LiEP CIS-2000-025: A Statistical Probability Theory for a Symbolic Management of Quantified Assertions.

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A Statistical Probability Theory for a Symbolic Management of Quantified Assertions.

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): nr 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.
Keywords:

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.

Keywords:

First posting 1999-04-06	In ETAI Newsletter and Decision and Reasoning under Uncertainty
Intended publication 1999-12-21	Postscript part I -- Checksum Postscript part II -- Checksum II
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