Introducing Grades in Deontic Logics

  • Pilar Dellunde
  • Lluís Godo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5076)

Abstract

In this paper we define a framework to introduce gradedness in Deontic logics through the use of fuzzy modalities. By way of example, we instantiate the framework to Standard Deontic logic (SDL) formulas. Given a deontic formula Φ ∈ SDL, our language contains formulas of the form \(\overline{r} \to N\Phi\) or \(\overline{r} \to P\Phi\), where r ∈ [0, 1], expressing that the preference or probability degree respectively of a norm Φ is at least r. We present sound and complete axiomatisations for these logics.

Keywords

Deontic Logic Fuzzy Logic Norms Institutions 

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References

  1. 1.
    Ågotnes, T., van der Hoek, W., Rodríguez-Aguilar, J.A., Sierra, C., Wooldridge, M.: On the Logic of Normative Systems. In: Twentieth International Joint Conference on AI, IJCAI 2007, pp. 1175–1180. AAAI Press, Menlo Park (2007)Google Scholar
  2. 2.
    Aqvist, L.: Deontic Logic. In: Gabbay, et al. (eds.) Handbook of Philosophical Logic, vol. 8, pp. 147–265 (2001)Google Scholar
  3. 3.
    Benferhat, S., Dubois, D., Prade, H.: Towards a possibilistic logic handling of preferences. Applied Intelligence 14, 303–317 (2001)CrossRefMATHGoogle Scholar
  4. 4.
    Burns, T.R., Carson, M.: Actors, Paradigms, and Institutional Dynamics: The Theory of Social Rule Systems Applied to Radical Reforms. In: Hollingsworth, R., et al. (eds.) Advancing Socio-Economics: An Institutionalist Perspective, pp. 109–147. Rowman and Littlefield Publishers, New York (2002)Google Scholar
  5. 5.
    Broersen, J., Dastani, M., Hustijin, J., Torre, L.W.: Goal generation in the BOID architecture. Cognitive Science Quaterly 2, 428–447 (2002)Google Scholar
  6. 6.
    Broersen, J., Dastani, M., Torre, L.W.: Resolving Conflicts between Beliefs, Obligations, Intentions, and Desires. In: Benferhat, S., Besnard, P. (eds.) ECSQARU 2001. LNCS (LNAI), vol. 2143, pp. 568–579. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  7. 7.
    Casali, A., Godo, L., Sierra, C.: Graded BDI Models for Agent Architectures. In: Leite, J.A., Torroni, P. (eds.) CLIMA 2004. LNCS (LNAI), vol. 3487, pp. 126–143. Springer, Heidelberg (2005)Google Scholar
  8. 8.
    Dignum, F., Morley, D., Sonenberg, E.A., Cavedon, L.: Towards Socially Sophisticated BDI Agents. In: Proc. 4th Int. Conf. on Multi-Agent Systems ICMAS-2000, Boston, MA, pp. 111–118 (2000)Google Scholar
  9. 9.
    García-Camino, A., Rodríguez-Aguilar, J.A., Vasconcelos, W.: Distributed Norm Management in Regulated Multi-agent Systems. In: Procs. of 6th Int’l Conf. on Autonomous Agents and Multiagent Systems (AAMAS 2007), Hawai’i, pp. 624–631 (2007)Google Scholar
  10. 10.
    Godo, L., Hájek, P., Esteva, F.: A Fuzzy Modal Logic for Belief Functions. Fundamenta Informaticae, pp. 1001–1020 (2001)Google Scholar
  11. 11.
    Governatori, G., Rotolo, A.: BIO Logical Agents: Norms, Beliefs, Intentions in Defeasible Logic. In: Boella, G., van der Torre, L., Verhagen, H. (eds.) Normative Multi-agent Systems. Dagstuhl Seminar Proceedings, 07122 (2007), http://drops.dagstuhl.de/opus/volltexte/2007/912
  12. 12.
