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leanCoP 2.0 and ileanCoP 1.2: High Performance Lean Theorem Proving in Classical and Intuitionistic Logic (System Descriptions)

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Automated Reasoning (IJCAR 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5195))

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Abstract

leanCoP is a very compact theorem prover for classical first-order logic, based on the connection (tableau) calculus and implemented in Prolog. leanCoP 2.0 enhances leanCoP 1.0 by adding regularity, lemmata, and a technique for restricting backtracking. It also provides a definitional translation into clausal form and integrates “Prolog technology” into a lean theorem prover. ileanCoP is a compact theorem prover for intuitionistic first-order logic and based on the clausal connection calculus for intuitionistic logic. leanCoP 2.0 extends the classical prover leanCoP 2.0 by adding prefixes and a prefix unification algorithm. We present details of both implementations and evaluate their performance.

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References

  1. Astrachan, O., Loveland, D.: METEORs: High Performance Theorem Provers Using Model Elimination. In: Bledsoe, W.W., Boyer, S. (eds.) Automated Reasoning: Essays in Honor of Woody Bledsoe, pp. 31–60. Kluwer, Amsterdam (1991)

    Google Scholar 

  2. Beckert, B., Posegga, J.: lean TA P: Lean Tableau-Based Theorem Proving. In: Bundy, A. (ed.) CADE 1994. LNCS, vol. 814, pp. 793–797. Springer, Heidelberg (1994)

    Google Scholar 

  3. Bibel, W.: Matings in Matrices. Commun. ACM 26, 844–852 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bibel, W.: Automated Theorem Proving. Vieweg, Wiesbaden (1987)

    Google Scholar 

  5. Bibel, W., Brüning, S., Egly, U., Rath, T.: KoMeT. In: Bundy, A. (ed.) CADE 1994. LNCS, vol. 814, pp. 783–787. Springer, Heidelberg (1994)

    Google Scholar 

  6. Kreitz, C., Otten, J.: Connection-based Theorem Proving in Classical and Non-classical Logics. Journal of Universal Computer Science 5, 88–112 (1999)

    MATH  MathSciNet  Google Scholar 

  7. Letz, R., Schumann, J., Bayerl, S., Bibel, W.: SETHEO: A High-Performance Theorem Prover. Journal of Automated Reasoning 8, 183–212 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  8. Letz, R., Mayr, K., Goller, C.: Controlled Integration of the Cut Rule into Connection Tableaux Calculi. Journal of Automated Reasoning 13, 297–337 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  9. Letz, R., Stenz, G.: Model Elimination and Connection Tableau Procedures. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, pp. 2015–2114. Elsevier, Amsterdam (2001)

    Chapter  Google Scholar 

  10. Loveland, D.: Mechanical Theorem-Proving by Model Elimination. Journal of the ACM 15, 236–251 (1968)

    Article  MATH  MathSciNet  Google Scholar 

  11. McCune, W.: Otter 3.0 Reference Manual and Guide. Technical report ANL-94/6, Argonne National Laboratory (1994)

    Google Scholar 

  12. McCune, W.: Release of Prover9. In: Mile High Conference on Quasigroups, Loops and Nonassociative Systems, Technical report, Denver (2005)

    Google Scholar 

  13. Otten, J.: ileanT AP: An Intuitionistic Theorem Prover. In: Galmiche, D. (ed.) TABLEAUX 1997. LNCS, vol. 1227, pp. 307–312. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  14. Otten, J.: Clausal Connection-Based Theorem Proving in Intuitionistic First-Order Logic. In: Beckert, B. (ed.) TABLEAUX 2005. LNCS (LNAI), vol. 3702, pp. 245–261. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  15. Otten, J.: Restricting Backtracking in Connection Calculi. Technical report, Institut für Informatik, University of Potsdam (2008)

    Google Scholar 

  16. Otten, J., Bibel, W.: leanCoP: Lean Connection-based Theorem Proving. Journal of Symbolic Computation 36, 139–161 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  17. Otten, J., Kreitz, C.: T-String-Unification: Unifying Prefixes in Non-classical Proof Methods. In: Miglioli, P., Moscato, U., Ornaghi, M., Mundici, D. (eds.) TABLEAUX 1996. LNCS, vol. 1071, pp. 244–260. Springer, Heidelberg (1996)

    Google Scholar 

  18. Raths, T., Otten, J.: randoCoP: Randomizing the Proof Search Order in the Connection Calculus. Technical report, Institut für Informatik, University of Potsdam (2008)

    Google Scholar 

  19. Raths, T., Otten, J., Kreitz, C.: The ILTP Problem Library for Intuitionistic Logic. Journal of Automated Reasoning 38, 261–271 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  20. Sahlin, D., Franzen, T., Haridi, S.: An Intuitionistic Predicate Logic Theorem Prover. Journal of Logic and Computation 2, 619–656 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  21. Schmitt, S., Lorigo, L., Kreitz, C., Nogin, A.: JProver: Integrating Connection-based Theorem Proving into Interactive Proof Assistants. In: Goré, R.P., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS (LNAI), vol. 2083, pp. 421–426. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  22. Stickel, M.: A Prolog Technology Theorem Prover: Implementation by an Extended Prolog Compiler. Journal of Automated Reasoning 4, 353–380 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  23. Sutcliffe, G.: The CADE-21 Automated Theorem Proving System Competition. AI Communications 21, 71–81 (2008)

    MATH  Google Scholar 

  24. Sutcliffe, G., Suttner, C.: The TPTP Problem Library. Journal of Automated Reasoning 21, 177–203 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  25. Urban, J.: MPTP 0.2: Design, Implementation, and Initial Experiments. Journal of Automated Reasoning 37, 21–43 (2006)

    Article  MATH  Google Scholar 

  26. Tammet, T.: A Resolution Theorem Prover for Intuitionistic Logic. In: McRobbie, M.A., Slaney, J.K. (eds.) CADE 1996. LNCS, vol. 1104, pp. 2–16. Springer, Heidelberg (1996)

    Google Scholar 

  27. Waaler, A.: Connections in Nonclassical Logics. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, pp. 1487–1578. Elsevier, Amsterdam (2001)

    Chapter  Google Scholar 

  28. Wallen, L.: Automated Deduction in Nonclassical Logics. MIT Press, Cambridge (1990)

    Google Scholar 

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Alessandro Armando Peter Baumgartner Gilles Dowek

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Otten, J. (2008). leanCoP 2.0 and ileanCoP 1.2: High Performance Lean Theorem Proving in Classical and Intuitionistic Logic (System Descriptions). In: Armando, A., Baumgartner, P., Dowek, G. (eds) Automated Reasoning. IJCAR 2008. Lecture Notes in Computer Science(), vol 5195. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71070-7_23

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  • DOI: https://doi.org/10.1007/978-3-540-71070-7_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-71069-1

  • Online ISBN: 978-3-540-71070-7

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