Studia Logica

, Volume 105, Issue 5, pp 915–942 | Cite as

Connecting Actions and States in Deontic Logic

  • Piotr Kulicki
  • Robert Trypuz
Open Access


This paper tackles the problem of inference in normative systems where norms concerning actions and states of affairs appear together. A deontic logic of actions and states is proposed as a solution. It is made up of two independent deontic logics, namely a deontic logic of action and a deontic logic of states, interlinked by bridging definitions. It is shown at a language and a model level how an agent should look for norms to follow in a concrete situation. It is pointed out that such specific norms are obtained by finding the most specific obligation and the most general prohibition. They are to be derived from all norms applicable to the situation by using the principles of the logic presented in this paper.


Deontic action logic Norms on actions and states General and specific norms 



This research is supported by the National Science Centre of Poland (UMO-2015/17/B/HS1/02569). The authors would like to thank Marek Sergot, Xavier Parent, Marek Piechowiak and anonymous reviewers for their remarks on the previous versions of the paper.


  1. 1.
    Anglberger, A. J. J., N. Gratzl, and O. Roy, Obligation, free choice, and the logic of weakest permissions. Rew. Symb. Logic 8(4):807–827, 2015.CrossRefGoogle Scholar
  2. 2.
    Atienza, M., and J. Ruiz Manero, A theory of legal sentences, Kluwer, 1998.Google Scholar
  3. 3.
    Broersen, J., D. Gabbay, and L. van der Torre, Changing norms is changing obligation change, in T. Agotnes, J. Brosen, and D. Elgesem, (eds.), Lectures on Logic and Computation, vol. 7393 of Lecture Notes in Computer Science, Springer Berlin/Heidelberg, 2012, pp. 199–214.Google Scholar
  4. 4.
    Craven, R., and M. Sergot, Agent strands in the action language nC+, J. Applied Logic 6(2):172–191, 2008.CrossRefGoogle Scholar
  5. 5.
    Czelakowski, J., Action and deontology, in E. Ejerhed and S. Lindström, (eds.), Logic, action, and cognition: essays in philosophical logic, Trends in Logic, Kluwer Academic, 1997, pp. 47–88.Google Scholar
  6. 6.
    d’Altan, P., J.-J.Ch. Meyer, and R. J. Wieringa, (eds.), An integrated framework for ought-to-be and ought-to-do constraints. Artificial Intelligence and Law 4(2):77–111, 1996.Google Scholar
  7. 7.
    Gabbay, D., L. Gammaitoni, and X. Sun, The paradoxes of permission: an action based solution. Journal of Applied Logic 12(2):179–191, 2014.CrossRefGoogle Scholar
  8. 8.
    Kulicki,  T., Two faces of obligation, in A. Brozek, J. Jadacki, and B. Zarnic (eds.), Theory of Imperatives from Different Points of View, Logic, Methodology and Philosophy of Science at Warsaw University 7. Wydawnictwo Naukowe Semper, 2013.Google Scholar
  9. 9.
    Kulicki, P., and R. Trypuz, Completely and partially executable sequences of actions in deontic context. Synthese 192(4):1117–1138, 2015.CrossRefGoogle Scholar
  10. 10.
    Pattaro, E., The Law and The Right, vol. 1 of A Treatise of Legal Philosophy and General Jurisprudence, Springer, 2012.Google Scholar
  11. 11.
    Roy, O., A. J. J. Anglberger, and N. Gratzl, The Logic of Obligation as Weakest Permission, in T., Ågotnes, J. Broersen, and D. Elgesem, (eds.), DEON 2012, vol 7393 of Lecture Notes in Computer Science, Springer, 2012, pp. 139–150.Google Scholar
  12. 12.
    Segerberg, K., A deontic logic of action. Studia Logica 41:269–282, 1982.CrossRefGoogle Scholar
  13. 13.
    Sergot, M., The logic of unwitting collective agency. Technical Report 2008/6, Department of Computing, Imperial College London, 2008.Google Scholar
  14. 14.
    Sergot, M., Some examples formulated in a ‘seeing to it that’ logic: Illustrations, observations, problems, in T. Müller, (ed.), Nuel Belnap on Indeterminism and Free Action, Springer, 2014, pp. 223–256.Google Scholar
  15. 15.
    Sergot, M. J., and R. Craven, The Deontic Component of Action Language nC+, in Deontic Logic and Artificial Normative Systems, 8th International Workshop on Deontic Logic in Computer Science, DEON 2006, Utrecht, The Netherlands, July 12-14, 2006, Proceedings, 2006, pp. 222–237.Google Scholar
  16. 16.
    Trypuz, R., and P. Kulicki, A systematics of deontic action logics based on boolean algebra. Logic and Logical Philosophy 18:263–279, 2009.Google Scholar
  17. 17.
    Trypuz, R., and P. Kulicki, Deontic logic of actions and states, in F. Carini, D. Grossi, J. Mehus, and X. Parent, (eds.), Deontic Logic and Normative System, LNAI 8554, Springer, 2014, pp. 258–272.Google Scholar
  18. 18.
    Trypuz,  R., and P. Kulicki, On deontic action logics based on boolean algebra. Journal of Logic Computation 25(5):1241–1260, 2015.Google Scholar
  19. 19.
    van der Meyden, R., The Dynamic Logic of Permission. Journal of Logic and Computation 6(3):465–479, 1996.CrossRefGoogle Scholar
  20. 20.
    von Wright, G. H., Norm and Action: A Logical Inquiry, Routledge & Kegan Paul, 1963.Google Scholar
  21. 21.
    Ziembinski, Z., Practical Logic, D. Reidel Pub. Co, Dordrecht, 1976.CrossRefGoogle Scholar

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Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made

Authors and Affiliations

  1. 1.Faculty of PhilosophyJohn Paul II Catholic University of LublinLublinPoland

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