Majority merging by adaptive counting

The present paper introduces a belief merging procedure by majority using the standard format of Adaptive Logics. The core structure of the logic ADMc (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.

[1]  Dov M. Gabbay,et al.  Belief revision, belief merging and voting , 2006 .

[2]  Won Kim,et al.  Modern Database Systems: The Object Model, Interoperability, and Beyond , 1995, Modern Database Systems.

[3]  Geoffrey Brennan,et al.  Collective coherence?☆9 , 2001 .

[4]  D. Batens.  A General Characterization of Adaptive Logics , 2001 .

[5]  Venkataraman Ramesh,et al.  Management of Heterogeneous and Autonomous Database Systems , 1999 .

[6]  Lawrence G. Sager,et al.  The One and the Many: Adjudication in Collegial Courts , 1993 .

[7]  Didier Dubois,et al.  Some Syntactic Approaches to the Handling of Inconsistent Knowledge Bases: A Comparative Study Part 1: The Flat Case , 1997, Stud Logica.

[8]  Giuseppe Primiero,et al.  Adaptive arbitration by variant counting on commutative bases with weights , 2008, 2008 11th International Conference on Information Fusion.

[9]  Anthony Hunter,et al.  Information Fusion in Logic: A Brief Overview , 1997, ECSQARU-FAPR.

[10]  Gabriella Pigozzi,et al.  Belief merging and the discursive dilemma: an argument-based account to paradoxes of judgment aggregation , 2006, Synthese.

[11]  Alexander Borgida,et al.  Decision Making in Commitees - A Framework for Dealing with Inconsistency and Non-Monotonicity , 1984, NMR.

[12]  Alistair J. Bray,et al.  Foundations of cognitive science ☆: Michael I. Posner, ed. , 1991 .

[13]  B. Chapman,et al.  More Easily Done than Said: Rules, Reasons, and Rational Social Choice , 1998 .

[14]  Marco Schaerf,et al.  Arbitration (or How to Merge Knowledge Bases) , 1998, IEEE Trans. Knowl. Data Eng..

[15]  W. Hoek,et al.  Dynamic Epistemic Logic , 2007 .

[16]  Giuseppe Primiero,et al.  Quasi-merging and Pure-arbitration on Information for the family of Adaptive Logics ADM , 2008 .

[17]  Peter Z. Revesz,et al.  On the Semantics of Arbitration , 1997, Int. J. Algebra Comput..

[18]  Diderik Batens,et al.  A Universal Logic Approach to Adaptive Logics , 2007, Logica Universalis.

[19]  B. Chapman,et al.  Rational Aggregation , 2002 .

[20]  Giuseppe Primiero.  Belief Merging based on Adaptive Interaction , 2007 .

[21]  Ken Satoh.  Nonmonotonic Reasoning by Minimal Belief Revision , 1988, FGCS.

[22]  Christian List,et al.  STRATEGY-PROOF JUDGMENT AGGREGATION* , 2005, Economics and Philosophy.

[23]  Mukesh Dalal,et al.  Investigations into a Theory of Knowledge Base Revision , 1988, AAAI.

[24]  Lawrence G. Sager,et al.  Unpacking the Court , 1986 .

[25]  Alberto O. Mendelzon,et al.  Knowledge Base Merging by Majority , 1999 .

[26]  Marco Schaerf,et al.  Arbitration: A Commutative Operator for Belief Revision , 1995, WOCFAI.

[27]  Diderik Batens.  Inconsistency-Adaptive Logics , 1999 .

[28]  Joseph Y. Halpern,et al.  A Guide to Completeness and Complexity for Modal Logics of Knowledge and Belief , 1992, Artif. Intell..

[29]  Sébastien Konieczny,et al.  Merging Information Under Constraints: A Logical Framework , 2002, J. Log. Comput..

[30]  Peter Gärdenfors,et al.  On the logic of theory change: Partial meet contraction and revision functions , 1985, Journal of Symbolic Logic.

[31]  Sarit Kraus,et al.  Combining Knowledge Bases Consisting of First Order Theories , 1991, ISMIS.