A Deontic Action Logic with Sequential Composition of Actions

  • Piotr Kulicki
  • Robert Trypuz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7393)

Abstract

We start our investigations from the deontic action model defined in multi-situation settings. Then we discuss the validity of formulas constructed in a language with a finite number of basic actions, parallel and sequential compositions of actions, a free choice operator and the standard deontic operators of obligation, strong permission and prohibition. The main achievements of the paper are definitions of metalogical counterparts of deontic operators and interpretation function of actions taking into account their terminating and non-terminating executions.

Keywords

deontic action logic sequential composition of actions terminated non-terminated actions 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Castro, P.F., Maibaum, T.S.E.: Deontic action logic, atomic boolean algebra and fault-tolerance. Journal of Applied Logic 7(4), 441–466 (2009)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Dignum, F., Meyer, J.-J.C., Wieringa, R.J.: Free choice and contextually permitted actions. Studia Logica 57(1), 193–220 (1996)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Fischer, M.J., Ladner, R.E.: Propositional dynamic logic of regular programs. Journal of Computer and System Sciences 18(2), 194–211 (1979)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Hoare, C.A.R.: An axiomatic basis for computer programming. Communications of the ACM 12(10), 576–580 (1969)MATHCrossRefGoogle Scholar
  5. 5.
    Kleene, S.C.: Representation of events in nerve nets and finite automata. Automata Studies (1956)Google Scholar
  6. 6.
    Lorini, E., Herzig, A.: A logic of intention and attempt. Synthese 163(1), 45–77 (2008)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Meyer, J.J.: A different approach to deontic logic: Deontic logic viewed as variant of dynamic logic. Notre Dame Journal of Formal Logic 29(1), 109–136 (1987)CrossRefGoogle Scholar
  8. 8.
    Prisacariu, C., Schneider, G.: A dynamic deontic logic for complex contracts. The Journal of Logic and Algebraic Programming 81 (to appear, 2012)Google Scholar
  9. 9.
    Segerberg, K.: A deontic logic of action. Studia Logica 41, 269–282 (1982)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Trypuz, R.: Simple theory of norm and action. In: Brożek, A., Jadacki, J., Żarnić, B. (eds.) Theory of Imperatives from Different Points of View, Logic, Methodology and Philosophy of Science at Warsaw University, vol. 6, pp. 120–136. Wydawnictwo Naukowe Semper (2011)Google Scholar
  11. 11.
    Trypuz, R., Kulicki, P.: A systematics of deontic action logics based on boolean algebra. Logic and Logical Philosophy 18, 263–279 (2009)MathSciNetGoogle Scholar
  12. 12.
    Trypuz, R., Kulicki, P.: Towards Metalogical Systematisation of Deontic Action Logics Based on Boolean Algebra. In: Governatori, G., Sartor, G. (eds.) DEON 2010. LNCS, vol. 6181, pp. 132–147. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  13. 13.
    Trypuz, R., Kulicki, P.: A norm-giver meets deontic action logic. Logic and Logical Philosophy 20, 59–72 (2011)MathSciNetMATHGoogle Scholar
  14. 14.
    van der Meyden, R.: The dynamic logic of permission. J. Log. Comput. 6(3), 465–479 (1996)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Piotr Kulicki
    • 1
  • Robert Trypuz
    • 1
  1. 1.John Paul II Catholic University of LublinLublinPoland

Personalised recommendations