Skip to main content

: A Resolution-Based Prover for Multimodal K

  • Conference paper
  • First Online:
Automated Reasoning (IJCAR 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9706))

Included in the following conference series:

Abstract

In this paper, we describe an implementation of a hyper-resolution-based calculus for the propositional basic multimodal logic, . The prover was designed to support experimentation with different combinations of refinements for its basic calculus: it is primarily based on the set of support strategy, which can then be combined with other refinements, simplification techniques and different choices for the underlying normal form and clause selection. The prover allows for both local and global reasoning. We show experimental results for different combinations of strategies and comparison with existing tools.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
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

Notes

  1. 1.

    We have excluded *SAT from the comparison as it produced incorrect results on a number of benchmark formulae.

References

  1. Areces, C., Gennari, R., Heguiabehere, J., Rijke, M.D.: Tree-based heuristics in modal theorem proving. In: Proceedings of ECAI 2000, pp. 199–203. IOS Press (2000)

    Google Scholar 

  2. Balsiger, P., Heuerding, A., Schwendimann, S.: A benchmark method for the propositional modal logics K, KT, S4. J. Autom. Reasoning 24(3), 297–317 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  3. Goranko, V., Passy, S.: Using the universal modality: gains and questions. J. Logic and Comput. 2(1), 5–30 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  4. Goré, R., Olesen, K., Thomson, J.: Implementing tableau calculi using BDDs: BDDTab system description. In: Demri, S., Kapur, D., Weidenbach, C. (eds.) IJCAR 2014. LNCS, vol. 8562, pp. 337–343. Springer, Heidelberg (2014)

    Google Scholar 

  5. Götzmann, D., Kaminski, M., Smolka, G.: Spartacus: a tableau prover for hybrid logic. Electr. Notes Theor. Comput. Sci. 262, 127–139 (2010)

    Article  MathSciNet  Google Scholar 

  6. Horrocks, I.R., Hustadt, U., Sattler, U., Schmidt, R.: Computational modal logic. In: Handbook of Modal Logic, pp. 181–245. Elsevier, Amsterdam (2006)

    Google Scholar 

  7. Kaminski, M., Tebbi, T.: InKreSAT: modal reasoning via incremental reduction to SAT. In: Bonacina, M.P. (ed.) CADE 2013. LNCS, vol. 7898, pp. 436–442. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  8. Kovács, L., Voronkov, A.: First-order theorem proving and Vampire. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 1–35. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  9. Lee, R.C.T.: A completeness theorem and computer program for finding theorems derivable from given axioms. Ph.D. thesis, Berkeley (1967)

    Google Scholar 

  10. Massacci, F., Donini, F.M.: Design and results of TANCS- non-classical (modal) systems comparison. TABLEAUX 2000. LNCS, vol. 1847, pp. 52–56. Springer, Heidelberg (2000)

    Google Scholar 

  11. McCune, W.W.: OTTER 3.0 reference manual and guide, 07 May 2007

    Google Scholar 

  12. Nalon, C., Dixon, C.: Anti-prenexing and prenexing for modal logics. In: Fisher, M., van der Hoek, W., Konev, B., Lisitsa, A. (eds.) JELIA 2006. LNCS (LNAI), vol. 4160, pp. 333–345. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  13. Nalon, C., Dixon, C.: Clausal resolution for normal modal logics. J. Algorithms 62, 117–134 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  14. Nalon, C., Hustadt, U., Dixon, C.: A modal-layered resolution calculus for K. In: De Nivelle, H. (ed.) TABLEAUX 2015. LNCS, vol. 9323, pp. 185–200. Springer, Heidelberg (2015). doi:10.1007/978-3-319-24312-2_13

    Chapter  Google Scholar 

  15. Nalon, C., Hustadt, U., Dixon, C.: KSP sources and benchmarks (2016). http://www.cic.unb.br/~nalon/#software

  16. Pan, G., Sattler, U., Vardi, M.Y.: BDD-based decision procedures for the modal logic K. J. Appl. Non-Class. Logics 16(1–2), 169–208 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  17. Patel-Schneider, P.F., Sebastiani, R.: A new general method to generate random modal formulae for testing decision procedures. J. Artif. Intell. Res. (JAIR) 18, 351–389 (2003)

    MathSciNet  MATH  Google Scholar 

  18. Schulz, S.: Simple and efficient clause subsumption with feature vector indexing. In: Bonacina, M.P., Stickel, M.E. (eds.) Automated Reasoning and Mathematics. LNCS, vol. 7788, pp. 45–67. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  19. Spaan, E.: Complexity of modal logics. Ph.D. thesis, University of Amsterdam (1993)

    Google Scholar 

  20. Tsarkov, D., Horrocks, I.: FaCT++ description logic reasoner: system description. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 292–297. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  21. Wos, L., Robinson, G., Carson, D.: Efficiency and completeness of the set of support strategy in theorem proving. J. ACM 12, 536–541 (1965)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Cláudia Nalon .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Nalon, C., Hustadt, U., Dixon, C. (2016). : A Resolution-Based Prover for Multimodal K . In: Olivetti, N., Tiwari, A. (eds) Automated Reasoning. IJCAR 2016. Lecture Notes in Computer Science(), vol 9706. Springer, Cham. https://doi.org/10.1007/978-3-319-40229-1_28

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-40229-1_28

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40228-4

  • Online ISBN: 978-3-319-40229-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics