Skip Navigation


Logic Journal of IGPL Advance Access originally published online on March 13, 2008
Logic Journal of IGPL 2008 16(3):249-267; doi:10.1093/jigpal/jzn004
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 Jerábek, E.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Independent Bases of Admissible Rules

Emil Jerábek *

Institute of Mathematics of the Academy of Sciences zitná 25, 115 67 Praha 1, Czech Republic. E-mail: jerabek{at}math.cas.cz

We show that IPC, K4, GL, and S4, as well as all logics inheriting their admissible rules, have independent bases of admissible rules.

Key Words: admissible rule • independent basis • modal logic • intuitionistic logic • MSC (2000): 03B45 • 03B55 • 08C15

Received for publication 18 January 2008.

*The research was done while the author was visiting the Department of Computer Science of the University of Toronto. Supported by grant IAA1019401 of GA AV CR, grant 1M0545 of MSMT CR, and NSERC Canada Discovery grant.



References

  1. Chagrov Alexander V, Zakharyaschev Michael. On the independent axiomatizability of modal and intermediate logics. In: Journal of Logic and Computation (1995) 5(3):287–302.[Abstract/Free Full Text]

  2. Chagrov Alexander V, Zakharyaschev Michael. Modal logic. In: Oxford Logic Guides vol. 35 (1997) Oxford University Press.

  3. Friedman Harvey M. One hundred and two problems in mathematical logic. In: Journal of Symbolic Logic (1975) 40(2):113–129.[CrossRef][ISI]

  4. Gencer Çigdem. Description of modal logics inheriting admissible rules for K4. In: Logic Journal of the IGPL (2002) 10(4):401–411.[CrossRef][ISI]

  5. Ghilardi Silvio. Unification in intuitionistic logic. In: Journal of Symbolic Logic (1999) 64(2):859–880.[CrossRef][ISI]

  6. Ghilardi Silvio. Best solving modal equations. In: Annals of Pure and Applied Logic (2000) 102(3):183–198.[CrossRef][ISI]

  7. Iemhoff Rosalie. On the admissible rules of intuitionistic propositional logic. In: Journal of Symbolic Logic (2001) 66(1):281–294.[CrossRef][ISI]

  8. Iemhoff Rosalie. Intermediate logics and Visser's rules. In: Notre Dame Journal of Formal Logic (2005) 46(1):65–81.[CrossRef]

  9. Iemhoff Rosalie. On the rules of intermediate logics. In: Archive for Mathematical Logic (2006) 45(5):581–599.[CrossRef][ISI]

  10. Jerábek Emil. Admissible rules of modal logics. In: Journal of Logic and Computation (2005) 15(4):411–431.[Abstract/Free Full Text]

  11. Jerábek Emil. Frege systems for extensible modal logics. In: Annals of Pure and Applied Logic (2006) 142:366–379.[CrossRef][ISI]

  12. Lorenzen Paul. Einführung in die operative Logik und Mathematik. (1955) Springer. (in German).

  13. Rybakov Vladimir V. Admissibility of logical inference rules. In: Studies in Logic and the Foundations of Mathematics vol. 136 (1997) Elsevier.

  14. Rybakov Vladimir V. Construction of an explicit basis for rules admissible in modal system S4. In: Mathematical Logic Quarterly (2001) 47(4):441–446.[CrossRef][ISI]

  15. Rybakov Vladimir V, Gencer Çigdem, Öner Tahsin. Description of modal logics inheriting admissible rules for S4. In: Logic Journal of the IGPL (1999) 7(5):655–664.[CrossRef]

  16. Rybakov Vladimir V, Kiyatkin Vladimir R, Terziler Mehmet. Independent bases for rules admissible in pretabular logics. In: Logic Journal of the IGPL (1999) 7(2):253–266.[CrossRef]


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 Jerábek, E.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?