Skip to main content
SpringerLink
Log in
Book cover

International Joint Conference on Automated Reasoning

IJCAR 2008: Automated Reasoning pp 491–506Cite as

THF0 – The Core of the TPTP Language for Higher-Order Logic

  • Conference paper

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

Abstract

One of the keys to the success of the Thousands of Problems for Theorem Provers (TPTP) problem library and related infrastructure is the consistent use of the TPTP language. This paper introduces the core of the TPTP language for higher-order logic – THF0, based on Church’s simple type theory. THF0 is a syntactically conservative extension of the untyped first-order TPTP language.

This is a preview of subscription content, 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   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andrews, P.B., Bishop, M., Issar, S., Nesmith, D., Pfenning, F., Xi, H.: TPS: A Theorem-Proving System for Classical Type Theory. Journal of Automated Reasoning 16(3), 321–353 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  2. Beeson, M.: Otter-lambda, a Theorem-prover with Untyped Lambda-unification. In: Sutcliffe, G., Schulz, S., Tammet, T. (eds.) Proceedings of the Workshop on Empirically Successful First Order Reasoning (2004)

    Google Scholar 

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

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  5. 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 

  6. Benzmüller, C., Paulson, L.: Exploring Properties of Normal Multimodal Logics in Simple Type Theory with LEO-II. In: Benzmüller, C., Brown, C., Siekmann, J., Statman, R. (eds.) Festschrift in Honour of Peter B. Andrews on his 70th Birthday. IfCoLog (to appear 2007)

    Google Scholar 

  7. Benzmüller, C., Sorge, V., Jamnik, M., Kerber, M.: Combined Reasoning by Automated Cooperation. Journal of Applied Logic (in print) (2008)

    Google Scholar 

  8. Benzmüller, C., Theiss, F., Paulson, L., Fietzke, A.: LEO-II - A Cooperative Automatic Theorem Prover for Higher-Order Logic. In: Armando, A., Baumgartner, P., Dowek, G. (eds.) Proceedings of the 4th International Joint Conference on Automated Reasoning (IJCAR 2008). LNCS (LNAI), vol. 5195. Springer, Heidelberg (2008)

    Google Scholar 

  9. Church, A.: A Formulation of the Simple Theory of Types. Journal of Symbolic Logic 5, 56–68 (1940)

    Article  MATH  MathSciNet  Google Scholar 

  10. Curry, H.B., Feys, R.: Combinatory Logic I. North Holland, Amsterdam (1958)

    Google Scholar 

  11. Frege, F.: Grundgesetze der Arithmetik. Jena (1893) (1903)

    Google Scholar 

  12. Godefroid, P.: Software Model Checking: the VeriSoft Approach. Technical Report Technical Memorandum ITD-03-44189G, Bell Labs, Lisle, USA (2003)

    Google Scholar 

  13. Gordon, M., Melham, T.: Introduction to HOL, a Theorem Proving Environment for Higher Order Logic. Cambridge University Press, Cambridge (1993)

    MATH  Google Scholar 

  14. Harper, R., Honsell, F., Plotkin, G.: A Framework for Defining Logics. Journal of the ACM 40(1), 143–184 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  15. Harrison, J.: HOL Light: A Tutorial Introduction. In: Srivas, M., Camilleri, A. (eds.) FMCAD 1996. LNCS, vol. 1166, pp. 265–269. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  16. Henkin, L.: Completeness in the Theory of Types. Journal of Symbolic Logic 15, 81–91 (1950)

    Article  MATH  MathSciNet  Google Scholar 

  17. Howard, W.: The Formulas-as-types Notion of Construction. In: Seldin, J., Hindley, J. (eds.) H B Curry, Essays on Combinatory Logic, Lambda Calculus and Formalism, pp. 479–490. Academic Press, London (1980)

    Google Scholar 

  18. Martin-Löf, P.: An Intuitionistic Theory of Types. In: Sambin, G., Smith, J. (eds.) Twenty-Five Years of Constructive Type Theory, pp. 127–172. Oxford University Press, Oxford (1973)

    Google Scholar 

  19. Matuszek, C., Cabral, J., Witbrock, M., DeOliveira, J.: An Introduction to the Syntax and Content of Cyc. In: Baral, C. (ed.) Proceedings of the 2006 AAAI Spring Symposium on Formalizing and Compiling Background Knowledge and Its Applications to Knowledge Representation and Question Answering, pp. 44–49 (2006)

    Google Scholar 

  20. Niles, I., Pease, A.: Towards A Standard Upper Ontology. In: Welty, C., Smith, B. (eds.) Proceedings of the 2nd International Conference on Formal Ontology in Information Systems, pp. 2–9 (2001)

    Google Scholar 

  21. Nipkow, T., Paulson, L.C., Wenzel, M.T.: Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  22. Owre, S., Rajan, S., Rushby, J.M., Shankar, N., Srivas, M.: PVS: Combining Specification, Proof Checking, and Model Checking. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 411–414. Springer, Heidelberg (1996)

    Google Scholar 

  23. 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 

  24. Rudnicki, P.: An Overview of the Mizar Project. In: Proceedings of the 1992 Workshop on Types for Proofs and Programs, pp. 311–332 (1992)

    Google Scholar 

  25. Siekmann, J., Benzmüller, C., Autexier, S.: Computer supported mathematics with omega. Journal of Applied Logic 4(4), 533–559 (2006)

    Article  MATH  MathSciNet  Google Scholar 

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

    Chapter  Google Scholar 

  27. Sutcliffe, G., Schulz, S., Claessen, K., Gelder, A.V.: 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 

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

    MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  30. Sutcliffe, G., Zimmer, J., Schulz, S.: TSTP Data-Exchange Formats for Automated Theorem Proving Tools. In: Zhang, W., Sorge, V. (eds.) Distributed Constraint Problem Solving and Reasoning in Multi-Agent Systems. Frontiers in Artificial Intelligence and Applications, vol. 112, pp. 201–215. IOS Press, Amsterdam (2004)

    Google Scholar 

  31. Gelder, A.V., 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 

  32. Zermelo, E.: Über Grenzzahlen und Mengenbereiche. Fundamenta Mathematicae 16, 29–47 (1930)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Saarland University, Germany

    Christoph Benzmüller

  2. Jacobs University Bremen, Germany

    Florian Rabe

  3. University of Miami, USA

    Geoff Sutcliffe

Authors
  1. Christoph Benzmüller
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Florian Rabe
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Geoff Sutcliffe
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Alessandro Armando Peter Baumgartner Gilles Dowek

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Benzmüller, C., Rabe, F., Sutcliffe, G. (2008). THF0 – The Core of the TPTP Language for Higher-Order Logic. 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_41

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-71070-7_41

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-71069-1

  • Online ISBN: 978-3-540-71070-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation