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Paraconsistent probabilistic reasoning: applied to scenario recognition and voting theory

Abstract : If we envisage delegating critical decisions to an autonomous computer, we should not only endow it with common sense, but also formally verify that such a machine is programmed to safely react in every situation, notably when the situation is depicted with uncertainty. In this thesis, I deem an uncertain situation to be a possibly inconsistent probabilistic propositional knowledge base, which is a possibly unsatisfiable multiset of constraints on a probability distribution over a propositional language, where each constraint can be given a reliability level. The main problem is to infer one probabilistic distribution that best represents the real world, with respect to a given knowledge base. The reactions of the computer, previously programmed then verified, will be determined by that distribution, which is the probabilistic model of the real world. J.B. Paris et al stated a set of seven commonsensical principles that characterises the inference from consistent knowledge bases. Following their approach, I suggest adhering to further principles intended to define common sense when reasoning from an inconsistent knowledge base. My contribution is thus the first principled framework of paraconsistent probabilistic reasoning that comprises not only an inference process, which coincides with J.B. Paris's one when dealing with consistent knowledge bases, but also several measures of dissimilarity, inconsistency, incoherence, and precision. Besides, I show that such an inference process is a solution to a problem originating from voting theory, namely reaching a consensus among conflicting opinions about a probability distribution; such a distribution can also represent a distribution of a financial investment. To conclude, this study enhances our understanding of common sense when dealing with inconsistencies; injecting common sense into decision systems should make them more trustworthy.
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Submitted on : Friday, November 19, 2010 - 11:07:30 AM
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Lionel Daniel. Paraconsistent probabilistic reasoning: applied to scenario recognition and voting theory. Automatic. École Nationale Supérieure des Mines de Paris, 2010. English. ⟨NNT : 2010ENMP0003⟩. ⟨pastel-00537758⟩

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