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Majority merging by adaptive counting

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Abstract

The present paper introduces a belief merging procedure by majority using the standard format of Adaptive Logics. The core structure of the logic ADM c (Adaptive Doxastic Merging by Counting) consists in the formulation of the conflicts arising from the belief bases of the agents involved in the procedure. A strategy is then defined both semantically and proof-theoretically which selects the consistent contents answering to a majority principle. The results obtained are proven to be equivalent to a standard majority operator for bases with partial support.

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References

  • Alchourrón C.E., Gärdenfors P., Makinson D. (1985) On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic 50: 510–530

    Article  Google Scholar 

  • Baral C., Kraus S., Minker J., Subrahmanian V.S. (1992) Combining knowledge bases consisting of first-order theories. Computational Intelligence 8: 45–71

    Article  Google Scholar 

  • Batens D. (1999) Inconsistency-adaptive logics. In: Orłowska E.(eds) Logic at work.. Essays dedicated to the memroy of Helena Rasiowa. Physica Verlag (Springer), Heidelberg, pp 445–472

    Google Scholar 

  • Batens, D. (2001). A general characterization of adaptive logics. Logique & Analyse, 173–175, 45–68.

  • Batens, D. (2007). A universal logic approach to adaptive logics. In Logica universalis 1 (pp. 221–242). Basel/Switzerland: Birkhäuser Verlag.

  • Batini C., Lenzerini M. (1986) A comparative analysis of methodologies for database schema integration. ACM Computing Surveys 18(4): 323–364

    Article  Google Scholar 

  • Benferhat S., Dubois D., Prade H. (1999) Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study, Part 1: The flat case. Studia Logica 58(1): 17–45

    Article  Google Scholar 

  • Brennan G. (2001) Collective coherence?. International Review of Law and Economics 21(2): 197–211

    Article  Google Scholar 

  • Borgida, A., & Imielinski, T. (1984). Decision making in committees—a framework for dealing with incon sistency and non-monotonicity. In Proceedings Nonmonotonic Reasoning Workshop (pp. 21–32).

  • Chapman B. (1998) More easily done than said: Rules, reason and rational choice. Oxford Journal of Legal Studies 18: 293–330

    Article  Google Scholar 

  • Chapman B. (2002) Rational aggregation. Politics, Philosophy and Economics 1(3): 337–354

    Article  Google Scholar 

  • Cholvy, L., & Hunter, T. (1997). Fusion in logic: A brief overview. In Proceedings of the 4th European Conference on Symbolic and Quantitative Approaches to reasoning with Uncertainty. Lectures Notes in Computer Science, 1244, 86–95.

  • Dalal, M. (1988). Investigations into a theory of knowledge base revision: Preliminary report. In Proceedings of the Seventh National Conference on Artificial Intelligence (AAAI-88) (pp. 475–479).

  • de Rijke, M. (1994). Meeting some neighbours: A dynamic modal logic meets theories of change and knowledge representation. In J. V. Eijck & A. Visser (Eds.), Logic and information flow (pp. 170–196). Cambridge: MIT Press.

  • Dietrich F., List C. (2007) Strategy-proof judgment aggregation. Economics and Philosophy 23(3): 269–300

    Article  Google Scholar 

  • Elmagarmid, A., Rusinliewicz, M., & Sheth, A. (1999). Management of heterogeneous and autonomous database systems. Morgan Kaufmann.

  • Gabbay, D., Pigozzi, G., & Rodrigues, O. (2006). Belief revision, belief merging and voting. In G. Bonanno, W. van der Hoek, & M. Wooldridge (Eds.), Proceedings of the 7th Conference on Logic and the Foundations of Games and Decision Theory (LOFT06) (pp. 169–176).

  • Gochet P., Gribomont P. (2003) Epistemic logic. In: Gabbay D.M., Woods J.(eds) Handbook of the history and philosophy of logic.. Elsevier Science, Amsterdam, pp 99–195

    Google Scholar 

  • Halpern J., Moses Y. (1992) A guide to completeness and complexity for modal logics of knowledge and belief. Artificial Intelligence 52: 319–379

    Article  Google Scholar 

  • Kim, W. (Ed.). (1995). Modern database systems: The object model, interoperability and beyond. Addison Wesley.

  • Konieczny S., Pino-Pérez R. (2002) Merging information under constraints: A logical framework. Journal of Logic and Computation 12(5): 773–808

    Article  Google Scholar 

  • Kornhauser L.A., Sager L.G. (1986) Unpacking the court. Yale Law Journal 96: 82–117

    Article  Google Scholar 

  • Kornhauser L.A., Sager L.G. (1993) The one and the many: Adjudication in collegial courts. California Law Review 81: 1–51

    Article  Google Scholar 

  • Liberatore, P., & Schaerf, M. (1995). Arbitration: A commutative operator for belief revision. In Proceedings of the Second World Conference on the Fundamentals of Articial Intelligence (pp. 217–228).

  • Liberatore P., Schaerf M. (1998) Arbitration (or how to merge knowledge bases). IEEE Transactions on Knowledge and Data Engineering 10: 76–90

    Article  Google Scholar 

  • Lin, J., & Mendelzon, A. O. (1999). Knowledge base merging by majority. In Dynamic worlds: From the frame problem to knowledge management (pp. 195–218). Dordrecht: Kluwer.

  • Pigozzi G. (2006) Belief merging and the discursive dilemma: An argument-based account to paradoxes of judgment aggregation. Synthese 152(2): 285–298

    Article  Google Scholar 

  • Primiero, G. (2007). Belief merging based on adaptive interaction. In A Meeting of the Minds, Proceedings of the Workshop on Logic, Rationality and Interaction (LORI) 2007, Beijing, China, Texts in Computer Science (Vol. 8, pp. 315–320). London: College Publications.

  • Primiero, G. (2008). Aggregating collective judgements by selecting disagreements. Paper presented at LOFT08, 8th Conference on Logic and the Foundations of Game and Decision Theory, 2008.

  • Primiero, G., & Meheus, J. (2008a). Adaptive arbitration by variant counting on commutative bases with weights. In Proceedings of the FUSION08, 11th International Conference on Information Fusion (pp. 1374–1380).

  • Primiero, G., & Meheus, J. (2008b). Quasi-merging and pure-arbitration on information for the family of adaptive logics ADM. In Proceedings of the Workshop on Logic and Intelligent Interaction, ESSLLI2008 (pp. 21–30).

  • Revesz P.Z. (1997) On the semantics of arbitration. Journal of Algebra and Computation 7(2): 133–160

    Article  Google Scholar 

  • Satoh, K. (1988). Nonmonotonic reasoning by minimal belief revision. In Proceedings of the International Conference on Fifth Generation Computer Systems (pp. 455–462).

  • van Ditmarsch, H., van der Hoek, W., & Kooi, B. (2006). Dynamic epistemic logic, Synthese Library Series (Vol. 337). Springer-Verlag.

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  1. Ghent University, Blandijnberg 2, 9000, Ghent, Belgium

    Giuseppe Primiero & Joke Meheus

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  1. Giuseppe Primiero
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  2. Joke Meheus
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Correspondence to Giuseppe Primiero.

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Primiero, G., Meheus, J. Majority merging by adaptive counting. Synthese 165, 203–223 (2008). https://doi.org/10.1007/s11229-008-9370-2

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