The relationship of the logic of big-stepped probabilities to standard probabilistic logics

Authors:
Christoph Beierle;Gabriele Kern-Isberner
Affiliations:
Dept. of Computer Science, FernUniversität in Hagen, Hagen, Germany;Dept. of Computer Science, TU Dortmund, Dortmund, Germany
Venue:
FoIKS'10 Proceedings of the 6th international conference on Foundations of Information and Knowledge Systems
Year:
2010

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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 or possibility distributions. 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 between big-stepped probabilities and standard probabilities, thereby establishing the exact relationships among these logics.