The Relationship of the Logic of Big-Stepped Probabilities to Standard Probabilistic Logics
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.
Keywordsconditional logic probabilistic logic big-stepped probability institution institution morphism
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