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Characterizing Frame Definability in Team Semantics via the Universal Modality

  • Katsuhiko Sano
  • Jonni VirtemaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9160)

Abstract

Let Open image in new window denote the fragment of modal logic extended with the universal modality in which the universal modality occurs only positively. We characterize the definability of Open image in new window in the spirit of the well-known Goldblatt–Thomason theorem. We show that an elementary class \({\mathbb {F}}\) of Kripke frames is definable in Open image in new window if and only if \({\mathbb {F}}\) is closed under taking generated subframes and bounded morphic images, and reflects ultrafilter extensions and finitely generated subframes. In addition, we initiate the study of modal frame definability in team-based logics. We show that, with respect to frame definability, the logics Open image in new window , modal logic with intuitionistic disjunction, and (extended) modal dependence logic all coincide. Thus we obtain Goldblatt–Thomason -style theorems for each of the logics listed above.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Japan Advanced Institute of Science and TechnologyIshikawa PrefectureJapan
  2. 2.Leibniz Universität Hannover HannoverGermany
  3. 3.University of TampereTampereFinland

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