The Relationship of the Logic of Big-Stepped Probabilities to Standard Probabilistic Logics

  • Christoph Beierle
  • Gabriele Kern-Isberner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5956)


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.


conditional logic probabilistic logic big-stepped probability institution institution morphism 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Christoph Beierle
    • 1
  • Gabriele Kern-Isberner
    • 2
  1. 1.Dept. of Computer ScienceFernUniversität in HagenHagenGermany
  2. 2.Dept. of Computer ScienceTU DortmundDortmundGermany

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