A Modified Subformula Property for the Modal Logics K5 and K5d

@inproceedings{Takano2007AMS,
  title={A Modified Subformula Property for the Modal Logics K5 and K5d},
  author={Mitio Takano},
  year={2007}
}
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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References

Publications referenced by this paper.
Showing 1-7 of 7 references

Modal Logic (Oxford Logic Guides

  • A. Chagrov, M. Zakharyaschev
  • 1997

Subformula property as a substitute for cut-elimination in modal propositional logics, Mathematica Japonica

  • M. Takano
  • 1992
1 Excerpt

Proof Theory, Second Edition (Studies in Logic and the Foundations of Mathematics 81)

  • G. Takeuti
  • Department of Mathematics Faculty of Education…
  • 1987
3 Excerpts

Subformula results in some propositional modal logics

  • M. Fitting
  • Studia Logica
  • 1978
1 Excerpt

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