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Progress in the Development of Automated Theorem Proving for Higher-Order Logic

  • Conference paper
Automated Deduction – CADE-22 (CADE 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5663))

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Abstract

The Thousands of Problems for Theorem Provers (TPTP) problem library is the basis of a well established infrastructure supporting research, development, and deployment of first-order Automated Theorem Proving (ATP) systems. Recently, the TPTP has been extended to include problems in higher-order logic, with corresponding infrastructure and resources. This paper describes the practical progress that has been made towards the goal of TPTP support for higher-order ATP systems.

This research has received funding from the European Community’s Seventh Framework Programme FP7/2007-2013, under grant agreement PIIF-GA-2008-219982.

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References

  1. Andrews, P.B.: Resolution in Type Theory. Journal of Symbolic Logic 36(3), 414–432 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  2. Andrews, P.B.: Theorem Proving via General Matings. Journal of the ACM 28(2), 193–214 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  3. Andrews, P.B.: On Connections and Higher-Order Logic. Journal of Automated Reasoning 5(3), 257–291 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  4. Andrews, P.B., Brown, C.E.: TPS: A Hybrid Automatic-Interactive System for Developing Proofs. Journal of Applied Logic 4(4), 367–395 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  5. Aspinall, D.: Proof General: A Generic Tool for Proof Development. In: Graf, S., Schwartzbach, M. (eds.) TACAS 2000. LNCS, vol. 1785, pp. 38–42. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  6. Benzmüller, C., Brown, C.E.: A Structured Set of Higher-Order Problems. In: Hurd, J., Melham, T. (eds.) TPHOLs 2005. LNCS (LNAI), vol. 3603, pp. 66–81. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  7. Benzmüller, C., Brown, C.E., Kohlhase, M.: Higher-order Semantics and Extensionality. Journal of Symbolic Logic 69(4), 1027–1088 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  8. Benzmüller, C., Kohlhase, M.: LEO - A Higher-Order Theorem Prover. In: Kirchner, C., Kirchner, H. (eds.) CADE 1998. LNCS (LNAI), vol. 1421, pp. 139–143. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  9. Benzmüller, C., Paulson, L.: Exploring Properties of Normal Multimodal Logics in Simple Type Theory with LEO-II. In: Benzmüller, C., Brown, C.E., Siekmann, J., Statman, R. (eds.) Reasoning in Simple Type Theory: Festschrift in Honour of Peter B. Andrews on his 70th Birthday. Studies in Logic, Mathematical Logic and Foundations, vol. 17. College Publications (2009)

    Google Scholar 

  10. Benzmüller, C., Paulson, L.: Exploring Properties of Propositional Normal Multimodal Logics and Propositional Intuitionistic Logics in Simple Type Theory. Journal of Symbolic Logic (submitted)

    Google Scholar 

  11. Benzmüller, C., Paulson, L., Theiss, F., Fietzke, A.: Progress Report on LEO-II - An Automatic Theorem Prover for Higher-Order Logic. In: Schneider, K., Brandt, J. (eds.) Proceedings of the 20th International Conference on Theorem Proving in Higher Order Logics, pp. 33–48 (2007)

    Google Scholar 

  12. Benzmüller, C., Paulson, L., Theiss, F., Fietzke, A.: LEO-II - A Cooperative Automatic Theorem Prover for Higher-Order Logic. In: Baumgartner, P., Armando, A., Gilles, D. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 162–170. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  13. Benzmüller, C., Rabe, F., Sutcliffe, G.: THF0 - The Core TPTP Language for Classical Higher-Order Logic. In: Baumgartner, P., Armando, A., Gilles, D. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 491–506. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  14. Benzmüller, C., Sorge, V., Jamnik, M., Kerber, M.: Combined Reasoning by Automated Cooperation. Journal of Applied Logic 6(3) (2008) (to appear)

    Google Scholar 

  15. Bibel, W.: On Matrices with Connections. Journal of the ACM 28(4), 633–645 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  16. Bishop, M.: A Breadth-First Strategy for Mating Search. In: Ganzinger, H. (ed.) CADE 1999. LNCS (LNAI), vol. 1632, pp. 359–373. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  17. Brown, C.E.: Dependently Typed Set Theory. Technical Report SWP-2006-03, Saarland University (2006)

    Google Scholar 

  18. Brown, C.E.: Automated Reasoning in Higher-Order Logic: Set Comprehension and Extensionality in Church’s Type Theory. Studies in Logic: Logic and Cognitive Systems, vol. 10. College Publications (2007)

    Google Scholar 

  19. Brown, C.E.: M-Set Models. In: Benzmüller, C., Brown, C.E., Siekmann, J., Statman, R. (eds.) Reasoning in Simple Type Theory: Festschrift in Honour of Peter B. Andrews on his 70th Birthday. Studies in Logic, Mathematical Logic and Foundations, vol. 17. College Publications (2009)

    Google Scholar 

  20. Garg, D.: Principal-Centric Reasoning in Constructive Authorization Logic. Technical Report CMU-CS-09-120, School of Computer Science, Carnegie Mellon University (2009)

    Google Scholar 

  21. Huet, G.: A Unification Algorithm for Typed Lambda-Calculus. Theoretical Computer Science 1(1), 27–57 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  22. Hurd, J.: First-Order Proof Tactics in Higher-Order Logic Theorem Provers. In: Archer, M., Di Vito, B., Munoz, C. (eds.) Proceedings of the 1st International Workshop on Design and Application of Strategies/Tactics in Higher Order Logics. NASA Technical Reports, number NASA/CP-2003-212448, pp. 56–68 (2003)

