Skip Navigation


Logic Journal of IGPL Advance Access originally published online on January 23, 2009
Logic Journal of IGPL 2009 17(2):159-172; doi:10.1093/jigpal/jzn032
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 Gencer, C.
Right arrow Articles by De Jongh, D.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Unifiability in extensions of K4

Çigdem Gencer

Department of Mathematics and Computer Science, Istanbul Kültür University, Ataköy Campus, Bakirköy, 34156, Istanbul, Türkiye.
Email: c.gencer{at}iku.edu.tr

Dick De Jongh

Institute for Logic, Language and Computation, Universiteit van Amsterdam, Plantage- Muidergracht 24, 1018 TV Amsterdam, The Netherlands.
Email: d.h.j.dejongh{at}uva.nl

We extend and generalize the work on unifiability of [8]. We give a semantic characterization for unifiability and non-unifiability in the extensions of K4. We apply this in particular to extensions of KD4, GL and K4.3 to obtain a syntactic characterization and give a concrete decision procedure for unifiability for those logics. For that purpose we use universal models.

Key Words: Unification • unifier • provability logic • closed formula • universal model

Received for publication 16 May 2008.

References

    [1]  Bezhanishvili N. Lattices of Intermediate and Cylindric Modal Logics (2006) University of Amsterdam. PhD-Thesis, ILLC Dissertation Series DS-2006-02.

    [2]  Boolos G. The Logic of Provability (1993) Cambridge University Press.

    [3]  Chagrov A, Zakharyaschev M. Modal Logic (1997) Oxford: Clarendon Press.

    [4]  Ghilardi S. Unification in Intuitionistic Logic, The. Journal of Symbolic Logic (1999) 64(2):859–880.[CrossRef][Web of Science]

    [5]  Ghilardi S. Best Solving Modal Equations. Annals of Pure and Applied Logic (2000) 102:183–198.[CrossRef][Web of Science]

    [6]  Japaridze G, de Jongh D. The Logic of Provability. In: Handbook of Proof Theory (1995) Elsevier. 360–422.

    [7]  Rybakov VV. Admissibility of Logical Inference Rules (1997) Elsevier Science B.V.

    [8]  Rybakov VV, Terziler M, Gencer Ç. An Essay on Unification and Inference Rules For Modal Logics, Bulletin of the Section of Logic (1999) 28/3:145–157.

    [9]  Solovay RM. Provability interpretations of modal logic, Israel Journal of Mathematics (1976) 25:287–304.[CrossRef][Web of Science]


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 Gencer, C.
Right arrow Articles by De Jongh, D.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?