Qualitative Dealing with Quantified Assertions

Abstract

In this paper we present a newapproach to a symbolic treatment ofquan-tified statements having the following form "Q A's are 5'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 ofM 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 formal-isation of direct inference principle allowing us to reason with particular individuals.