Synthese

, Volume 177, Supplement 1, pp 97–123 | Cite as

Equilibria in social belief removal

Article

Abstract

In studies of multi-agent interaction, especially in game theory, the notion of equilibrium often plays a prominent role. A typical scenario for the belief merging problem is one in which several agents pool their beliefs together to form a consistent “group” picture of the world. The aim of this paper is to define and study new notions of equilibria in belief merging. To do so, we assume the agents arrive at consistency via the use of a social belief removal function, in which each agent, using his own individual removal function, removes some belief from his stock of beliefs. We examine several notions of equilibria in this setting, assuming a general framework for individual belief removal due to Booth et al. We look at their inter-relations as well as prove their existence or otherwise. We also show how our equilibria can be seen as a generalisation of the idea of taking maximal consistent subsets of agents.

Keywords

Belief removal Belief revision Belief merging Multi-agent systems Equilibrium 

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References

  1. Alchourrón C., Gärdenfors P., Makinson D. (1985) On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic 50(2): 510–530CrossRefGoogle Scholar
  2. Areces, C., & Becher, V. (2001). Iterable AGM functions. In H. Rott & M. A. Williams (Eds.), Frontiers in belief revision (pp. 261–277). Kluwer Academic Publishers.Google Scholar
  3. Arrow, K., Sen, A., Suzumura, K. (eds) (2002) Handbook of social choice and welfare. Elsevier, AmsterdamGoogle Scholar
  4. Aumann, R. (1959). Acceptable points in general cooperative n-person games. In Contributions to the theory of games (Vol. IV, pp. 287–324). Princeton: Princeton University Press.Google Scholar
  5. Bochman A. (2001) A logical theory of nonmonotonic inference and belief change. Springer, BerlinGoogle Scholar
  6. Booth R. (2006) Social contraction and belief negotiation. Information Fusion 7(1): 19–34Google Scholar
  7. Booth R., Chopra S., Ghose A., Meyer T. (2005) Belief liberation (and retraction). Studia Logica 79(1): 47–72CrossRefGoogle Scholar
  8. Booth, R., Chopra, S., Meyer, T., & Ghose, A. (2004). A unifying semantics for belief change. In Proceedings of ECAI’04 (pp. 793–797).Google Scholar
  9. Brams, S., & Fishburn, P. (2002). Voting procedures. In K. Arrow, A. Sen & K. Suzumura (Eds.), Handbook of social choice and welfare (Vol. 1, pp. 173–236). Elsevier.Google Scholar
  10. Caminada, M., & Pigozzi, G. (2009). On judgment aggregation in abstract argumentation. Autonomous Agents and Multi-Agent Systems, 1–39.Google Scholar
  11. Cantwell J. (2003) Eligible contraction. Studia Logica 73: 167–182CrossRefGoogle Scholar
  12. Coste-Marquis S., Devred C., Konieczny S., Lagasquie-Schiex M., Marquis P. (2007) On the merging of Dung’s argumentation systems. Artificial Intelligence 171(10–15): 730–753CrossRefGoogle Scholar
  13. Dietrich, F. (2007). Aggregation theory and the relevance of some issues to others. Working paper, London School of Economics.Google Scholar
  14. Dokow E., Holzman R. (2009) Aggregation of binary evaluations with abstentions. Journal of Economic Theory. 145(2): 544–561CrossRefGoogle Scholar
  15. Dung P. (1995) On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artificial intelligence 77(2): 321–357CrossRefGoogle Scholar
  16. Falappa, M. A., Kern-Isberner, G., & Simari, G. R. (2009). Belief Revision and argumentation theory. In I. Rahwan & G. R. Simari (Eds.), Argumentation in artificial intelligence (pp. 341–360). Berlin: Springer.Google Scholar
  17. Gärdenfors P. (1988) Knowledge in flux. MIT Press, Cambridge, MAGoogle Scholar
  18. Hansson S. O. (1991) Belief contraction without recovery. Studia Logica 50(2): 251–260CrossRefGoogle Scholar
