New Modification of the Subformula Property for a Modal Logic
Bulletin of the Section of Logic (2020)
- Volume: 49, Issue: 3, page 255-268
- ISSN: 0138-0680
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topMitio Takano. "New Modification of the Subformula Property for a Modal Logic." Bulletin of the Section of Logic 49.3 (2020): 255-268. <http://eudml.org/doc/296793>.
@article{MitioTakano2020,
abstract = {A modified subformula property for the modal logic KD with the additionalaxiom □ ◊(A ∨ B) ⊃ □ ◊ 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.},
author = {Mitio Takano},
journal = {Bulletin of the Section of Logic},
keywords = {subformula property; modal logic; sequent calculus; scope of □},
language = {eng},
number = {3},
pages = {255-268},
title = {New Modification of the Subformula Property for a Modal Logic},
url = {http://eudml.org/doc/296793},
volume = {49},
year = {2020},
}
TY - JOUR
AU - Mitio Takano
TI - New Modification of the Subformula Property for a Modal Logic
JO - Bulletin of the Section of Logic
PY - 2020
VL - 49
IS - 3
SP - 255
EP - 268
AB - A modified subformula property for the modal logic KD with the additionalaxiom □ ◊(A ∨ B) ⊃ □ ◊ 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.
LA - eng
KW - subformula property; modal logic; sequent calculus; scope of □
UR - http://eudml.org/doc/296793
ER -
References
top- [1] G. E. Hughes, M. J. Cresswell, A new introduction to modal logic, Routledge (1996), DOI: http://dx.doi.org/10.4324/9780203028100
- [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.
- [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
- [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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