On the Strong Completeness of Åqvist’s Dyadic Deontic Logic G

  • Xavier Parent
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5076)

Abstract

Åqvist’s dyadic deontic logic G, which aims at providing an axiomatic characterization of Hansson’s seminal system DSDL3 for conditional obligation, is shown to be strongly complete with respect to its intended modelling.

Keywords

Conditional obligation preference-based semantics strong completeness DSDL3 

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References

  1. 1.
    Hansson, B.: An analysis of some deontic logics. Noûs 4, 373–398 (1969)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Mott, P.: On Chisholm’s paradox. Journal of Philosophical Logic 2, 197–211 (1973)CrossRefMathSciNetMATHGoogle Scholar
  3. 3.
    Tomberlin, J.: Contrary-to-duty imperatives and conditional obligation. Noûs 16, 357–375 (1981)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Loewer, B., Belzer, M.: Dyadic deontic detachment. Synthese 54, 295–318 (1983)CrossRefMathSciNetMATHGoogle Scholar
  5. 5.
    Prakken, H., Sergot, M.: Dyadic deontic logic and contrary-to-duty obligation. In: [29], pp. 223–262Google Scholar
  6. 6.
    van der Torre, L., Tan, Y.H.: The many faces of defeasibility in defeasible deontic logic. In: [29], pp. 79–121Google Scholar
  7. 7.
    Carmo, J., Jones, A.: Deontic logic and contrary-to-duties. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, 2nd edn., vol. 8, pp. 265–343. Kluwer Academic Publishers, Dordrecht (2002)Google Scholar
  8. 8.
    Parent, X.: Remedial interchange, contrary-to-duty obligation and commutation. Journal of Applied Non-Classical Logics 3/4, 345–375 (2003)CrossRefGoogle Scholar
  9. 9.
    Spohn, W.: An analysis of Hansson’s dyadic deontic logic. Journal of Philosophical Logic 4, 237–252 (1975)CrossRefMathSciNetMATHGoogle Scholar
  10. 10.
    Åqvist, L.: An Introduction to Deontic logic and the Theory of Normative Systems, Bibliopolis, Naples (1987)Google Scholar
  11. 11.
    Åqvist, L.: Deontic logic. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, 2nd edn., vol. 8, pp. 147–264. Kluwer Academic Publishers, Dordrecht (2002)Google Scholar
  12. 12.
    Goranko, V., Passy, S.: Using the universal modality: Gains and questions. Journal of Logic and Computation 2, 5–30 (1992)CrossRefMathSciNetMATHGoogle Scholar
  13. 13.
    Sen, A.: Maximization and the act of choice. Econometrica 65, 745–779 (1997)CrossRefMathSciNetMATHGoogle Scholar
  14. 14.
    Makinson, D.: Bridges from Classical to Nonmonotonic logic. King’s College Publications, London (2005)MATHGoogle Scholar
  15. 15.
    Schlechta, K.: Coherent Systems. Elsevier, Amsterdam (2004)MATHGoogle Scholar
  16. 16.
    Lewis, D.: Counterfactuals. Blackwell, Oxford (1973)Google Scholar
  17. 17.
    Parent, X.: Non-monotonic Logics and Modes of Argumentation − The Case of Conditional Obligation. PhD thesis, University of Aix-Marseille I, France (2002)Google Scholar
  18. 18.
    Kraus, S., Lehmann, D., Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence 44, 167–207 (1990)CrossRefMathSciNetMATHGoogle Scholar
  19. 19.
    Lehmann, D., Magidor, M.: What does a conditional knowledge base entail? Artificial Intelligence 55, 1–60 (1992)CrossRefMathSciNetMATHGoogle Scholar
  20. 20.
    Goble, L.: A proposal for dealing with deontic dilemmas. In: Lomuscio, A., Nute, D. (eds.) DEON 2004. LNCS (LNAI), vol. 3065, pp. 74–113. Springer, Heidelberg (2004)Google Scholar
  21. 21.
    Chellas, B.: Modal Logic. Cambridge University Press, Cambridge (1980)MATHGoogle Scholar
  22. 22.
    Blackburn, P., de Rijke, M., de Venema, Y.: Modal Logic, vol. 53. Cambrigde University Press, Cambridge (2001)MATHGoogle Scholar
  23. 23.
    Åqvist, L.: A completeness theorem in deontic logic with systematic frame constants. Logique & Analyse 36, 177–192 (1993)MATHGoogle Scholar
  24. 24.
    Hansen, J.: On relations between Åqvist’s deontic system G and van Eck’s deontic temporal logic. In: Mc Namara, P., Prakken, H. (eds.) Norms, Logics and Information Systems. Frontiers in Artificial Intelligence and Applications, pp. 127–144. IOS Press, Amsterdam (1999)Google Scholar
  25. 25.
    Makinson, D.: General patterns in nonmonotonic reasoning. In: Gabbay, D., Hogger, C., Robinson, J. (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming, pp. 35–110. Clarendon Press, Oxford (1994)Google Scholar
  26. 26.
    Boutilier, G.: Unifying default reasoning and belief revision in a modal framework. Artificial Intelligence 68, 33–85 (1994)CrossRefMathSciNetMATHGoogle Scholar
  27. 27.
    van der Torre, L., Tan, Y.H.: Contrary-to-duty reasoning with preference-based dyadic obligations. Annals of Mathematics and Artificial Intelligence 27(1-4), 49–78 (1999)CrossRefMathSciNetMATHGoogle Scholar
  28. 28.
    Makinson, D.: General theory of cumulative inference. In: Reinfrank, M., Ginsberg, M.L., de Kleer, J., Sandewall, E. (eds.) Non-Monotonic Reasoning 1988. LNCS, vol. 346, pp. 1–18. Springer, Heidelberg (1989)Google Scholar
  29. 29.
    Nute, D. (ed.): Defeasible Deontic Logic. Kluwer Academic Publishers, Dordrecht (1997)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Xavier Parent
    • 1
  1. 1. ToulonFrance

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