condensed Detachment. In Proc. 11th International Conference on Automated Deduction, volume 607 of Lecture Notes in Artificial Intelligence, pages 209–223, Saratoga Springs, NY, USA, 1992. Springer-Verlag.

    Google Scholar 

  40. Jack Minker. On indefinite databases and the closed world assumption. In Proc. 6th International Conference on Automated Deduction, volume 138 of Lecture Notes in Computer Science, pages 292–308, Courant Institute, USA, 1982. Springer-Verlag.

    Chapter  Google Scholar 

  41. Ugo Montanari and Francesca Rossi. Finite Domain Constraint Solving and Constraint Logic Programming. In Constraint Logic Programming: Selected Research, pages 201–221. The MIT press, 1993.

    Google Scholar 

  42. Hiroshi Nakashima, Katsuto Nakajima, Seiichi Kondo, Yasutaka Takeda, Yū Ina-mura, Satoshi Onishi, and Kanae Matsuda. Architecture and Implementation of PIM/m. In Proc. International Conference on Fifth Generation Computer Systems, volume 1, pages 425–435, Tokyo, Japan, June 1992.

    Google Scholar 

  43. Ilkka Niemelä. A Tableau Calculus for Minimal Model Reasoning. In Proc. 5th International Workshop, TABLEAUX’96, volume 1071 of Lecture Notes in Artificial Intelligence, pages 278–294, Terrasini, Palermo, Italy, May 1996. Springer-Verlag.

    Google Scholar 

  44. Katsumi Nitta, Yoshihisa Ohtake, Shigeru Maeda, Masayuki Ono, Hiroshi Ohsaki, and Kiyokazu Sakane. HELIC-II: A Legal Reasoning System on the Parallel Inference Machine. In Proc. International Conference on Fifth Generation Computer Systems, volume 2, pages 1115–1124, Tokyo, Japan, June 1992.

    Google Scholar 

  45. Yoshihiko Ohta, Katsumi Inoue, and Ryuzo Hasegawa. On the Relationship Between Non-Horn Magic Sets and Relevancy Testing. In Proc. 15th International Conference on Automated Deduction, volume 1421 of Lecture Notes in Artificial Intelligence, pages 333–349, Lindau, Germany, July 1998. Springer-Verlag.

    Google Scholar 

  46. Franz Oppacher and E. Suen. HARP: A Tableau-Based Theorem Prover. Journal of Automated Reasoning, 4:69–100, 1988.

    Article  MathSciNet  Google Scholar 

  47. Henry Prakken and Giovanni Sartor. Argument-based Extended Logic Programming with Defeasible Priorities. Journal of Applied Non-Classical Logics, 7:25–75, 1997.

    MATH  MathSciNet  Google Scholar 

  48. Chiaki Sakama and Katsumi Inoue. Representing Priorities in Logic Programs. In Proc. International Conference and Symposium on Logic Programming, pages 82–96, 1996.

    Google Scholar 

  49. Heribert Schütz and Tim Geisler. Efficient Model Generation through Compilation. In Proc. 13th International Conference on Automated Deduction, volume 1104 of Lecture Notes in Artificial Intelligence, pages 433–447. Springer-Verlag, 1996.

    Google Scholar 

  50. Yasuyuki Shirai and Ryuzo Hasegawa. Two Approaches for Finite-domain Constraint Satisfaction Problem-CP and MGTP-. In Proc. 12th International Conference on Logic Programming, pages 249–263. MIT Press, 1995.

    Google Scholar 

  51. Mark Stickel. The Path-Indexing Method For Indexing Terms. Technical Note 473, AI Center, SRI, 1989.

    Google Scholar 

  52. Mark E. Stickel. Upside-Down Meta-Interpretation of the Model Elimination Theorem-Proving Procedure for Deduction and Abduction. Journal of Automated Reasoning, 13(2):189–210, October 1994.

    Google Scholar 

  53. Geoff Sutcliffe, Christian Suttner, and Theodor Yemenis. The TPTP Problem Library. In Proc. 12th International Conference on Automated Deduction, volume 814 of Lecture Notes in Artificial Intelligence, pages 252–266, Nancy, France, 1994. Springer-Verlag.

    Google Scholar 

  54. Evan Tick and Miyuki Koshimura. Static Mode Analyses of Concurrent Logic Programs. Journal of Programming Languages, 2:283–312, 1994.

    Google Scholar 

  55. Kazunori Ueda and Takashi Chikayama. Design of the Kernel Language for the Parallel Inference Machine. Computer Journal, 33:494–500, December 1990.

    Google Scholar 

  56. Debra S. Wilson and Donald W. Loveland. Incorporating Relevancy Testing in SATCHMO. Technical Reports CS-1989-24, Department of Computer Science, Duke University, Durham, North Carolina, USA, 1989.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate School of Information Science and Electrical Engineering, Kyushu University, 6-1, Kasuga-koen, Kasuga, Fukuoka, 816-8580, Japan

    Ryuzo Hasegawa, Hiroshi Fujita, Miyuki Koshimura & Yasuyuki Shirai

Authors
  1. Ryuzo Hasegawa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hiroshi Fujita
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Miyuki Koshimura
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yasuyuki Shirai
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Cyprus, 75 Kallipoleos St., 1678, Nicosia, Cyprus

    Antonis C. Kakas

  2. Department of Computing, Imperial College of Science, Technology and Medicine, 180 Queen’s Gate, London, SW7 2BZ, UK

    Fariba Sadri

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Hasegawa, R., Fujita, H., Koshimura, M., Shirai, Y. (2002). A Model Generation Based Theorem Prover MGTP for First-Order Logic. In: Kakas, A.C., Sadri, F. (eds) Computational Logic: Logic Programming and Beyond. Lecture Notes in Computer Science(), vol 2408. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45632-5_8

Download citation

  • DOI: https://doi.org/10.1007/3-540-45632-5_8

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43960-8

  • Online ISBN: 978-3-540-45632-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation