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Title: | Characterising Modal Definability of Team-Based Logics via the Universal Modality | Authors: | Sano, Katsuhiko VIRTEMA, Jonni |
Issue Date: | 2019 | Publisher: | ELSEVIER | Source: | ANNALS OF PURE AND APPLIED LOGIC, 170 (9), p. 110-1127 | Abstract: | We study model and frame definability of various modal logics. Let denote the fragment of modal logic extended with the universal modality in which the universal modality occurs only positively. We show that a class of Kripke models is definable in if and only if the class is elementary and closed under disjoint unions and surjective bisimulations. We also characterise the definability of in the spirit of the well-known Goldblatt–Thomason theorem. We show that an elementary class of Kripke frames is definable in if and only if is closed under taking generated subframes and bounded morphic images, and reflects ultrafilter extensions and finitely generated subframes. In addition we study frame definability relative to finite transitive frames and give an analogous characterisation of -definability relative to finite transitive frames. Finally, we initiate the study of model and frame definability in team-based logics. We study (extended) modal dependence logic, (extended) modal inclusion logic, and modal team logic. We establish strict linear hierarchies with respect to model definability and frame definability, respectively. We show that, with respect to model and frame definability, the before mentioned team-based logics, except modal dependence logic, either coincide with or plain modal logic . Thus as a corollary we obtain model theoretic characterisation of model and frame definability for the team-based logics. This article subsumes and extends the conference articles [30] and [31]. | Notes: | Virtema, J (reprint author), Hasselt Univ, Hasselt, Belgium. katsuhiko.sano@gmail.com; jonni.virtema@gmail.com | Keywords: | Model definability;Frame definability;Team semantics;Universal modality;Modal logic | Document URI: | http://hdl.handle.net/1942/28314 | ISSN: | 0168-0072 | e-ISSN: | 1873-2461 | DOI: | 10.1016/j.apal.2019.04.009 | ISI #: | 000474317400008 | Rights: | © 2019 Elsevier B.V. All rights reserved. | Category: | A1 | Type: | Journal Contribution |
Appears in Collections: | Research publications |
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