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On provability logics with linearly ordered modalities

(2014) STUDIA LOGICA. 102(3). p.541-566
Author
Organization
Abstract
We introduce the logics GLP (I >), a generalization of Japaridze's polymodal provability logic GLP (omega) where I > is any linearly ordered set representing a hierarchy of provability operators of increasing strength. We shall provide a reduction of these logics to GLP (omega) yielding among other things a finitary proof of the normal form theorem for the variable-free fragment of GLP (I >) and the decidability of GLP (I >) for recursive orderings I >. Further, we give a restricted axiomatization of the variable-free fragment of GLP (I >).
Keywords
Provability logic, Modal logic, CLOSED FRAGMENT, GLP, COMPLETENESS, PROOF

Citation

Please use this url to cite or link to this publication:

MLA
Beklemishev, Lev D, David Fernández-Duque, and Joost J Joosten. “On Provability Logics with Linearly Ordered Modalities.” STUDIA LOGICA 102.3 (2014): 541–566. Print.
APA
Beklemishev, L. D., Fernández-Duque, D., & Joosten, J. J. (2014). On provability logics with linearly ordered modalities. STUDIA LOGICA, 102(3), 541–566.
Chicago author-date
Beklemishev, Lev D, David Fernández-Duque, and Joost J Joosten. 2014. “On Provability Logics with Linearly Ordered Modalities.” Studia Logica 102 (3): 541–566.
Chicago author-date (all authors)
Beklemishev, Lev D, David Fernández-Duque, and Joost J Joosten. 2014. “On Provability Logics with Linearly Ordered Modalities.” Studia Logica 102 (3): 541–566.
Vancouver
1.
Beklemishev LD, Fernández-Duque D, Joosten JJ. On provability logics with linearly ordered modalities. STUDIA LOGICA. 2014;102(3):541–66.
IEEE
[1]
L. D. Beklemishev, D. Fernández-Duque, and J. J. Joosten, “On provability logics with linearly ordered modalities,” STUDIA LOGICA, vol. 102, no. 3, pp. 541–566, 2014.
@article{8566417,
  abstract     = {We introduce the logics GLP (I >), a generalization of Japaridze's polymodal provability logic GLP (omega) where I > is any linearly ordered set representing a hierarchy of provability operators of increasing strength. We shall provide a reduction of these logics to GLP (omega) yielding among other things a finitary proof of the normal form theorem for the variable-free fragment of GLP (I >) and the decidability of GLP (I >) for recursive orderings I >. Further, we give a restricted axiomatization of the variable-free fragment of GLP (I >).},
  author       = {Beklemishev, Lev D and Fernández-Duque, David and Joosten, Joost J},
  issn         = {0039-3215},
  journal      = {STUDIA LOGICA},
  keywords     = {Provability logic,Modal logic,CLOSED FRAGMENT,GLP,COMPLETENESS,PROOF},
  language     = {eng},
  number       = {3},
  pages        = {541--566},
  title        = {On provability logics with linearly ordered modalities},
  url          = {http://dx.doi.org/10.1007/s11225-013-9490-7},
  volume       = {102},
  year         = {2014},
}

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