A Glance at Non-Standard Models and Logics of Uncertainty and Vagueness

  • Didier Dubois
  • Henri Prade
Part of the Philosophical Studies Series book series (PSSP, volume 56)


Historically, it is well known that the notion of probability emerged in the 17th century as a dual concept: chance, related to gaming problems, and subjective uncertainty, related to the question of reliability of testimonies. In the works of pioneers of probability theory, such as J. Bernoulli, chance, very soon connected to frequency of occurrence, was an additive notion but subjective probability was not so. However with the development of physical sciences, the non-additive side of probability was forgotten (see Shafer, 1978). So much so as 20th century researchers in decision theory have devoted much effort in the non-frequentist justification of additive probability as a model for subjective uncertainty in rational decision strategies.


Membership Function Belief Function Possibility Distribution Possibility Measure Vague Predicate 
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Copyright information

© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

  • Didier Dubois
    • 1
  • Henri Prade
    • 1
  1. 1.Institut de Recherche en Informatique de ToulouseToulouseFrance

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