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Semantics for Modelling Reason-Based Preferences

  • Erica Calardo
  • Guido Governatori
  • Antonino Rotolo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9387)

Abstract

In [13] the authors developed a logical system based on the definition of a new non-classical connective \(\otimes \) originally capturing the notion of reparative obligation. The operator \(\otimes \) and the system were proved to be appropriate for rather handling well-known contrary-to-duty paradoxes. Later on, a suitable model-theoretic possible-world semantics has been developed [4, 5]. In this paper we show how a version of this semantics can be used to develop a sound and complete logic of preference and offer a suitable possible-world semantics. The semantics is a sequence-based non-normal one extending and generalising semantics for classical modal logics.

Keywords

Modal Logic Canonical Model Deontic Logic Propositional Formula Sequence Frame 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Boutilier, C., Brafman, R.I., Domshlak, C., Hoos, H.H., Poole, D.: Cp-nets: A tool for representing and reasoning with conditional ceteris paribus preference statements. J. Artif. Intell. Res. (JAIR) 21, 135–191 (2004)MathSciNetMATHGoogle Scholar
  2. 2.
    Brandt, F., Conitzer, V., Endriss, U.: Computational social choice. In: Multiagent Systems, MIT Press (2012)Google Scholar
  3. 3.
    Brewka, G., Benferhat, S., Le Berre, D.: Qualitative choice logic. Artif. Intell. 157(1–2), 203–237 (2004)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Calardo, E., Governatori, G., Rotolo, A.: A preference-based semantics for CTD reasoning. In: Cariani, F., Grossi, D., Meheus, J., Parent, X. (eds.) DEON 2014. LNCS, vol. 8554, pp. 49–64. Springer, Heidelberg (2014) Google Scholar
  5. 5.
    Calardo, E., Governatori, G., Rotolo, A.: A sequence semantics for deontic logic. Under submission (2015)Google Scholar
  6. 6.
    Chellas, B.F.: Modal Logic: An Introduction. Cambridge University Press (1980)Google Scholar
  7. 7.
    Coste-Marquis, S., Lang, J., Liberatore, P., Marquis, P.: Expressive power and succinctness of propositional languages for preference representation. In: Principles of Knowledge Representation and Reasoning: Proceedings of the Ninth International Conference (KR2004), pp. 203–212, Whistler, Canada, June 2–5, 2004 (2004)Google Scholar
  8. 8.
    Dastani, M., Governatori, G., Rotolo, A., van der Torre, L.W.N.: Preferences of agents in defeasible logic. In: Zhang, S., Jarvis, R.A. (eds.) AI 2005. LNCS (LNAI), vol. 3809, pp. 695–704. Springer, Heidelberg (2005) CrossRefGoogle Scholar
  9. 9.
    Dastani, M., Governatori, G., Rotolo, A., van der Torre, L.W.N.: Programming cognitive agents in defeasible logic. In: Sutcliffe, G., Voronkov, A. (eds.) LPAR 2005. LNCS (LNAI), vol. 3835, pp. 621–636. Springer, Heidelberg (2005) CrossRefGoogle Scholar
  10. 10.
    Fitting, M.: Proof Methods for Modal and Intuitionistic Logics. Springer (1983)Google Scholar
  11. 11.
    Gaertner, W.: A Primer in Social Choice Theory: Revised Edition. Oup Oxford (2009)Google Scholar
  12. 12.
    Governatori, G., Olivieri, F., Scannapieco, S., Rotolo, A., Cristani, M.: The rational behind the concept of goal. Theory and Practice of Logic Programming, forthcomingGoogle Scholar
  13. 13.
    Governatori, G., Rotolo, A.: Logic of violations: A Gentzen system for reasoning with contrary-to-duty obligations. Australasian Journal of Logic 4, 193–215 (2006)MathSciNetMATHGoogle Scholar
  14. 14.
    Hansen, J.: Conflicting imperatives and dyadic deontic logic. J. Applied Logic 3(3–4), 484–511 (2005)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Hansson, B.: An analysis of some deontic logics. Nous 3, 373–398 (1969)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Jiang, G., Zhang, D., Perrussel, L., Zhang, H.: A logic for collective choice. In: Proceedings of the 2015 International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2015, pp. 979–987, Istanbul, Turkey, May 4–8, 2015 (2015)Google Scholar
  17. 17.
    Lang, J.: Logical preference representation and combinatorial vote. Ann. Math. Artif. Intell. 42(1–3), 37–71 (2004)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Osherson, D., Weinstein, S.: Preference based on reasons. The Review of Symbolic Logic 5, 122–147 (2012)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Prakken, H., Sergot, M.J.: Contrary-to-duty obligations. Studia Logica 57(1), 91–115 (1996)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Sen, A.: Social choice theory: A re-examination. Econometrica 45(1), 53–89 (1977)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    van Benthem, J., Grossi, D., Liu, F.: Priority structures in deontic logic. Theoria (2013)Google Scholar
  22. 22.
    van der Torre, L.: Reasoning about obligations: defeasibility in preference-based deontic logic. PhD thesis, Erasmus University Rotterdam (1997)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Erica Calardo
    • 1
  • Guido Governatori
    • 2
  • Antonino Rotolo
    • 1
  1. 1.CIRSFIDUniversity of BolognaBolognaItaly
  2. 2.Software Systems Research GroupNICTABrisbaneAustralia

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