A Van Benthem Theorem for Modal Team Semantics

Authors Juha Kontinen, Julian-Steffen Müller, Henning Schnoor, Heribert Vollmer



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Juha Kontinen
Julian-Steffen Müller
Henning Schnoor
Heribert Vollmer

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Juha Kontinen, Julian-Steffen Müller, Henning Schnoor, and Heribert Vollmer. A Van Benthem Theorem for Modal Team Semantics. In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 277-291, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
https://doi.org/10.4230/LIPIcs.CSL.2015.277

Abstract

The famous van Benthem theorem states that modal logic corresponds exactly to the fragment of first-order logic that is invariant under bisimulation. In this article we prove an exact analogue of this theorem in the framework of modal dependence logic (MDL) and team semantics. We show that Modal Team Logic (MTL) extending MDL by classical negation captures exactly the FO-definable bisimulation invariant properties of Kripke structures and teams. We also compare the expressive power of MTL to most of the variants and extensions of MDL recently studied in the area.
Keywords
  • modal logic
  • dependence logic
  • team semantics
  • expressivity
  • bisimulation
  • independence
  • inclusion
  • generalized dependence atom

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References

  1. Samson Abramsky and Jouko A. Väänänen. From IF to BI. Synthese, 167(2):207-230, 2009. Google Scholar
  2. Patrick Blackburn, Maarten de Rijke, and Yde Venema. Modal Logic, volume 53 of Cambridge Tracts in Theoretical Computer Scie. Cambridge University Press, Cambridge, 2001. Google Scholar
  3. J. Ebbing and P. Lohmann. Complexity of model checking for modal dependence logic. In Theory and Practice of Computer Science (SOFSEM), number 7147 in Lecture Notes in Computer Science, pages 226-237, Berlin Heidelberg, 2012. Springer Verlag. Google Scholar
  4. Johannes Ebbing, Lauri Hella, Arne Meier, Julian-Steffen Müller, Jonni Virtema, and Heribert Vollmer. Extended modal dependence logic. In Leonid Libkin, Ulrich Kohlenbach, and Ruy J. G. B. de Queiroz, editors, WoLLIC, volume 8071 of Lecture Notes in Computer Science, pages 126-137. Springer, 2013. Google Scholar
  5. Pietro Galliani. Inclusion and exclusion dependencies in team semantics - on some logics of imperfect information. Ann. Pure Appl. Logic, 163(1):68-84, 2012. Google Scholar
  6. Pietro Galliani and Lauri Hella. Inclusion logic and fixed point logic. In Simona Ronchi Della Rocca, editor, CSL, volume 23 of LIPIcs, pages 281-295. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2013. Google Scholar
  7. Valentin. Goranko and Martin Otto. Handbook of Modal Logic, chapter Model Theory of Modal Logic, pages 255-325. Elsevier, 2006. Google Scholar
  8. Rajeev Goré, Barteld P. Kooi, and Agi Kurucz, editors. Advances in Modal Logic 10, invited and contributed papers from the tenth conference on "Advances in Modal Logic," held in Groningen, The Netherlands, August 5-8, 2014. College Publications, 2014. Google Scholar
  9. Erich Grädel and Jouko Väänänen. Dependence and independence. Studia Logica, 101(2):399-410, 2013. Google Scholar
  10. Lauri Hella, Kerkko Luosto, Katsuhiko Sano, and Jonni Virtema. The expressive power of modal dependence logic. In Goré et al. [Antti Kuusisto, 2015], pages 294-312. Google Scholar
  11. Juha Kontinen, Julian-Steffen Müller, Henning Schnoor, and Heribert Vollmer. Modal independence logic. In Goré et al. [Antti Kuusisto, 2015], pages 353-372. Google Scholar
  12. Juha Kontinen, Julian-Steffen Müller, Henning Schnoor, and Heribert Vollmer. A van benthem theorem for modal team semantics. CoRR, abs/1410.6648, 2014. Google Scholar
  13. Antti Kuusisto. A double team semantics for generalized quantifiers. Journal of Logic, Language and Information, 24(2):149-191, 2015. Google Scholar
  14. Peter Lohmann and Heribert Vollmer. Complexity results for modal dependence logic. Studia Logica, 101(2):343-366, 2013. Google Scholar
  15. Julian-Steffen Müller. Complexity of model checking in modal team logic. Computation in Europe, 2012. Google Scholar
  16. Julian-Steffen Müller. Satisfiability and Model Checking in Team Based Logics. PhD thesis, Leibniz Universität Hannover, 2014. Google Scholar
  17. M. Otto. Elementary proof of the van Benthem-Rosen characterisation theorem. Technical Report 2342, Darmstadt University of Technology, 2004. Google Scholar
  18. David Michael Ritchie Park. Concurrency and automata on infinite sequences. In Peter Deussen, editor, Theoretical Computer Science, 5th GI-Conference, Karlsruhe, Germany, March 23-25, 1981, Proceedings, volume 104 of Lecture Notes in Computer Science, pages 167-183. Springer, 1981. Google Scholar
  19. Katsuhiko Sano and Jonni Virtema. Axiomatizing propositional dependence logics. CoRR, abs/1410.5038, 2014. Google Scholar
  20. Merlijn Sevenster. Model-theoretic and computational properties of modal dependence logic. J. Log. Comput., 19(6):1157-1173, 2009. Google Scholar
  21. Jouko Väänänen. Dependence Logic. Cambridge University Press, 2007. Google Scholar
  22. Jouko Väänänen. Modal dependence logic. New Perspectives on Games and Interaction, 5:237-254, 2009. Google Scholar
  23. Johan van Benthem. Modal Correspondence Theory. PhD thesis, Universiteit van Amsterdam, Instituut voor Logica en Grondslagenonderzoek van de Exacte Wetenschappen, 1977. Google Scholar
  24. Johan van Benthem. Modal Logic and Classical Logic. Bibliopolis, 1985. Google Scholar
  25. Fan Yang. On Extensions and Variants of Dependence Logic. PhD thesis, University of Helsinki, 2014. Google Scholar