Group Knowledge Isn’t Always Distributed

W. van der Hoek, B. van Linder, J.-J. Ch. Meyer

In this paper we study the notion of group knowledge in a modal epistemic context. Starting with the standard definition of this kind of knowledge on Kripke models, we show that it may behave quite counterintuitively. Firstly, using a strong notion of derivability, we show that group knowledge in a state can always, but trivially be derived from each of the agents’ individual knowledge. In that sense, group knowledge is not really implicit, but rather explicit knowledge of the group. Thus, a weaker notion of derivability seems to be more adequate. However, adopting this more local view, we argue that group knowledge need not be distributed over (the members of) the group: we give an example in which (the traditional concept of) group knowledge is stronger than what can be derived from the individual agents’ knowledge. We then propose two additional properties on Kripke models: we show that together they are suiHcient to guarantee distributivity, while, when leaving one out, one may construct models that do not fulfill this principle.

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