Axiomatizations for Propositional and Modal Team Logic

Author Martin Lück



PDF
Thumbnail PDF

File

LIPIcs.CSL.2016.33.pdf
  • Filesize: 0.55 MB
  • 18 pages

Document Identifiers

Author Details

Martin Lück

Cite As Get BibTex

Martin Lück. Axiomatizations for Propositional and Modal Team Logic. In 25th EACSL Annual Conference on Computer Science Logic (CSL 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 62, pp. 33:1-33:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.CSL.2016.33

Abstract

A framework is developed that extends Hilbert-style proof systems for propositional and modal logics to comprehend their team-based counterparts. The method is applied to classical propositional logic and the modal logic K. Complete axiomatizations for their team-based extensions, propositional team logic PTL and modal team logic MTL, are presented.

Subject Classification

Keywords
  • team logic
  • propositional team logic
  • modal team logic
  • proof system
  • axiomatization

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. William Ward Armstrong. Dependency structures of data base relationships. In IFIP Congress, pages 580-583, 1974. Google Scholar
  2. Pietro Galliani. Inclusion and exclusion dependencies in team semantics — On some logics of imperfect information. Annals of Pure and Applied Logic, 163(1):68-84, January 2012. URL: http://dx.doi.org/10.1016/j.apal.2011.08.005.
  3. Valentin Goranko and Martin Otto. Model theory of modal logic. In Johan Van Benthem Patrick Blackburn and Frank Wolter, editors, Handbook of Modal Logic, volume 3 of Studies in Logic and Practical Reasoning, pages 249-329. Elsevier, 2007. URL: http://dx.doi.org/10.1016/S1570-2464(07)80008-5.
  4. Erich Grädel and Jouko Väänänen. Dependence and independence. Studia Logica, 101(2):399-410, 2013. Google Scholar
  5. Raul Hakli and Sara Negri. Does the deduction theorem fail for modal logic? Synthese, 187(3):849-867, 2012. URL: http://dx.doi.org/10.1007/s11229-011-9905-9.
  6. Lauri Hella, Antti Kuusisto, Arne Meier, and Heribert Vollmer. Modal Inclusion Logic: Being Lax is Simpler than Being Strict. In Giuseppe F Italiano, Giovanni Pighizzini, and Donald T. Sannella, editors, Mathematical Foundations of Computer Science 2015, volume 9234, pages 281-292. Springer Berlin Heidelberg, Berlin, Heidelberg, 2015. Google Scholar
  7. Jaakko Hintikka and Gabriel Sandu. Informational Independence as a Semantical Phenomenon. In Studies in Logic and the Foundations of Mathematics, volume 126, pages 571-589. Elsevier, 1989. URL: http://dx.doi.org/10.1016/S0049-237X(08)70066-1.
  8. Wilfrid Hodges. Compositional semantics for a language of imperfect information. Logic Journal of the IGPL, 5(4):539-563, 1997. Google Scholar
  9. 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, September 7-10, 2015, Berlin, Germany, pages 277-291, 2015. URL: http://dx.doi.org/10.4230/LIPIcs.CSL.2015.277.
  10. Juha Kontinen and Ville Nurmi. Team Logic and Second-Order Logic. In Logic, Language, Information and Computation, volume 5514, pages 230-241. Springer Berlin Heidelberg, Berlin, Heidelberg, 2009. Google Scholar
  11. Juha Kontinen and Jouko Väänänen. Axiomatizing first-order consequences in dependence logic. Annals of Pure and Applied Logic, 164(11):1101-1117, November 2013. URL: http://dx.doi.org/10.1016/j.apal.2013.05.006.
  12. Martin Lück. The axioms of team logic. CoRR, abs/1510.08786, 2016. URL: http://arxiv.org/abs/1510.08786.
  13. Katsuhiko Sano and Jonni Virtema. Axiomatizing Propositional Dependence Logics. In Stephan Kreutzer, editor, 24th EACSL Annual Conference on Computer Science Logic (CSL 2015), volume 41 of Leibniz International Proceedings in Informatics (LIPIcs), pages 292-307, Dagstuhl, Germany, 2015. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik. URL: http://dx.doi.org/10.4230/LIPIcs.CSL.2015.292.
  14. Jouko Väänänen. Modal dependence logic. New perspectives on games and interaction, 4:237-254, 2008. Google Scholar
  15. Jouko Väänänen. Dependence logic: a new approach to independence friendly logic. Number 70 in London Mathematical Society student texts. Cambridge University Press, Cambridge ; New York, 2007. Google Scholar
  16. Fan Yang. On extensions and variants of dependence logic. PhD thesis, University of Helsinki, 2014. URL: http://www.math.helsinki.fi/logic/people/fan.yang/dissertation_fyang.pdf.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail