Nonmonotonic reasoning with multiple belief sets

  • Joeri Engelfriet
  • Heinrich Herre
  • Jan Treur
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1085)


In the present paper we introduce nonmonotonic belief set operators and selection operators to formalize and to analyze multiple belief sets in an abstract setting. We define and investigate formal properties of belief set operators as absorption, congruence, supradeductivity and weak belief monotony. Furthermore, it is shown that for each belief set operator satisfying strong belief cumulativity there exists a largest monotonic logic underlying it, thus generalizing a result for nonmonotonic inference operations. Finally, we study abstract properties of selective inference operations connected to belief set operators and which are used to choose one of the possible views.


nonmonotonic inference knowledge representation belief sets 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Joeri Engelfriet
    • 1
  • Heinrich Herre
    • 2
  • Jan Treur
    • 1
  1. 1.Department of Mathematics and Computer ScienceFree University AmsterdamHV AmsterdamThe Netherlands
  2. 2.Department of Computer ScienceUniversity of LeipzigLeipzigGermany

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