Studia Logica

, Volume 102, Issue 1, pp 41–66 | Cite as

IF Modal Logic and Classical Negation

  • Tero TulenheimoEmail author


The present paper provides novel results on the model theory of Independence friendly modal logic. We concentrate on its particularly well-behaved fragment that was introduced in Tulenheimo and Sevenster (Advances in Modal Logic, 2006). Here we refer to this fragment as ‘Simple IF modal logic’ (IFML s ). A model-theoretic criterion is presented which serves to tell when a formula of IFML s is not equivalent to any formula of basic modal logic (ML). We generalize the notion of bisimulation familiar from ML; the resulting asymmetric simulation concept is used to prove that IFML s is not closed under complementation. In fact we obtain a much stronger result: the only IFML s formulas admitting their classical negation to be expressed in IFML s itself are those whose truth-condition is in fact expressible in ML.


Complementation Expressivity IF logic Independence Modal logic Slash logic 


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© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.CNRS Research Unit “Savoirs, Textes, Langage”, Lille, France, Department of PhilosophyUniversity of Lille 3, Domaine Universitaire du “Pont de Bois”Villeneuve d’AscqFrance

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