IF Modal Logic and Classical Negation

• Authors: Tero Tulenheimo
• Venue: Studia Logica
• Year: 2014

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' (IFMLs). A model-theoretic criterion is presented which serves to tell when a formula of IFMLs 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 IFMLs is not closed under complementation. In fact we obtain a much stronger result: the only IFMLs formulas admitting their classical negation to be expressed in IFMLs itself are those whose truth-condition is in fact expressible in ML.