Studia Logica

, Volume 57, Issue 1, pp 91–115 | Cite as

Contrary-to-duty obligations

  • Henry Prakken
  • Marek Sergot


We investigate under what conditions contrary-to-duty (CTD) structures lacking temporal and action elements can be given a coherent reading. We argue, contrary to some recent proposals, that CTD is not an instance of defeasible reasoning, and that methods of nonmonotonic logics are inadequate since they are unable to distinguish between defeasibility and violation of primary obligations. We propose a semantic framework based on the idea that primary and CTD obligations are obligations of different kinds: a CTD obligation pertains to, or pre-supposes, a certain context in which a primary obligation is already violated. This framework is presented initially as an extension of Standard Deontic Logic (SDL), a normal modal logic of type KD, and is illustrated by application to a series of examples. The concluding section is concerned with some resemblances between CTD and defeasible reasoning. We show first that the SDL-based framework contains a flaw and must be adjusted. A discussion of possible adjustments, including an alternative treatment in terms of a preference-based semantics, reveals difficulties that are reminiscent of problems in defeasible reasoning and intensional accounts of defeasible conditionals.

Key words

deontic logic deontic conditionals contrary-to-duty obligations reparational obligations formalisation of norms 


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  1. [1]
    Belzer, M., 1987, ‘Legal reasoning in 3-D’, Proc. First International Conference on Artificial Intelligence and Law, Boston. ACM Press, 155–163.Google Scholar
  2. [2]
    Brown, A. L., Jr., S. Mantha and T. Wakayama, 1993, ‘Exploiting the normative aspect of preference: a deontic logic without actions’, Annals of Mathematics and Artificial Intelligence 9, 167–204.Google Scholar
  3. [3]
    Chellas, B., 1980, Modal logic: An introduction, Cambridge University Press.Google Scholar
  4. [4]
    Chisholm, R. M., 1963, ‘Contrary-to-duty imperatives and deontic logicr’, Analysis 24, 33–36.Google Scholar
  5. [5]
    Forrester, J. W., 1984, ‘Gentle murder, or the adverbial Samaritan’, Journal of Philosophy 81, 193–197.Google Scholar
  6. [6]
    Hansson, S. O., 1990, ‘Preference-based deontic logic (PDL)’, Journal of Philosophical Logic 19, 75–93.Google Scholar
  7. [7]
    Hilpinen, R., 1993, ‘Actions in Deontic Logic’, In J.-J.Ch. Meyer and R.J. Wieringa (eds.): Deontic Logic in Computer Science: Normative System Specification’, John Wiley & Sons, Chichester, 85–100.Google Scholar
  8. [8]
    Jones, A. J. I., and I. Pörn, 1985, ‘Ideality, sub-ideality and deontic logic’, Synthese 65, 275–290.Google Scholar
  9. [9]
    Lewis, D., 1974, ‘Semantic analyses for dyadic deontic logic’, In S. Stenlund (ed.): Logical Theory and Semantic Analysis, D. Reidel, Dordrecht, 1–14.Google Scholar
  10. [10]
    McCarty, L. T., 1994, ‘Defeasible deontic reasoning’, Fundamenta Informaticae 21, 125–148.Google Scholar
  11. [11]
    Makinson, D., 1993, ‘Five faces of minimality’, Studia Logica 52, no. 3.Google Scholar
  12. [12]
    Meyer, J. -J. Ch., 1988, ‘A different approach to deontic logic: deontic logic viewed as a variant of dynamic logic’, Notre Dame Journal of Formal Logic 29 109–136.Google Scholar
  13. [13]
    Morreau, M., 1994, ‘Prima facie and Seeming Duties’, In A. J. I. Jones and M. J. Sergot (eds.): Proceedings of DEON'94: Second International Workshop on Deontic Logic and Computer Science, Oslo, January 1994. Complex 1/94, Tano Publishers, Norway.Google Scholar
  14. [14]
    Ryu, Y. H., and R. M. Lee, 1991, ‘Defeasible deontic reasoning: a logic programming model’, Proceedings of the First International Workshop on Deontic Logic in Computer Science, DEON-91, Amsterdam, 347–363.Google Scholar
  15. [15]
    Veltman, F., 1991, Defaults in Update Semantics. Report LP-91-02, Institute for Language, Logic and Information, University of Amsterdam.Google Scholar
  16. [16]
    Aqvist, L., and J. Hoepelman, 1981, ‘Some theorems about a “tree” system of deontic tense logic’, In R. Hilpinen (ed.): New studies in deontic logic, Reidel, Dordrecht, 187–221.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Henry Prakken
    • 1
  • Marek Sergot
    • 2
  1. 1.Computer/Law InstituteFree University AmsterdamHV Amsterdam
  2. 2.Department of ComputingImperial College of Science Technology and MedicineLondon

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