Title: A Statistical Probability Theory for a Symbolic Management of Quantified Assertions
Authors: Y. Khayata and D. Pacholczyk
Series: Linköping Electronic Articles in Computer and Information Science
ISSN 1401-9841
Issue: Vol. 5 (2000), No. 025
URL: http://www.ep.liu.se/ea/cis/2000/025/

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.

First posting
In ETAI Newsletter and Decision and Reasoning under Uncertainty
Original publication
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