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Consensus-finding plays a ubiquitous role in A.I. In this paper, a consensus among agents is defined as a non-contradictory fragment of all the information conveyed by the agents such that this fragment does not logically conflict with any of the agents. This concept is investigated in modal logic S5 in order to meet representation needs that are put in light by this concept of consensus itself. Interestingly, an optimization-based approach to compute maximal consensuses is developed and shown experimentally efficient very often for both the standard Boolean and S5 frameworks.
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