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Qualitative Dealing with Quantified Assertions

In this paper we present a newapproach to a symbolic treatment of quan-tified statements having the following form "Q A's are B's", knowing that A and Bare 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. Finally, we present a symbolic formalisation of direct inference principle allowing us to reason with particular individuals.