Abstract

First-order modal logics (FMLs) can be modeled as natural fragments of classical higher-order logic (HOL). The FMLtoHOL tool exploits this fact and it enables the application of off-the-shelf HOL provers and model finders for reasoning within FMLs. The tool bridges between the qmf-syntax for FML and the TPTP thf0-syntax for HOL. It currently supports logics K, K4, D, D4, T, S4, and S5 with respect to constant, varying and cumulative domain semantics. The approach is evaluated in combination with a meta-prover for HOL, which sequentially schedules various HOL reasoners. The resulting system is very competitive.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Benzmüller, C., Otten, J., Raths, T.: Implementing and evaluating provers for first-order modal logics. In: Proc. of ECAI 2012, Montpellier, France (2012)Google Scholar
  2. 2.
    Benzmüller, C., Paulson, L.: Exploring Properties of Normal Multimodal Logics in Simple Type Theory with LEO-II. In: Reasoning in Simple Type Theory: Festschrift in Honour of Peter B. Andrews. Studies in Logic, Mathematical Logic and Foundations, vol. 17, pp. 401–422. College Publications (2008)Google Scholar
  3. 3.
    Benzmüller, C., Paulson, L.C.: Quantified multimodal logics in simple type theory. Logica Universalis (Special Issue on Multimodal Logics) 7(1), 7–20 (2013)CrossRefMATHGoogle Scholar
  4. 4.
    Benzmüller, C., Paulson, L.C., Theiss, F., Fietzke, A.: LEO-II - a cooperative automatic theorem prover for higher-order logic. In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 162–170. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  5. 5.
    Blanchette, J.C., Nipkow, T.: Nitpick: A counterexample generator for higher-order logic based on a relational model finder. In: Kaufmann, M., Paulson, L.C. (eds.) ITP 2010. LNCS, vol. 6172, pp. 131–146. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  6. 6.
    Brown, C.E.: Satallax: An automated higher-order prover. In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR 2012. LNCS (LNAI), vol. 7364, pp. 111–117. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  7. 7.
    Fitting, M., Mendelsohn, R.L.: First-Order Modal Logic. Kluwer (1998)Google Scholar
  8. 8.
    Hustadt, U., Schmidt, R.: MSPASS: Modal Reasoning by Translation and First-Order Resolution. In: Dyckhoff, R. (ed.) TABLEAUX 2000. LNCS (LNAI), vol. 1847, pp. 67–71. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  9. 9.
    Lindblad, F.: agsyHol (2012), https://github.com/frelindb/agsyHOL
  10. 10.
    Nipkow, T., Paulson, L.C., Wenzel, M.T.: Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002)CrossRefMATHGoogle Scholar
  11. 11.
    Otten, J.: 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.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 283–291. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    Otten, J.: Implementing connection calculi for first-order modal logics. In: Schulz, S., Ternovska, E., Korovin, K. (eds.) Intl. WS on the Implementation of Logics (2012)Google Scholar
  13. 13.
    Raths, T., Otten, J.: The QMLTP problem library for first-order modal logics. In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR 2012. LNCS (LNAI), vol. 7364, pp. 454–461. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  14. 14.
    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)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Sutcliffe, G.: The TPTP problem library and associated infrastructure. Journal of Automated Reasoning 43(4), 337–362 (2009)CrossRefMATHGoogle Scholar
  16. 16.
    Sutcliffe, G., Benzmüller, C.: Automated reasoning in higher-order logic using the TPTP THF infrastructure. Journal of Formalized Reasoning 3(1), 1–27 (2010)MathSciNetMATHGoogle Scholar
  17. 17.
    Thion, V., Cerrito, S., Cialdea Mayer, M.: A general theorem prover for quantified modal logics. In: Egly, U., Fermüller, C. (eds.) TABLEAUX 2002. LNCS (LNAI), vol. 2381, pp. 266–280. Springer, Heidelberg (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Christoph Benzmüller
    • 1
  • Thomas Raths
    • 2
  1. 1.Dep. of Mathematics and Computer ScienceFreie Universität BerlinGermany
  2. 2.Institute for Computer ScienceUniversity of PotsdamGermany

Personalised recommendations