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Semantical investigations into nonmonotonic and probabilistic logics

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Abstract

Different forms of semantics have been proposed for conditionals of the form “Usually, if A then B”, ranging from quantitative probability distributions to qualitative approaches using plausibility orderings, possibility distributions, or conditional objects. Atomic-bound systems, also called big-stepped probabilities, allow qualitative reasoning with probabilities, aiming at bridging the gap between qualitative and quantitative argumentation and providing a model for the nonmonotonic reasoning system P. By using Goguen and Burstall’s notion of institutions for the formalization of logical systems, we elaborate precisely which formal connections exist among big-stepped probabilities, standard probabilities, and qualitative logics. Based on our investigations, we also develop two variants of conditional objects, one of them having a simpler semantics while still providing a model for system P.

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Correspondence to Christoph Beierle.

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The research reported here was supported by the Deutsche Forschungsgemeinschaft (grants BE 1700/7-2 and KE 1413/2-2).

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Beierle, C., Kern-Isberner, G. Semantical investigations into nonmonotonic and probabilistic logics. Ann Math Artif Intell 65, 123–158 (2012). https://doi.org/10.1007/s10472-012-9310-1

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Mathematics Subject Classifications (2010)

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