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Pfeifer, Niki; Kleiter, Gernot D. (2006): Towards a Probability Logic Based on Statistical Reasoning. In: Proceedings of the 11th IPMU Conference (Information Processing and Management of Uncertainty in Knowledge-Based Systems). pp. 2308-2315
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Logical argument forms are investigated by second order probability density functions. When the premises are expressed by beta distributions, the conclusions usually are mixtures of beta distributions. If the shape parameters of the distributions are assumed to be additive (natural sampling), then the lower and upper bounds of the mixing distributions (Pólya-Eggenberger distributions) are parallel to the corresponding lower and upper probabilities in conditional probability logic.