Semantical investigations into nonmonotonic and 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, 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.