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- S. Arnborg, G. Sjödin
- 2001

We discuss precise assumptions entailing Bayesianism in the line of investigations started by Cox, and relate them to a recent critique by Halpern. We show that every finite model which cannot be rescaled to probability violates a natural and simple refinability principle. A new condition, separability, was found sufficient and necessary for rescalability… (More)

We discuss the justifications of Bayesianism by Cox and Jaynes, and relate them to a recent critique by Halpern(JAIR, vol 10(1999), pp 67–85). We show that a problem with Halperns example is that a finite and natural refinement of the model leads to inconsistencies , and that the same is the case with every model in which rescalability to probability cannot… (More)

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 measure 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)

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)

We discuss precise assumptions entailing Bayesianism in the line of investigations started by Cox, and relate them to a recent critique by Halpern. We show that every finite model which cannot be rescaled to probability violates a natural and simple refinability principle. We characterize the acceptable ways to handle uncertainty in infinite models based on… (More)

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