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acquis i t ion from mul t i-agent resources

Rational agents, information systems and knowledge bases all share the property that they may become more effective by combining information from multiple sources. However, as was clearly indicated by the notorious "Judge puzzle" proposed by W. J. Schoenmakers in 1986, combining information from several sources is a dangerous operation. The resulting database may turn out to be inconsistent, or even worse: there are situations where the result is consistent but supports inferences which contradict the beliefs of all contributing agents. In this paper we investigate the possibilities and limitations of strategies for coping with this problem. Our first attempt tries to characterize those situations where information can be combined without risking the undesirable situation that some derivable proposition contradicts the beliefs of all agents involved. The resulting notion is called Absolute safely. It turns out however that for that case only trivial solutions exist. Consequently any non-trivial strategy must use information about the epistemic states of the agents involved. Subsequently we investigate less restrictive notions of safety. The more interesting ones involve not only propositions about the world but also epistemic information about the knowledge of the agents. This information can be formulated conveniently using the logic of belief dependence which has been designed by the first author, and which has been used previously for designing effectively computable belief revision procedures. The results characterizing the alternative safety notions generalize for this extended logic. We present a notion of restricted almost safety within this framework which describes the safety of combining information under the hypothesis that the contributing agents eventually would have exchanged their information among themselves. For this notion an explicit solution to the Judge puzzle is given.