    Grossi, D., Meyer, J.-J.Ch., Dignum, F.: Modal logic investigations in the semantics of counts-as. In: ICAIL 2005: Proceedings of the 10th international conference on Artificial intelligence and law, Bologna, Italy, pp. 1–9. ACM, New York (2005)CrossRefGoogle Scholar
  13. 13.
    Hájek, P.: Metamatematics of Fuzzy Logic. Trends in Logic, vol. 4. Kluwer Academic Publishers, Dordrecht (1998)Google Scholar
  14. 14.
    Halpern, J.Y.: Reasoning about Uncertainty. The MIT Press, Cambridge Massachusetts (2003)MATHGoogle Scholar
  15. 15.
    Harel, D.: Dynamic logic. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, vol. II, pp. 497–604 (1984)Google Scholar
  16. 16.
    Knijnenburg, P.M.W., van Leeuwen, J.: On Models for Propositional Dynamic Logic. Theor. Comput. Sci. 91(2), 181–203 (1991)CrossRefMATHGoogle Scholar
  17. 17.
    Liau, C.J.: On the possibility theory-based semantics for logics of preference. International Journal of Approximate Reasoning 20, 173–190 (1999)CrossRefMathSciNetMATHGoogle Scholar
  18. 18.
    Meyer, J.-J.Ch., Veltman, F.: Intelligent Agents and Common-Sense Reasoning. In: Blackburn, P., et al. (eds.) Handbook of Modal Logic. Studies in Logic and Practical Reasoning, vol. 3, pp. 991–1030 (2006)Google Scholar
  19. 19.
    Meyer, J.-J.Ch.: A Different Approach to Deontic Logic: Deontic Logic viewed as a variant of Dynamic Logic. Notre Dame Journal of Formal Logic 29(1), 109–136 (1998)CrossRefGoogle Scholar
  20. 20.
    Nickles, M.: Towards a Logic of Graded Normativity and Norm Adherence. In: Boella, G., van der Torre, L., Verhagen, H. (eds.) Normative Multi-agent Systems. Dagstuhl Seminar Proceedings, 07122 (2007), http://drops.dagstuhl.de/opus/volltexte/2007/926
  21. 21.
    Pavelka, J.: On fuzzy logic I, II, III. Zeitschrift für Mathematische Logik and Grundlagen der Mathematik 25, 45–52, 119–134, 447–464 (1979)CrossRefMathSciNetMATHGoogle Scholar
  22. 22.
    Pratt, V.R.: Semantical considerations on Floyd-Hoare logic. In: Proceedings of the 17th IEEE Symposium on the Foundations of Computer Science, pp. 109–121 (1976)Google Scholar
  23. 23.
    Ross, W.D.: Foundations of Ethics. Oxford University Press, London (1939)Google Scholar
  24. 24.
    Thomason, R.H.: Desires and Defaults: A Framework for Planning with Inferred Goals. In: Proceedings of the KR 2000, pp. 702–713. Morgan Kaufmann, San Francisco (2000)Google Scholar
  25. 25.
    van der Hoek, W., Wooldridge, M.: On obligations and normative ability: towards a logical analysis of the social contract. Journal of Applied Logic 3, 396–420 (2005)CrossRefMathSciNetMATHGoogle Scholar
  26. 26.
    van der Torre, L., Tan, Y.-H.: Contrary-to-duty reasoning with preference-based dyadic obligations. Annals of Mathematics and Artificial Intelligence 27, 49–78 (1999)CrossRefMathSciNetMATHGoogle Scholar
  27. 27.
    van Linder, B.: Modal Logics for Rational Agents, PhD. Thesis, Utrecht University (1996)Google Scholar
  28. 28.
    von Wright, G.H.: Deontic Logic. Mind 60, 1–15 (1951)CrossRefGoogle Scholar
  29. 29.
    von Wright, G.H.: A New System of Deontic Logic. Danish Yearbook of Philosophy 1 (1964)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Pilar Dellunde
    • 1
    • 2
  • Lluís Godo
    • 2
  1. 1.Univ. Autònoma de BarcelonaBellaterraSpain
  2. 2.IIIA - CSICBellaterraSpain

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