Advertisement

Tableaux for Acceptance Logic

  • Mathijs de Boer
  • Andreas Herzig
  • Tiago de Lima
  • Emiliano Lorini
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5948)

Abstract

We continue the work initiated in [1,2,3], where the acceptance logic, a modal logic for modelling individual and collective acceptances was introduced. This logic is aimed at capturing the concept of acceptance qua member of an institution as the kind of attitude that agents are committed to when they are “functioning as members of an institution”. Acceptance logic can also be used to model judgement aggregation: it deals with how a collective acceptance of the members of an institution about a certain fact φ is created from the individual acceptances of the members of the institution. The contribution of this paper is to present a tableau method for the logic of acceptance. The method automatically decides whether a formula of the logic of acceptance is satisfiable thereby providing an automated reasoning procedure for judgement aggregation in the logic of acceptance.

Keywords

Semantic tableaux method acceptance logic judgement aggregation discursive dilemma 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Gaudou, B., Longin, D., Lorini, E., Tummolini, L.: Anchoring institutions in agents’ attitudes: Towards a logical framework for autonomous MAS. In: Padgham, L., Parkes, D.C. (eds.) Proceedings of AAMAS 2008., pp. 728–735 (2008)Google Scholar
  2. 2.
    Lorini, E., Longin, D., Gaudou, B., Herzig, A.: The logic of acceptance: Grounding institutions on agents’ attitudes. Journal of Logic and Computation (2009), doi:10.1093/logcom/exn103Google Scholar
  3. 3.
    Lorini, E., Longin, D.: A logical account of institutions: From acceptances to norms via legislators. In: Brewka, G., Lang, J. (eds.) Proceedings of KR 2008, pp. 38–48 (2008)Google Scholar
  4. 4.
    Bratman, M.E.: Practical reasoning and acceptance in context. Mind 101(401), 1–15 (1992)CrossRefGoogle Scholar
  5. 5.
    Cohen, L.J.: An essay on belief and acceptance. Oxford University Press, New York (1992)Google Scholar
  6. 6.
    Tuomela, R.: Belief versus acceptance. Philosophical Explorations 2, 122–137 (2000)CrossRefGoogle Scholar
  7. 7.
    Tuomela, R.: The Philosophy of Social Practices: A Collective Acceptance View. Cambridge University Press, Cambridge (2002)CrossRefGoogle Scholar
  8. 8.
    Boella, G., van der Torre, L.: Norm negotiation in multiagent systems. International Journal of Cooperative Information Systems 16(1), 97–122 (2007)CrossRefGoogle Scholar
  9. 9.
    Hart, H.L.A.: The concept of law, new edn. Clarendon Press, Oxford (1992) Google Scholar
  10. 10.
    Gilbert, M.: On Social Facts. Routledge, London (1989)Google Scholar
  11. 11.
    Herzig, A., de Lima, T., Lorini, E.: On the dynamics of institutional agreements (manuscript, 2009)Google Scholar
  12. 12.
    Pettit, P.: Deliberative democracy and the discursive dilemma. Philosophical Issues 11, 268–299 (2001)CrossRefGoogle Scholar
  13. 13.
    Kornhauser, L.A., Sager, L.G.: Unpacking the court. Yale Law Journal 96, 82–117 (1986)CrossRefGoogle Scholar
  14. 14.
    Fitting, M.: Proof Methods for Modal and Intuitionistic Logics. Springer, Heidelberg (1983)zbMATHGoogle Scholar
  15. 15.
    Halpern, J., Moses, Y.: A guide to completeness and complexity for modal logics of knowledge and belief. Artificial Intelligence 54, 311–379 (1992)MathSciNetGoogle Scholar
  16. 16.
    Goré, R.: Tableau methods for modal and temporal logics. In: D’Agostino, M., Gabbay, D.M., Hahnle, R., Posegga, J. (eds.) Handbook of Tableau Methods, pp. 297–396. Springer, Heidelberg (1999)Google Scholar
  17. 17.
    Pauly, M., van Hees, M.: Logical constraints on judgment aggregation. Journal of Philosophical Logic 35(6), 569–585 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    List, C., Pettit, P.: Aggregating sets of judgments: An impossibility result. Economics and Philosophy 18, 89–110 (2002)Google Scholar
  19. 19.
    Goldman, A.: Group knowledge versus group rationality: Two approaches to social epistemology. Episteme 1(1), 11–22 (2004)CrossRefGoogle Scholar
  20. 20.
    List, C.: Group knowledge and group rationality: A judgment aggregation perspective. Episteme 2(1), 25–38 (2005)CrossRefMathSciNetGoogle Scholar
  21. 21.
    Ågotnes, T., van der Hoek, W., Wooldridge, M.: Reasoning about judgment and preference aggregation. In: Proceedings of AAMAS 2007, pp. 566–573 (2007)Google Scholar
  22. 22.
    Pauly, M.: Axiomatizing collective judgment sets in a minimal logical language. Synthese 158, 233–250 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Castilho, M.A., Fariñas del Cerro, L., Gasquet, O., Herzig, A.: Modal tableaux with propagation rules and structural rules. Fundamenta Informaticae 20, 1–17 (1998)Google Scholar
  24. 24.
    Herzig, A., de Lima, T., Lorini, E.: What do we accept after an announcement? In: Meyer, J.-J.C., Broersen, J. (eds.) Pre-proceedings of the KR’08-Workshop KRAMAS, pp. 81–94 (2008), http://www.cs.uu.nl/events/kramas2008/PreProceedingsKRAMAS2008.pdf

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Mathijs de Boer
    • 1
  • Andreas Herzig
    • 2
  • Tiago de Lima
    • 3
  • Emiliano Lorini
    • 2
  1. 1.University of LuxembourgLuxembourg
  2. 2.IRITUniversity of Toulouse 3France
  3. 3.Eindhoven University of TechnologyThe Netherlands

Personalised recommendations