, Volume 187, Issue 2, pp 623–660 | Cite as

Two dimensional Standard Deontic Logic [including a detailed analysis of the 1985 Jones–Pörn deontic logic system]

  • Mathijs de Boer
  • Dov M. Gabbay
  • Xavier Parent
  • Marija Slavkovic


This paper offers a two dimensional variation of Standard Deontic Logic SDL, which we call 2SDL. Using 2SDL we can show that we can overcome many of the difficulties that SDL has in representing linguistic sets of Contrary-to-Duties (known as paradoxes) including the Chisholm, Ross, Good Samaritan and Forrester paradoxes. We note that many dimensional logics have been around since 1947, and so 2SDL could have been presented already in the 1970s. Better late than never! As a detailed case study illustrating the power of 2SDL, we examine the system DL of Deontic Logic of Andrew Jones and Ingmar Pörn offered in 1985 to solve the Chisholm paradox of Contrary to Duties. The critical examination is done using logics and methods available in 1985 and solutions are proposed using what was available in 1985.


Deontic Logic Contrary to Duties Chisholm paradox Two dimensional temporal logic 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Aqvist, L. (1965). A new approach to the logical theory of interrogatives, Part I, Analysis. Philosophical Society and Department of Philosophy, University of Uppsala, Sect. 6.2.Google Scholar
  2. Aqvist L. (1966) “Next” and “Ought”, alternative foundations for Von Wrights’s tense-logic, with an application to deontic logic. Logique et Analyse 9: 231–251Google Scholar
  3. Carmo J., Jones A. J. I. (2002) Deontic logic and contrary to duties. In: Gabbay D., Guenther F. (eds) Handbook of philosophical logic, 2nd ed. Springer, Heidelberg, pp 256–344Google Scholar
  4. Chellas B. F. (1980) Modal logic—an introduction. Cambridge University Press, Cambridge, UKCrossRefGoogle Scholar
  5. Chisholm R.M. (1963) Contrary-to-duty imperatives and deontic logic. Analysis 24: 33–36CrossRefGoogle Scholar
  6. Forrester J. W. (1984) Gentle murder, or the adverbial samartian. The Journal of Philosophy 81(4): 193–197CrossRefGoogle Scholar
  7. Gabbay D. (1970) Selective filtration in modal logics I. Theoria 36: 323–330CrossRefGoogle Scholar
  8. Gabbay D. (1974) Tense logics and the tenses of English. In: Moravcsik J. M. E. (Ed.) Readings in logic. Mouton Publishing Co., The Hague, pp 177–186Google Scholar
  9. Gabbay D. M. (1976a) Modal and tense logics. D Reidel, DordrechGoogle Scholar
  10. Gabbay D. (1976b) Investigations in modal and tense logic with applications, Synthese Volume 92. D Reidel, DordrechGoogle Scholar
  11. Gabbay, D. (2008a). Reactive Kripke semantics and arc accessibility. In A. Avron, N. Dershowitz, & A. Rabinovich (Eds.), Pillars of computer science: Essays dedicated to Boris (Boaz) Trakhtenbrot on the Occasion of His 85th Birthday (pp. 292–341). Lecture notes in computer science, Vol. 4800. Berlin: Springer-Verlag.Google Scholar
  12. Gabbay D. M. (2008b) Reactive Kripke models and contrary-to-duty obligations. In: Meyden R., Torre L. (eds) DEON-2008, Deontic logic in computer science, LNAI 5076. Springer, Berlin, pp 155–173CrossRefGoogle Scholar
  13. Gabbay, D. M. (2010). Reactive standard deontic logic. Draft, February.Google Scholar
  14. Gabbay, D. (2011). Reactive Kripke models and contrary-to-duty obligations. Expanded version. Journal of Applied Logic. (to appear)Google Scholar
  15. Gabbay D. M., Marcelino S. (2009) Modal logics of reactive frames. Studia Logica 93: 403–444Google Scholar
  16. Gabbay, D., & Schlechta, K. (2009). Critical analysis of the Carmo–Jones model of contrary-to-duty obligations. Draft paper 358.Google Scholar
  17. Hansson S. O. (1989) A note on the Deontic System DL of Jones and Pörn. Synthese 80: 427–428CrossRefGoogle Scholar
  18. Jones A. J. I. (1993) Towards a formal theory of defeasible deontic conditionals. Annals of Mathematics and Artificial Intelligence 9: 151–166CrossRefGoogle Scholar
  19. Jones A.J.I., Pörn I. (1985) Ideality, sub-ideality and deontic logic. Synthese 65: 275–290CrossRefGoogle Scholar
  20. Jones A.J.I., Pörn I. (1986) “Ought” and “must”. Synthese 66: 89–93CrossRefGoogle Scholar
  21. Jones A. I. J., Pörn I. (1989) A rejoinder to Hansson. Synthese 80: 429–432CrossRefGoogle Scholar
  22. Jones, A. J. I., & Pörn, I. (1991). On the logic of deontic conditionals. In J.-J. Ch. Meyer & R. J. Wieringa (Eds.) DEON91—Proceedings of Ist international workshop on deontic logic in computer science. Amsterdam.Google Scholar
  23. Kamp H. (1971) Formal properties of ‘Now’. Theoria 37: 227–274CrossRefGoogle Scholar
  24. Kanger, S. (1971). New foundations for ethical theory, 1957. Reprinted In R. Hilpinen & D. Follesdal (Eds.), Deontic logic: Introductory and systematic readings (pp. 36–58). Dordrecht: D. Reidel.Google Scholar
  25. Lewis D. (1970) Anselm and actuality. Nous 4: 175–188CrossRefGoogle Scholar
  26. Loewer B., Belzer M. (1983) Dyadic deontic detachment. Synthese 54: 295–318CrossRefGoogle Scholar
  27. Prakken H., Sergot M. (1996) Contrary to duty obligations. Studia Logica 57: 91–115CrossRefGoogle Scholar
  28. Prior A. N. (1958) Escapism: The logical basis of ethics. In: Melden A. I. (Ed.) Essays in moral philosophy. University of Washington Press, Washington, pp 135–146Google Scholar
  29. Prior A. N. (1968) Now. Nous 2: 101–119CrossRefGoogle Scholar
  30. Reichenbach, H. (1947). Elements of symbolic logic. New York: McMillan. Republished, Free Press (1966).Google Scholar
  31. Ross A. (1941) Imperatives and logic. Theoria 7: 53–71Google Scholar
  32. Segerberg K. (1967) On the logic of ‘Tomorrow’. Theoria 33: 46–52Google Scholar
  33. Segerberg K. (1973) Two-dimensional modal logic. Journal of Philosophical Logic 2: 77–96CrossRefGoogle Scholar
  34. van der Torre L., Tan Y.-H. (1999) Contrary-to-duty reasoning with preference-based dyadic obligations. Annals of Mathematics and Artificial Intelligence 27: 49–78CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Mathijs de Boer
    • 3
  • Dov M. Gabbay
    • 1
    • 2
    • 3
  • Xavier Parent
    • 3
  • Marija Slavkovic
    • 3
  1. 1.King’s CollegeLondonUK
  2. 2.Bar Ilan UniversityRamat GanIsrael
  3. 3.Individual and Collective Reasoning Group, Computer Science and CommunicationsUniversity of LuxembourgLuxembourgUK

Personalised recommendations