A Modified Subformula Property for the Modal Logics K5 and K5d

  title={A Modified Subformula Property for the Modal Logics K5 and K5d},
  author={Mitio Takano},
The sequent calculus GK5 (GK5D) for the modal propositional logic K5 (K5D) is presented, and it is shown that, every provable sequent Γ → Θ in GK5 (GK5D) has a GK5-proof (GK5D-proof) such that every formula occurring in it is either a subformula of some formulas in Γ, Θ, or the formula 2¬2B or ¬2B, where 2B occurs in the scope of some occurrence of 2 in some formulas of Γ, Θ. Some corollaries including the interpolation property for K5 (K5D) follow from this. 
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