New Modification of the Subformula Property for a Modal Logic

Authors

  • Mitio Takano Niigata University Niigata 950-2181, Japan

DOI:

https://doi.org/10.18778/0138-0680.2020.15

Keywords:

subformula property, modal logic, sequent calculus, scope of □

Abstract

A modified subformula property for the modal logic KD with the additional
axiom □ ◊(AB) ⊃ □ ◊ A ∨ □ ◊B is shown. A new modification of the notion of subformula is proposed for this purpose. This modification forms a natural extension of our former one on which modified subformula property for the modal logics K5, K5D and S4.2 has been shown ([2] and [4]). The finite model property as well as decidability for the logic follows from this.

References

[1] G. E. Hughes, M. J. Cresswell, A new introduction to modal logic, Routledge (1996), DOI: http://dx.doi.org/10.4324/9780203028100
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[2] M. Takano, A modified subformula property for the modal logics K5 and K5D, Bulletin of the Section of Logic, vol. 30(2) (2001), pp. 115–122.
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[3] M. Takano, A semantical analysis of cut-free calculi for modal logics, Reports on Mathematical Logic, vol. 53 (2018), pp. 43–65, DOI: http://dx.doi.org/10.4467/20842589RM.18.003.8836
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[4] M. Takano, A modified subformula property for the modal logic S4.2, Bulletin of the Section of Logic, vol. 48(1) (2019), pp. 19–28, DOI: http://dx.doi.org/10.18778/0138-0680.48.1.02
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Published

2020-11-04

How to Cite

Takano, M. (2020). New Modification of the Subformula Property for a Modal Logic. Bulletin of the Section of Logic, 49(3), 255-268. https://doi.org/10.18778/0138-0680.2020.15

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Section

Research Article