Skip to main content
SpringerLink
Log in

MleanCoP: A Connection Prover for First-Order Modal Logic

  • Conference paper
Automated Reasoning (IJCAR 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8562))

Included in the following conference series:

Abstract

MleanCoP is a fully automated theorem prover for first-order modal logic. The proof search is based on a prefixed connection calculus and an additional prefix unification, which captures the Kripke semantics of different modal logics. MleanCoP is implemented in Prolog and the source code of the core proof search procedure consists only of a few lines. It supports the standard modal logics D, T, S4, and S5 with constant, cumulative, and varying domain conditions. The most recent version also supports heterogeneous multimodal logics and outputs a compact prefixed connection proof. An experimental evaluation shows the strong performance of MleanCoP.

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 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Beckert, B., Goré, R.: Free Variable Tableaux for Propositional Modal Logics. In: Galmiche, D. (ed.) TABLEAUX 1997. LNCS (LNAI), vol. 1227, pp. 91–106. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  2. Benzmüller, C., Otten, J., Raths, T.: Implementing and Evaluating Provers for First-order Modal Logics. In: De Raedt, L., et al. (eds.) 20th European Conference on Artificial Intelligence, ECAI 2012, pp. 163–168. IOS Press, Amsterdam (2012)

    Google Scholar 

  3. Benzmüller, C., Raths, T.: HOL Based First-Order Modal Logic Provers. In: McMillan, K., Middeldorp, A., Voronkov, A. (eds.) LPAR-19 2013. LNCS, vol. 8312, pp. 127–136. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

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

    Book  MATH  Google Scholar 

  5. Blackburn, P., van Bentham, J., Wolter, F.: Handbook of Modal Logic. Elsevier, Amsterdam (2006)

    Google Scholar 

  6. Brown, C.: Reducing Higher-Order Theorem Proving to a Sequence of SAT Problems. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS (LNAI), vol. 6803, pp. 147–161. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  7. Carnielli, W., Pizzi, C.: Modalities and Multimodalities. Springer, Heidelberg (2008)

    Book  MATH  Google Scholar 

  8. Fitting, M., Mendelsohn, R.L.: First-Order Modal Logic. Kluwer, Dordrecht (1998)

    Book  MATH  Google Scholar 

  9. Hustadt, U., Schmidt, R.: MSPASS: Modal Reasoning by Translation and First-Order Resolution. In: Dyckhoff, R. (ed.) TABLEAUX 2000. LNCS (LNAI), vol. 1847, pp. 67–81. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  10. Otten, J.: leanCop 2.0 and ileanCop 1.2: High Performance Lean Theorem Proving in Classical and Intuitionistic Logic. In: Armando, A., Baumgartner, P., Dowek, G., et al. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 283–291. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  11. Otten, J.: Restricting backtracking in connection calculi. AI Communications 23, 159–182 (2010)

    MATH  MathSciNet  Google Scholar 

  12. Otten, J.: A Non-clausal Connection Calculus. In: Brünnler, K., Metcalfe, G. (eds.) TABLEAUX 2011. LNCS (LNAI), vol. 6793, pp. 226–241. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  13. Otten, J.: Implementing Connection Calculi for First-order Modal Logics. In: Korovin, K., et al. (eds.) IWIL 2012. EPiC, vol. 22, pp. 18–32. EasyChair (2012)

    Google Scholar 

  14. 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)

    Chapter  Google Scholar 

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik, University of Potsdam, August-Bebel-Str. 89, 14482, Potsdam-Babelsberg, Germany

    Jens Otten

Authors
  1. Jens Otten
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. CNRS,, New York University &amp, USA

    Stéphane Demri

  2. Department of Computer Science, University of New Mexico, 87131-0001, Albuquerque, NM, USA

    Deepak Kapur

  3. Max Planck Institute for Informatics, Campus E1 4, 66123, Saarbrücken, Germany

    Christoph Weidenbach

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Otten, J. (2014). MleanCoP: A Connection Prover for First-Order Modal Logic. In: Demri, S., Kapur, D., Weidenbach, C. (eds) Automated Reasoning. IJCAR 2014. Lecture Notes in Computer Science(), vol 8562. Springer, Cham. https://doi.org/10.1007/978-3-319-08587-6_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-08587-6_20

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08586-9

  • Online ISBN: 978-3-319-08587-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation