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Journal of Logic and Computation, Volume 9, Issue 1, pp. 81-103: Abstract.

A modal logic for fusing partial belief of multiple reasoners

L Boldrin1 and A Saffiotti2

1Department of Pure and Applied Mathematics, University of Padova, Padova, Italy. E-mail: boldrin@ladseb.pd.cnr.it, 2Department of Technology and Science, University of Örebro, S-70182 Örebro, Sweden. E-mail: alessandro.saffiotti@ton.oru.se

We present PLn[otimes], a multi-agent epistemic logic where each agent can perform uncertain (possibilistic) reasoning. The original feature of this logic is the presence of a distributed belief operator, with the purpose of merging the belief of different agents. Unlike the corresponding operator in the categorical (non-uncertain) case, our distributed belief operator accumulates support for the same fact coming from different agents. This means that opinions shared by different agents can be combined into a stronger distributed belief. This feature is useful in problems like pooling expert opinions and combining information from multiple unreliable sources. We provide a possible worlds semantics and an axiomatic calculus for our logic, and prove soundness, completeness and decidability results. We hint at some possible applications of PLn[otimes] in the conclusions.

Key words: Epistemic logic, distributed belief, data fusion, possibility theory, fuzzy logic, multiple agents.

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