This paper shows how the logic of gambles corresponding to Peter Walley's system of Imprecise Probability can be extended to allow gambles involving infinitesimal values and infinite values. This logic can then be used for reasoning with infinitesimal probabilities alongside conventional reasoning with linear constraints on probabilities. The proof theory is shown to be sound and complete for finite input sets.
Keywords. Imprecise Probability, Probabilistic Logic, infinitesimals, order of magnitude probabilistic reasoning.
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School of Computing