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Of the many justifications of Bayesianism, most imply some assumption that is not very compelling, like the differentiability or continuity of some auxiliary function. We show how such assumptions can be replaced by weaker assumptions for finite domains. The new assumptions are a non-informative refinement principle and a concept of information… (More)

We present and examine a result related to uncertainty reasoning, namely that a certain plausibility space of Cox's type can be uniquely embedded in a minimal ordered field. This, although a purely mathematical result, can be claimed to imply that every rational method to reason with uncertainty must be based on sets of extended probability distributions,… (More)

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