# Multiple agent possibilistic logic

Belhadi, Asma and Dubois, Didier and Khellaf, Faiza and Prade, Henri Multiple agent possibilistic logic. (2013) Journal of Applied Non-Classical Logics, 23 (4). 299-320. ISSN 1166-3081

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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 Thanks to Taylor & Francis editor. The definitive version is available at http://www.tandfonline.com/doi/abs/10.1080/11663081.2013.864470#.VP7LXuHVp3O hal-01123493 International peer-reviewed journal French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (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) download IRIT IRIT 05 Mar 2015 07:30

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