Skip to main content

Anti-prenexing and Prenexing for Modal Logics

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4160))

Abstract

Efficient proof methods for normal modal logics are highly desirable, as such logical systems have been widely used in computer science to represent complex situations. Resolution-based methods are often designed to deal with formulae in a normal form and the efficiency of the method (also) relies on how efficient (in the sense of producing fewer and/or shorter clauses) the translation procedure is. We present a normal form for normal modal logics and show how the use of simplification, for specific normal logics, together with anti-prenexing and prenexing techniques help us to produce better sets of clauses.

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

Buying options

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. Dixon, C., Fisher, M.: Resolution-Based Proof for Multi-Modal Temporal Logics of Knowledge. In: Goodwin, S., Trudel, A. (eds.) Proceedings of the 7th International Workshop on Temporal Representation and reasoning (TIME 2000), Cape Breton, Canada, July 2000, pp. 69–78. IEEE Computer Society Press, Los Alamitos (2000)

    Chapter  Google Scholar 

  2. Egly, U.: On the value of antiprenexing. In: Pfenning, F. (ed.) LPAR 1994. LNCS (LNAI), vol. 822, pp. 69–83. Springer, Heidelberg (1994)

    Google Scholar 

  3. Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning About Knowledge. MIT Press, Cambridge (1995)

    MATH  Google Scholar 

  4. Fisher, M., Dixon, C., Peim, M.: Clausal Temporal Resolution. ACM Transactions on Computational Logic 2(1) (January 2001)

    Google Scholar 

  5. Jaeger, G., Balsiger, P., Heuerding, A., Schwendimann, S., Bianchi, M., Guggisberg, K., Janssen, G., Heinle, W., Achermann, F., Boroumand, A.D., Brambilla, P., Bucher, I., Zimmermann, H.: LWB–The Logics Workbench 1. University of Berne, Switzerland, http://www.lwb.unibe.ch/

  6. Meyer, J.J.C., van der Hoek, W.: Epistemic Logic for Computer Science and Artificial Intelligence. Cambridge Tracts in Theoretical Computer Science, vol. 41. Cambridge University Press, Cambridge (1995)

    Book  Google Scholar 

  7. Nalon, C., Dixon, C.: Anti-prenexing and prenexing for modal logics (extended version). Technical Report ULCS-06-003, University of Liverpool (April 2006), Available at: http://www.csc.liv.ac.uk/research/techreports/tr2006/ulcs-06-003.pdf

  8. Nalon, C., Dixon, C.: Normal modal resolution (June 2006) (submitted)

    Google Scholar 

  9. Nonnengart, A., Weidenbach, C.: Computing small clause normal forms. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, ch. 6, vol. I, pp. 335–367. Elsevier Science B.V., Amsterdam (2001)

    Chapter  Google Scholar 

  10. Plaisted, D.A., Greenbaum, S.A.: A Structure-Preserving Clause Form Translation. Journal of Logic and Computation 2, 293–304 (1986)

    MATH  MathSciNet  Google Scholar 

  11. Rao, A.S., Georgeff, M.P.: Decision procedures for BDI logics. Journal of Logic and Computation 8(3), 293–342 (1998)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Nalon, C., Dixon, C. (2006). Anti-prenexing and Prenexing for Modal Logics. In: Fisher, M., van der Hoek, W., Konev, B., Lisitsa, A. (eds) Logics in Artificial Intelligence. JELIA 2006. Lecture Notes in Computer Science(), vol 4160. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11853886_28

Download citation

  • DOI: https://doi.org/10.1007/11853886_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-39625-3

  • Online ISBN: 978-3-540-39627-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics