Reasoning About Permission and Obligation

Part of the Outstanding Contributions to Logic book series (OCTR, volume 3)


How is deontic logic possible on a positivistic philosophy of norms? D. Makinson (1999) considered this question the ‘fundamental problem of deontic logic’, and called to reconstruct deontic logic as a logic of reasoning about norms. A solution is to use a semantics which defines the truth of monadic and dyadic deontic sentences with respect to an explicitly modelled set of norms. Here, I explore how such a norm-based semantics can be adapted to include not just mandatory but also permissive norms that possibly conflict with the first, and describe how this may affect the validity of well-known theorems. All studied proposals are based on a definition of consistency from the later theory of G. H. von Wright. The approach may shed new light on the problem of ‘free choice permission,’ while D. Lewis’s ‘problem of permission’ persists. Finally, I question a persistent belief about permissions: that unlike obligations they must be considered one by one, and not collectively.


Deontic logic Logic of norms Free choice permission 



A draft of this contribution was presented at a workshop held in Ghent, Belgium, on 25 May 2012 in honor of the Ph.D. obtained by F. van de Putte, and I thank D. Makinson, D. Batens and M. Beirlaen for critical remarks at this occasion and later on. I thank A. Stolpe and M. Sergot for their criticism and help in overcoming countless mistakes. I am indebted to L. Goble, whose comments and suggestions improved anything of value in this contribution considerably.


  1. Alchourrón, C. E. (1969). Logic of norms and logic of normative propositions. Logique and Analyse, 12, 242–268.Google Scholar
  2. Alchourrón, C. E. (1972). The intuitive background of normative legal discourse and its formalization. Journal of Philosophical Logic, 1, 447–463.Google Scholar
  3. Alchourrón, C. E., Bulygin, E. (1981). The expressive conception of norms. In R. Hilpinen (Ed.), New studies in deontic logic (pp. 95–124). Dordrecht: Reidel.Google Scholar
  4. Alchourrón, C. E., & Bulygin, E. (1984). Permission and permissive norms. In W. Krawietz, H. Schelsky, O. Weinberger, & G. Winkler (Eds.), Theorie der Normen (pp. 349–371). Berlin: Duncker & Humblot.Google Scholar
  5. Alchourrón, C. E., & Bulygin, E. (1993). On the logic of normative systems. In H. Stachowiak (Ed.), Handbuch pragmatischen Denkens (pp. 273–293). Hamburg: Meiner.Google Scholar
  6. Alchourrón, C. E., & Makinson, D. (1981). Hierarchies of regulations and their logic. In R. Hilpinen (Ed.), New studies in deontic logic (pp. 125–148). Dordrecht: Reidel.Google Scholar
  7. Barcan Marcus, R. (1980). Moral dilemmas and consistency. Journal of Philosophy, 77, 121–136.Google Scholar
  8. Bentham, J. (1970). Of laws in general. In H. L. A. Hart (Ed.). London: Athlone Press (first appeared 1782).Google Scholar
  9. Bochman, A. (1999). Credulous nonmonotonic inference. In T. Dean (Ed.), Proceedings of the 16th International Joint Conference on Artificial Intelligence, IJCAI ’99, Stockholm, August 1999 (pp. 30–35). San Francisco: Morgan Kaufmann.Google Scholar
  10. Boella, G., van der Torre, L. (2003). Permissions and obligations in hierarchical normative systems. In Proceedings of the 9th International Conference on Artificial Intelligence and Law, ICAIL ’03 (pp. 109–118) (republ. w. minor changes as Boella (2008)).Google Scholar
  11. Boella, G., van der Torre, L. (2008). Institutions with a hierarchy of authorities in distributed dynamic environments. Artificial Intelligence and Law, 16, 53–71.Google Scholar
  12. Brewka, G. (1989). Preferred subtheories: An extended logical framework for default reasoning. In N. S. Sridharan (Ed.), Proceedings of the Eleventh International Joint Conference on Artificial Intelligence IJCAI-89, Detroit, Michigan, USA, August 20–25, 1989 (pp. 1043–1048). San Mateo: Kaufmann.Google Scholar
  13. Brewka, G. (1991). Belief revision in a framework for default reasoning. In A. Fuhrmann & M. Morreau (Eds.), The Logic of Theory Change, Workshop, Konstanz, Germany, October 13–15, 1989 (pp. 206–222). Berlin: Springer.Google Scholar
  14. Bulygin, E. (1986). Permissive norms and normative systems. In A. A. Martino & F. Socci Natali (Eds.), Automated Analysis of Legal Texts (pp. 211–218). North-Holland: Elsevier.Google Scholar
  15. van Fraassen, B. (1973). Values and the heart’s command. Journal of Philosophy, 70, 5–19.Google Scholar
  16. Goble, L. (1990). A logic of good, should, and would. Journal of Philosophical Logic, 19, 169–199.Google Scholar
  17. Goble, L. (2000). Multiplex semantics for deontic logics. Nordic Journal of Philosophical Logic, 5, 113–134.Google Scholar
  18. Goble, L. (2003). Preference semantics for deontic logics: Part I—simple models. Logique et Analyse, 46, 383–418.Google Scholar
  19. Goble, L. (2004). Preference semantics for deontic logics: Part II—multiplex models. Logique et Analyse, 47, 335–363.Google Scholar
  20. Hamblin, C. L. (1987). Imperatives. Oxford: Blackwell.Google Scholar
  21. Hansen, J. (2001). Sets, sentences, and some logics about imperatives. Fundamenta Informaticae, 48, 205–226.Google Scholar
  22. Hansen, J. (2004). Problems and results for logics about imperatives. Journal of Applied Logic, 2, 39–61.Google Scholar
  23. Hansen, J. (2005). Conflicting imperatives and dyadic deontic logic. Journal of Applied Logic, 3, 484–511.Google Scholar
  24. Hansen, J. (2006). Deontic logics for prioritized imperatives. Artificial Intelligence and Law, 14, 1–34.Google Scholar
  25. Hansen, J. (2008a). Imperatives and deontic logic: On the semantic foundations of deontic logic. Ph.D. thesis, Universität Leipzig, Inst. f. Philosophie, Leipzig.Google Scholar
  26. Hansen, J. (2008b). Prioritized conditional imperatives: Problems and a new proposal. Autonomous Agents and Multi-Agent Systems, 17, 11–35.Google Scholar
  27. Hansson, B. (1969). An analysis of some deontic logics. Noûs, 3, 373–398 (reprinted in Hilpinen (1971)).Google Scholar
  28. Hansson, S. O. (1999). A textbook of belief dynamics: Theory change and dabase updating. Dordrecht: Kluwer.Google Scholar
  29. Hansson, S. O. (2013). The varieties of permission. In D. Gabbay, J. F. Horty, R. van der Meyden, & L. van der Torre (Eds.), Handbook of deontic logic and normative systems (Vol. 1). London: College Publications.Google Scholar
  30. Hare, R. M. (1967). Some alleged differences between imperatives and indicatives. Mind, 76, 309–326.Google Scholar
  31. Hart, H. L. A. (1961). The concept of law. Oxford: Clarendon Press.Google Scholar
  32. Hilpinen, R. (1971). Deontic logic: Introductory and systematic readings. Dordrecht: Reidel.Google Scholar
  33. Hilpinen, R. (1982). Disjunctive permissions and conditionals with disjunctive antecedents. Acta Philosophica Fennica, 35, 175–194.Google Scholar
  34. Horty, J. F. (1993). Deontic logic as founded on nonmonotonic logic. Annals of Mathematics and Artificial Intelligence, 9, 69–91.Google Scholar
  35. Horty, J. F. (1994). Moral dilemmas and nonmonotonic logic. Journal of Philosophical Logic, 23, 35–65.Google Scholar
  36. Horty, J. F. (1997). Nonmonotonic foundations for deontic logic. In D. Nute (Ed.), Defeasible deontic logic (pp. 17–44). Dordrecht: Kluwer.Google Scholar
  37. Hruschka, J. (1986). Das deontologische Sechseck bei Gottfried Achenwall im Jahre 1767. Göttingen: Vandenhoek & RuprechtGoogle Scholar
  38. Kamp, H. (1973). Free choice permission. Proceedings of the Aristotelian Society, 74, 57–74.Google Scholar
  39. Kamp, H. (1978). Semantics versus pragmatics. In F. Guenthner & S. J. Schmidt (Eds.), Formal semantics and pragmatics for natural languages (pp. 255–287). Dordrecht: Reidel.Google Scholar
  40. Kraus, S., Lehmann, D., & Magidor, M. (1990). Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence, 44, 167–207.Google Scholar
  41. Leibniz, G. W. (1930). Elementa juris naturalis [2nd half 1671, holographic concept B (Hannover)]. In Preussische Akademie der Wissenschaften (Ed.), Gottfried Wilhelm Leibniz: Sämtliche Schriften und Briefe, 6. Reihe: Philosophische Schriften (Vol. 1, pp. 465–485). Darmstadt: Otto Reichl.Google Scholar
  42. Lewis, D. (1974). Semantic analyses for dyadic deontic logic. In S. Stenlund (Ed.), Logical theory and semantic analysis (pp. 1–14). Dordrecht: Reidel.Google Scholar
  43. Lewis, D. (1979). A problem about permission. In E. Saarinen, R. Hilpinen, I. Niiniluoto, & M. Provence Hintikka (Eds.), Essays in honour of Jaakko Hintikka (pp. 163–175). Dordrecht: D. Reidel.Google Scholar
  44. Makinson, D. (1999). On a fundamental problem of deontic logic. In P. McNamara & H. Prakken (Eds.), Norms, logics and information systems (pp. 29–53). Amsterdam: IOS.Google Scholar
  45. Makinson, D. (2005). Bridges from classical to nonmonotonic logic. London: King’s College.Google Scholar
  46. Makinson, D., & van der Torre, L. (2000). Input/output logics. Journal of Philosophical Logic, 29, 383–408.Google Scholar
  47. Makinson, D., & van der Torre, L. (2001). Constraints for input/output logics. Journal of Philosophical Logic, 30, 155–185.Google Scholar
  48. Makinson, D., & van der Torre, L. (2003). Permissions from an input/output perspective. Journal of Philosophical Logic, 32, 391–416.Google Scholar
  49. Prakken, H., Sergot, M. (1997). Dyadic deontic logic and contrary-to-duty obligations. In D. Nute (Ed.), Defeasible deontic logic (pp. 223–262). Dordrecht: Kluwer.Google Scholar
  50. Ross, A. (1941). Imperatives and logic. Theoria, 7, 53–71.Google Scholar
  51. Schwager, M. (2006). Interpreting imperatives. Ph.D. thesis, Johann-Wolfgang-von-Goethe Universität, Institut für Kognitive Linguistik, Frankfurt am Main.Google Scholar
  52. Spohn, W. (1975). An analysis of Hansson’s dyadic deontic logic. Journal of Philosophical Logic, 4, 237–252.Google Scholar
  53. Stolpe, A. (2010). A theory of permission based on the notion of derogation. Journal of Applied Logic, 8, 97–113.Google Scholar
  54. Weinberger, O. (1958). Die Sollsatzproblematik in der modernen Logik: Können Sollsätze (Imperative) als wahr bezeichnet werden? Prague: Nakladatelství Ceskoslovenské Akademie Ved. Page numbers refer to the reprint in Weinberger (1974) pp. 59–186.Google Scholar
  55. Weinberger, O. (1974). Studien zur Normlogik und Rechtsinformatik. Berlin: Schweitzer.Google Scholar
  56. Weinberger, O. (1989). Rechtslogik (2nd ed.). Berlin: Duncker & Humblot.Google Scholar
  57. Weinberger, O. (1991). The logic of norms founded on descriptive language. Ratio Juris, 4, 284–307.Google Scholar
  58. Weinberger, O. (1996). Alternative Handlungstheorie. Wien: Böhlau.Google Scholar
  59. Weinberger, O. (1999). Logical analysis in the realm of law . In G. Meggle (Ed.), Actions, norms, values: Discussions with Georg Henrik von Wright (pp. 291–304). Berlin: De Gruyter.Google Scholar
  60. von Wright, G. H. (1951). Deontic logic. Mind, 60, 1–15.Google Scholar
  61. von Wright, G. H. (1963). Norm and action. London: Routledge & Kegan Paul.Google Scholar
  62. von Wright, G. H. (1980). Problems and prospects of deontic logic. In E. Agazzi (Ed.), Modern logic: A survey (pp. 399–423). Dordrecht: D. Reidel.Google Scholar
  63. von Wright, G.H. (1983). Norms, truth and logic. In G. H. von Wright (Ed.), Practical reason: Philosophical papers (Vol. 1, pp. 130–209). Oxford: Blackwell.Google Scholar
  64. von Wright, G. H. (1991). Is there a logic of norms? Ratio Juris, 4, 265–283.Google Scholar
  65. von Wright, G. H. (1993). A pilgrim’s progress. In G. H. von Wright (Ed.), The tree of knowledge and other essays (pp. 103–113). Leiden: Brill.Google Scholar
  66. von Wright, G. H. (1999a). Deontic logic—as I see it. In P. McNamara & H. Prakken (Eds.), Norms, logics and information systems (pp. 15–25). Amsterdam: IOS.Google Scholar
  67. von Wright, G. H. (1999b). Ought to be—ought to do. In G. Meggle (Ed.), Actions, norms, values: Discussions with Georg Henrik von Wright (pp. 3–9). Berlin: De Gruyter.Google Scholar

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© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.EisenachGermany

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