Belhadi, Asma and Dubois, Didier and Khellaf, Faiza and Prade, Henri Multiple agent possibilistic logic. (2013) Journal of Applied NonClassical Logics, 23 (4). 299320. ISSN 11663081

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Official URL: http://dx.doi.org/10.1080/11663081.2013.864470
Abstract
The paper presents a ‘multiple agent’ logic where formulas are pairs of the form (a, A), made of a proposition a and a subset of agents A. The formula (a, A) is intended to mean ‘(at least) all agents in A believe that a is true’. The formal similarity of such formulas with those of possibilistic logic, where propositions are associated with certainty levels, is emphasised. However, the subsets of agents are organised in a Boolean lattice, while certainty levels belong to a totally ordered scale. The semantics of a set of ‘multiple agent’ logic formulas is expressed by a mapping which associates a subset of agents with each interpretation (intuitively, the maximal subset of agents for whom this interpretation is possibly true). Soundness and completeness results are established. Then a joint extension of the multiple agent logic and possibilistic logic is outlined. In this extended logic, propositions are then associated with both sets of agents and certainty levels. A formula then expresses that ‘all agents in set A believe that a is true at least at some level’. The semantics is then given in terms of fuzzy sets of agents that find an interpretation more or less possible. A specific feature of possibilistic logic is that the inconsistency of a knowledge base is a matter of degree. The proposed setting enables us to distinguish between the global consistency of a set of agents and their individual consistency (where both can be a matter of degree). In particular, given a set of multiple agent possibilistic formulas, one can compute the subset of agents that are individually consistent to some degree.
Item Type:  Article 

Additional Information:  Thanks to Taylor & Francis editor. The definitive version is available at http://www.tandfonline.com/doi/abs/10.1080/11663081.2013.864470#.VP7LXuHVp3O 
HAL Id:  hal01123493 
Audience (journal):  International peerreviewed journal 
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Institution:  French research institutions > Centre National de la Recherche Scientifique  CNRS (FRANCE) Université de Toulouse > Institut National Polytechnique de Toulouse  Toulouse INP (FRANCE) Université de Toulouse > Université Toulouse III  Paul Sabatier  UT3 (FRANCE) Other partners > Université des Sciences et de la Technologie Houari Boumediene  USTHB (ALGERIA) Université de Toulouse > Université Toulouse  Jean Jaurès  UT2J (FRANCE) Université de Toulouse > Université Toulouse 1 Capitole  UT1 (FRANCE) 
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Deposited On:  05 Mar 2015 07:30 
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