Dear Konrad,
Thank you for raising important questions relating to the
relationship between probabilistic and non-probabilistic approaches to
uncertainty.
The probability community stubbornly holds to the Dennis Lindley
view that standard probability theory is all that is needed to deal with
uncertainty. I argued to the contrary in many papers, among them my 1978
<http://dx.doi.org/10.1016/S0165-0114%2899%2980004-9> paper on
possibility theory, my 1995
<http://www-bisc.cs.berkeley.edu/zadeh/papers/Discussion_Technometrics_1995-1.pdf>
paper on the complementarity of probability theory and fuzzy logic, my
2002 <http://www-bisc.cs.berkeley.edu/zadeh/papers/> paper on the
perception-based theory of probabilistic reasoning, and in my 2005
<http://www-bisc.cs.berkeley.edu/zadeh/papers/> and 2006
<http://www-bisc.cs.berkeley.edu/zadeh/papers/GTU--Principal%20Concepts%20and%20Ideas-2006.pdf>
papers on the Generalized Theory of Uncertainty (GTU). Basically, my
view is that uncertainty has many facets which are non-probabilistic in
nature. One such facet relates to possibility theory. Probability and
possibility are distinct concepts. Probability theory and possibility
theory are complementary rather than competitive, and have distinct
agendas. Elasticity of meaning relates to possibility rather than
probability. Strangely enough, the basic issue of elasticity of meaning
is not addressed in the literature of linguistics or the literature of
computational linguistics.
To illustrate my point, how would you represent the meaning of the
following. (a) X is a real-valued variable. What is known about X is
that X is much larger than approximately a. (b) X is a real-valued
variable. What is known about X is that X is much larger than
approximately a and is much smaller than approximately b, with a less
than b.
Since the publication of my first paper on possibility theory,
possibility theory has grown in visibility and acceptance. Use Google to
search on possibility theory.
With cordial regards,
Lotfi
--
Lotfi A. Zadeh
Professor in the Graduate School
Director, Berkeley Initiative in Soft Computing (BISC)
Tel.(office): (510) 642-4959
Fax (office): (510) 642-1712
URL: http://www.cs.berkeley.edu/~zadeh/
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