Semantical investigations into nonmonotonic and probabilistic logics

  • Christoph BeierleEmail author
  • Gabriele Kern-Isberner


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.


Conditional logic Probabilistic logic Qualitative logic Big-stepped probability Conditional object Institution Institution morphism 

Mathematics Subject Classifications (2010)

68T27 68T30 68T37 


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© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Dept. of Computer ScienceFernUniversität in HagenHagenGermany
  2. 2.Dept. of Computer ScienceTU DortmundDortmundGermany

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