Majority merging by adaptive counting | Synthese Skip to main content
Springer Nature Link
Log in

Majority merging by adaptive counting

  • Published:
Synthese Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

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.

Download references

Author information

Authors and Affiliations

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

    Giuseppe Primiero & Joke Meheus

Authors
  1. Giuseppe Primiero
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Joke Meheus
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Giuseppe Primiero.

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11229-008-9370-2

Keywords

Search

Navigation