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A Dyadic Operator for the Gradation of Desirability

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Deontic Logic in Computer Science (DEON 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6181))

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Abstract

We propose a normal modal deontic logic based on a dyadic operator, similar in structure to the temporal “until”. By bringing significant expressiveness to the logic, it allows both the definition of a monadic desirability operator similar to the SDL obligation, and the expression of the relative level of desirability of target formulae. The interpretation of this logic on a linear structure of worlds ordered by desirability makes its semantics more intuitive and concrete than the SDL deontic accessibility relation. We also show that the core modality of the logic permits to represent the Chisholm and Forrester paradoxes of deontic logic in a more precise way, which does not lead to inconsistencies.

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References

  1. von Wright, G.H.: Deontic logic. Mind 60, 1–15 (1951)

    Article  Google Scholar 

  2. Ryu, Y.U.: Relativized deontic modalities for contractual obligations in formal business communication. In: Proceedings of the 30th Hawaii International Conference on System Sciences (HICCS’97), p. 485. IEEE Computer Society, Washington (1997)

    Google Scholar 

  3. Hansson, B.: An analysis of some deontic logics. Nôus 3, 373–398 (1969)

    MathSciNet  Google Scholar 

  4. Prakken, H., Sergot, M.J.: Dyadic deontic logics and contrary-to-duty obligations. Synthese Library 263, 223–262 (1997)

    Google Scholar 

  5. Pnueli, A.: The temporal logic of programs. In: Proceedings of the 18th IEEE Symposium on the Foundations of Computer Science (FOCS-77), pp. 46–57. IEEE Computer Society Press, Providence (1977)

    Google Scholar 

  6. Chisholm, R.M.: Contrary-to-duties imperatives and deontic logic. Analysis 24, 33–36 (1963)

    Article  Google Scholar 

  7. Forrester, J.W.: Gentle murderer, or the adverbial samaritan. Journal of Philosophy 81, 193–196 (1984)

    Article  MathSciNet  Google Scholar 

  8. Kamp, J.A.W.: Tense Logic and the Theory of Linear Order. PhD thesis, University of California at Los Angeles (1968)

    Google Scholar 

  9. Chellas, B.F.: Modal Logic, an Introduction. Cambridge University Press, Cambridge (1980)

    MATH  Google Scholar 

  10. Reynolds, M.: The complexity of the temporal logic with until over general linear time. Journal of Computer and System Sciences 66(2), 393–426 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  11. Ladner, R.: The computational complexity of provability in systems of modal propositional logic. SIAM Journal of Computing 6, 467–480 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  12. Ross, A.: Imperatives and logic. Theoria, 53–71 (1941)

    Google Scholar 

  13. Prior, A.N.: The paradoxes of derived obligation. Mind 63, 64–65 (1954)

    Article  Google Scholar 

  14. Prior, A.N.: Escapism. In: Essays in Moral Philosophy, pp. 135–146. University of Washington Press, Seattle (1958)

    Google Scholar 

  15. Lemmon, E.J.: Moral dilemmas. Philosophical Review 71, 139–158 (1962)

    Article  Google Scholar 

  16. McNamara, P.: Deontic logic. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy. Stanford University, Standford (2006)

    Google Scholar 

  17. Jones, A.J.I., Pörn, I.: Ideality, sub-ideality and deontic logic. Synthese 65, 275–290 (1985)

    Article  MathSciNet  Google Scholar 

  18. Prakken, H., Sergot, M.J.: Contrary-to-duty obligations. Studia Logica 57(1), 91–115 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  19. Hansson, S.O.: Semantics for more plausible deontic logics. In: DEON’02, London, UK (May 2002)

    Google Scholar 

  20. Sahlqvist, H.: Correspondence and completeness in the first- and second-order semantics for modal logic. In: Proceedings of the Third Scandinavian Logic Symposium. North-Holland, Amsterdam (1975)

    Google Scholar 

  21. Cholvy, L., Cuppens, F.: Analyzing consistency of security policies. In: Proceedings of the 18th IEEE Symposium on Research in Security and Privacy, Oakland, CA, USA (May 1997)

