Opis

• Tytuł:
  A Modified Subformula Property for the Modal Logic S4.2
• Twórca:
  Takano, Mitio
• Współtwórca:
  Niigata University, Niigata, Japan;
  takano@emeritus.niigata-u.ac.jp
• Opis:
  The modal logic S4.2 is S4 with the additional axiom ◊□A ⊃ □◊A. In this article, the sequent calculus GS4.2 for this logic is presented, and by imposing an appropriate restriction on the application of the cut-rule, it is shown that, every GS4.2-provable sequent S has a GS4.2-proof such that every formula occurring in it is either a subformula of some formula in S, or the formula □¬□B or ¬□B, where □B occurs in the scope of some occurrence of □ in some formula of S. These are just the K5-subformulas of some formula in S which were introduced by us to show the modied subformula property for the modal logics K5 and K5D (Bull Sect Logic 30(2): 115–122, 2001). Some corollaries including the interpolation property for S4.2 follow from this. By slightly modifying the proof, the finite model property also follows.
• Dostępność obiektu:
  Dostęp otwarty
• Prawa:
  This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.;
  http://creativecommons.org/licenses/by-nc-nd/4.0
• Data:
  2019.10.13;
  2019
• Typ:
  Article
• Język:
  angielski;
  eng
• Format:
  application/pdf
• Wydawca:
  Wydawnictwo Uniwersytetu Łódzkiego
• Relacja:
  Bulletin of the Section of Logic; 1;
  48
• Temat i słowa kluczowe:
  modal logic S4.2;
  sequent calculus;
  subformula property
• Identyfikator:
  0138-0680;
  http://hdl.handle.net/11089/30604 ;
  2449-836X;
  10.18778/0138-0680.48.1.02
• Dostawca danych:
  Repozytorium Uniwersytetu Łódzkiego
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