Multiple agent possibilistic logic

Abstract

International audienceThe 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