A Symbolic Approach to Syllogistic Reasoning

  • Mohamed Yasser Khayata
  • Daniel Pacholczyk
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 89)


In this paper we present a new approach to a symbolic treatment of quantified statements having the following form “Q A’s are B’s”, knowing that A and B are labels denoting sets, and Q is a linguistic quantifier interpreted as a proportion evaluated in a qualitative way. Our model can be viewed as a symbolic generalization of statistical conditional probability notions as well as a symbolic generalization of the classical probabilistic operators. Our approach is founded on a symbolic finite M-valued logic in which the graduation scale of M symbolic quantifiers is translated in terms of truth degrees of a particular predicate. Then, we present symbolic syllogisms allowing us to deal with quantified statements.


Statistical Probability Inference Rule Truth Degree Default Reasoning Syllogistic Reasoning 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Mohamed Yasser Khayata
    • 1
  • Daniel Pacholczyk
    • 1
  1. 1.LERIA, U.F.R SciencesAngers Cedex 01France

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