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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
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© 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


  Abstract

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.
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