  19. Hansson S. O. (1993a) Changes on disjunctively closed bases. Journal of Logic, Language and Information 2: 255–284CrossRefGoogle Scholar
  20. Hansson S. O. (1993b) Theory contraction and base contraction unified. Journal of Symbolic Logic 58: 602–625CrossRefGoogle Scholar
  21. Katsuno, H., & Mendelzon, A. (1992). On the difference between updating a knowledge base and revising it. In Belief revision (pp. 183–203). Cambridge: Cambridge University Press.Google Scholar
  22. Konieczny S., Grégoire E. (2006) Logic-based approaches to information fusion. Information Fusion 7(1): 4–18Google Scholar
  23. Konieczny, S., & Pino Pérez, R. (1998). On the logic of merging. In Proceedings of KR’98 (pp. 488–498).Google Scholar
  24. Konieczny S., Pino Pérez R. (2002) Merging information under constraints: A logical framework. Journal of Logic and Computation 12(5): 773–808CrossRefGoogle Scholar
  25. Kraus S., Lehmann D., Magidor M. (1991) Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence 44: 167–207CrossRefGoogle Scholar
  26. Levi I. (1991) The fixation of belief and its undoing. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  27. Levi I. (1996) For the sake of argument. Cambridge University Press, Cambridge, MACrossRefGoogle Scholar
  28. Levi, I. (1998). Contraction and information value. Unpublished manuscript (sixth version), Columbia University.Google Scholar
  29. Lindström, S., & Rabinowicz, W. (1991). Epistemic entrenchment with incomparabilities and relational belief revision. In The logic of theory change (pp. 93–126). Berlin: Springer.Google Scholar
  30. List C., Puppe C. (2009) Judgment aggregation: A survey. In: Anand P., Pattanaik P., Puppe C. (eds) Handbook of rational and social choice. Oxford University Press, OxfordGoogle Scholar
  31. Meyer, T., Foo, N., Kwok, R., & Zhang, D. (2004a). Logical foundations of negotiation: Outcome, concession and adaptation. In Proceedings of AAAI’04 (pp. 293–298).Google Scholar
  32. Meyer, T., Foo, N., Kwok, R., & Zhang, D. (2004b). Logical foundations of negotiation: Strategies and preferences. In Proceedings of KR’04 (pp. 311–318).Google Scholar
  33. Meyer T., Heidema J., Labuschagne W., Leenen L. (2002) Systematic withdrawal. Journal of Philosophical Logic 31(5): 415–443CrossRefGoogle Scholar
  34. Nash J. (1950) Equilibrium points in n-person games. Proceedings of the National Academy of Sciences 36(1): 48–49CrossRefGoogle Scholar
  35. Nayak A., Pagnucco M., Peppas P. (2003) Dynamic belief revision operators. Artificial Intelligence 146: 193–228CrossRefGoogle Scholar
  36. Nebel, B. (1994). Base revision operations and schemes: Semantics, representation and complexity. In Proceedings of ECAI’94 (pp. 342–345).Google Scholar
  37. Osborne M., Rubinstein A. (1994) A course in game theory. MIT Press, Cambridge, MAGoogle Scholar
  38. Pigozzi G. (2006) Belief merging and the discursive dilemma: An argument-based account to paradoxes of judgment aggregation. Synthese 152(2): 285–298CrossRefGoogle Scholar
  39. Rahwan, I., & Tohmé, F. (2010). Collective argument evaluation as judgement aggregation. In Proceedings of AAMAS.Google Scholar
  40. Rott H. (1992) Preferential belief change using generalized epistemic entrenchment. Journal of Logic, Language and Information 1: 45–78CrossRefGoogle Scholar
  41. Rott H. (1999) Coherence and conservatism in the dynamics of belief. Part I: Finding the right framework. Erkenntnis 50: 387–412CrossRefGoogle Scholar
  42. Rott H., Pagnucco M. (1999) Severe withdrawal (and recovery). Journal of Philosophical Logic 28: 501–547CrossRefGoogle Scholar
  43. Zhang, D., Foo, N., Meyer, T., & Kwok, R. (2004). Negotiation as mutual belief revision. In Proceedings of AAAI’04 (pp. 317–323).Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.University of LuxembourgLuxembourgLuxembourg
  2. 2.CSIR Meraka and School of Computer ScienceUniversity of Kwazulu-NatalPretoriaSouth Africa

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