Abstract
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. Moreover, we propose symbolic inference rules allowing us to manage quantified statements.
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Khayata, M.Y., Pacholczyk, D. & Garcia, L. A Qualitative Approach to Syllogistic Reasoning. Annals of Mathematics and Artificial Intelligence 34, 131–159 (2002). https://doi.org/10.1023/A:1014425907059
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DOI: https://doi.org/10.1023/A:1014425907059