    Google Scholar 

  23. Kohlhase, M.: OMDoc - An Open Markup Format for Mathematical Documents [version 1.2]. LNCS (LNAI), vol. 4180. Springer, Heidelberg (2006)

    Book  Google Scholar 

  24. Landau, E.: Grundlagen der Analysis. Akademische Verlagsgesellschaft M.B.H. (1930)

    Google Scholar 

  25. Miller, D.: A Compact Representation of Proofs. Studia Logica 46(4), 347–370 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  26. Nieuwenhuis, R.: The Impact of CASC in the Development of Automated Deduction Systems. AI Communications 15(2-3), 77–78 (2002)

    Google Scholar 

  27. Nipkow, T., Paulson, L., Wenzel, M.: Isabelle/HOL: A Proof Assistant for Higher-Order Logic. LNCS, vol. 2283. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  28. Pfenning, F., Schürmann, C.: System Description: Twelf - A Meta-Logical Framework for Deductive Systems. In: Ganzinger, H. (ed.) CADE 1999. LNCS (LNAI), vol. 1632, pp. 202–206. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  29. Raths, T., Otten, J., Kreitz, C.: The ILTP Problem Library for Intuitionistic Logic - Release v1.1. Journal of Automated Reasoning 38(1-2), 261–271 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  30. Riazanov, A., Voronkov, A.: The Design and Implementation of Vampire. AI Communications 15(2-3), 91–110 (2002)

    MATH  Google Scholar 

  31. Schulz, S.: E: A Brainiac Theorem Prover. AI Communications 15(2-3), 111–126 (2002)

    MATH  Google Scholar 

  32. Siekman, J., Benzmüller, C., Autexier, S.: Computer Supported Mathematics with OMEGA. Journal of Applied Logic 4(4), 533–559 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  33. Sutcliffe, G.: Semantic Derivation Verification. International Journal on Artificial Intelligence Tools 15(6), 1053–1070 (2006)

    Article  Google Scholar 

  34. Sutcliffe, G.: TPTP, TSTP, CASC, etc. In: Diekert, V., Volkov, M., Voronkov, A. (eds.) CSR 2007. LNCS, vol. 4649, pp. 7–23. Springer, Heidelberg (2007)

    Google Scholar 

  35. Sutcliffe, G.: The SZS Ontologies for Automated Reasoning Software. In: Sutcliffe, G., Rudnicki, P., Schmidt, R., Konev, B., Schulz, S. (eds.) Proceedings of the LPAR Workshops: Knowledge Exchange: Automated Provers and Proof Assistants, and The 7th International Workshop on the Implementation of Logics. CEUR Workshop Proceedings, vol. 418, pp. 38–49 (2008)

    Google Scholar 

  36. Sutcliffe, G., Schulz, S., Claessen, K., Van Gelder, A.: Using the TPTP Language for Writing Derivations and Finite Interpretations. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 67–81. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  37. Sutcliffe, G., Suttner, C.: The State of CASC. AI Communications 19(1), 35–48 (2006)

    MathSciNet  MATH  Google Scholar 

  38. Sutcliffe, G., Suttner, C.B.: The TPTP Problem Library: CNF Release v1.2.1. Journal of Automated Reasoning 21(2), 177–203 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  39. Trac, S., Puzis, Y., Sutcliffe, G.: An Interactive Derivation Viewer. In: Autexier, S., Benzmüller, C. (eds.) Proceedings of the 7th Workshop on User Interfaces for Theorem Provers, 3rd International Joint Conference on Automated Reasoning. Electronic Notes in Theoretical Computer Science, vol. 174, pp. 109–123 (2006)

    Google Scholar 

  40. van Benthem Jutting, L.S.: Checking Landau’s “Grundlagen” in the AUTOMATH System. PhD thesis, Eindhoven University, Eindhoven, The Netherlands (1979)

    Google Scholar 

  41. Van Gelder, A., Sutcliffe, G.: Extending the TPTP Language to Higher-Order Logic with Automated Parser Generation. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 156–161. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  42. Weidenbach, C., Schmidt, R., Hillenbrand, T., Rusev, R., Topic, D.: SPASS Version 3.0. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 514–520. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  43. Wiedijk, F.: The Seventeen Provers of the World. LNCS, vol. 3600. Springer, Heidelberg (2006)

    Google Scholar 

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Author information

Authors and Affiliations

  1. University of Miami, USA

    Geoff Sutcliffe

  2. International University, Germany

    Christoph Benzmüller

  3. Saarland University, Germany

    Chad E. Brown & Frank Theiss

Authors
  1. Geoff Sutcliffe
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  2. Christoph Benzmüller
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  3. Chad E. Brown
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  4. Frank Theiss
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Editor information

Editors and Affiliations

  1. School of Computer Science, The University of Manchester, Manchester, UK

    Renate A. Schmidt

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Sutcliffe, G., Benzmüller, C., Brown, C.E., Theiss, F. (2009). Progress in the Development of Automated Theorem Proving for Higher-Order Logic. In: Schmidt, R.A. (eds) Automated Deduction – CADE-22. CADE 2009. Lecture Notes in Computer Science(), vol 5663. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02959-2_8

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  • DOI: https://doi.org/10.1007/978-3-642-02959-2_8

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