    Google Scholar 

  22. Cholvy, L., Cuppens, F.: Reasoning about norms provided by conflicting regulations. In: Prakken, H., McNamara, P. (eds.) Norms, Logics and Information Systems: New Studies in Deontic Logic and Computer Science, pp. 247–264. IOS Press, Amsterdam (1998)

    Google Scholar 

  23. Lewis, D.: Semantic analyses for dyadic deontic logic. Logical theory and semantic analysis, 1–14 (1974)

    Google Scholar 

  24. Cholvy, L., Garion, C.: Utilisation d’une logique de préférences conditionnelles pour raisonner avec des normes contrary-to-duties. Journées Nationales sur les Modéles de Raisonnement, Arras, France (May 2001)

    Google Scholar 

  25. Dignum, F., Broersen, J., Dignum, V., Meyer, J.J.: Meeting the deadline: Why, when and how. In: Hinchey, M.G., Rash, J.L., Truszkowski, W., Rouff, C. (eds.) FAABS 2004. LNCS (LNAI), vol. 3228, pp. 30–40. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  26. Governatori, G., Rotolo, A.: A gentzen system for reasoning with contrary-to-duty obligations. a preliminary study. In: Jones, A.J.I., Horty, J. (eds.) Sixth international workshop on deontic logic in computer science (DEON’02), London, UK, Imperial College, May 2002, pp. 97–116 (2002)

    Google Scholar 

  27. Nute, D.: Apparent obligation. In: Defeasible Deontic Logic: Essays in Nonmonotonic Normative Reasoning, pp. 287–316. Kluwer Academic Publishers, Dordrecht (1997)

    Google Scholar 

  28. van der Torre, L.W.N.: Violated obligations in a defeasible deontic logic. In: Cohn, A. (ed.) Proceedings of the 11th European Conference on Artificial Intelligence, pp. 371–375. John Wiley and Sons, Chichester (1994)

    Google Scholar 

  29. Governatori, G.: Representing business contracts in ruleml. International Journal of Cooperative Information Systems 14(2-3), 181–216 (2005)

    Article  Google Scholar 

  30. Demolombe, R.: Formalisation de l’obligation de faire avec délais. Troisièmes journées francophones des modèles formels de l’interaction (MFI’05), Caen, France (May 2005)

    Google Scholar 

  31. Brunel, J., Cuppens, F., Cuppens-Boulahia, N., Sans, T., Bodeveix, J.P.: Security policy compliance with violation management. In: ACM workshop on Formal methods in security engineering (FMSE’07), Fairfax, Virginia, USA, pp. 31–40. ACM Press, New York (2007)

    Chapter  Google Scholar 

  32. Dignum, F., Kuiper, R.: Specifying deadlines with dense time using deontic and temporal logic. International Journal of Electronic Commerce 3(2), 67–86 (1999)

    Google Scholar 

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Author information

Authors and Affiliations

  1. INRIA Grenoble Rhône-Alpes, Inovallée, 655 avenue de l’Europe, 38334, Saint-Ismier Cedex, France

    Guillaume Piolle

Authors
  1. Guillaume Piolle
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Editors and Affiliations

  1. Queensland Research Laboratory, National ICT Australia, 4067, St Lucia, QLD, Australia

    Guido Governatori

  2. European University Institute, Badia Fiesolana, 50016 San Domenico di Fiesole, Florence, Italy, and University of Bologna, Via Zamboni, 33, 40126, Bologna, Italy

    Giovanni Sartor

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Piolle, G. (2010). A Dyadic Operator for the Gradation of Desirability. In: Governatori, G., Sartor, G. (eds) Deontic Logic in Computer Science. DEON 2010. Lecture Notes in Computer Science(), vol 6181. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14183-6_5

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  • DOI: https://doi.org/10.1007/978-3-642-14183-6_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14182-9

  • Online ISBN: 978-3-642-14183-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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