Skip Navigation



Journal of Logic and Computation Advance Access published online on January 8, 2008
Journal of Logic and Computation, doi:10.1093/logcom/exm077
This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Kashima, R.
Right arrow Articles by Okamoto, K.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original papers

General Models and Completeness of First-Order Modal µ-calculus

Ryo Kashima

Department of Mathematical and Computing Sciences, Tokyo Institute of Technology. Ookayama, Meguro, Tokyo 152-8552, Japan. E-mail: kashima{at}is.titech.ac.jp

Keishi Okamoto

Research Center for Verification and Semantics, National Institute of Advanced Industrial Science and Technology, 1-2-14 Shin-Senri Nishi, Toyonaka, Osaka 560-0083, Japan. E-mail: keishi-okamoto{at}aist.go.jp

Received 16 April 2007.

There is no recursive axiomatization of first-order modal µ-calculus that is complete with respect to usual Kripke models. Then we introduce `general' models, and we prove that the natural axiom system of first-order modal µ-calculus is complete with respect to general models.

Keywords: First-order modal µ-calculus; modal logic; Kripke model; general model; completeness



References

  1. Ambler S, Kwiatkowska M, Measor N. Duality and the completeness of the modal $\mu$-calculus. Theoretical Computer Science (1995) 151:3–27.[CrossRef][ISI]
  2. Boolos GS, Burgess JP, Jeffrey RC. Computability and Logic, Fourth edition (2003) Cambridge: Cambridge University Press.
  3. Bradfield J, Stirling C, mu-calculi Modal. In . In: Handbook of Modal Logic—Blackburn P, Van Benthem J, Wolter F, eds. (2007) Amsterdam: Elsevier.
  4. van Dalen D. Logic and Structure, Third edition (1997) Berlin: Springer.
  5. Fitting M. Modal Proof Theory. In. In: Handbook of Modal Logic—Blackburn P, Van Benthem J, Wolter F, eds. (2007) Amsterdam: Elsevier.
  6. Hartonas C. Duality for modal µ-logics. Theoretical Computer Science (1998) 202:193–222.[CrossRef][ISI]
  7. HodkInson I, Wolter F, Zakharyaschev M. Decidable fragment of first-order temporal logics. Annals of Pure and Applied Logic (2000) 106:85–134.[CrossRef][ISI]
  8. Kashima R, Okamoto K. Completeness theorem of first-order modal mu-Calculus. In: Research Reports on Mathematical and Computing Sciences (2007) Tokyo Institute of Technology: Department of Mathematical and Computing Sciences. C-244.
  9. Okamoto K. A first-order extension of modal µ-calculus. Programming Science Technical Report, PS-2006-003. Research Center for Verification and Semantics, National Institute of Advanced Industrial Science and Technology, 2006.
  10. Walukiewicz I. Completeness of Kozen's axiomatization of the propositional µ-calculus. Information and Computation (2000) 157:142–182.[CrossRef][ISI]

Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?



This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Kashima, R.
Right arrow Articles by Okamoto, K.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?