[FOM] Expressive Power of Natural Languages/ Kadvany

[Lotfi A. Zadeh]

Dear John,

     Thank you very much for drawing attention to the work of Kahneman 
and Tversky, and to the work of Lichtenstein and Slovic. It is of 
interest to observe that the works which you cited are important 
contributions to decision-making under uncertainty. However, they do not 
have the capability to deal with computational problems in which 
probabilities and events are imprecise, as they are in most realistic 
settings. In everyday settings, imprecise probabilities and events are 
frequently described in a natural language, e.g., likely, very unlikely, 
high, low, etc. As a simple illustration, consider the following 
problem. A and B are boxes, each containing twenty black and white 
balls. A ball is drawn from a box at random. In the case of A, if I draw 
a white ball I win ten dollars, and if I draw a black ball I lose five 
dollars. In the case of B, if I draw a white ball I win twenty dollars, 
and if I draw a black ball I lose ten dollars. I am shown boxes A and B 
for a few seconds, not long enough to count the number of balls. Assume 
that my perception is that there are approximately fifteen white balls 
in A, and approximately twelve white balls in B. I am free to choose the 
box from which to draw a ball. Which box should I choose? In this 
problem, the probabilities are perception-based and hence imprecise. In 
many realistic settings, the same applies to gains and loses. So far as 
I know, this simple problem is beyond the reach of any theory of 
decision-making. Recently, Professor Rafik Aliev, Azerbaijan University, 
has generalized the prospect theory of Kahneman and Tversky, and 
developed methods for dealing with the posed problem. Note that the 
posed problem falls within the class of CNL problems--computational 
problems which are stated in a natural language. As stated in my 
message, I believe that CNL problems cannot be dealt with through the 
use of concepts and techniques drawn from traditional mathematics, 
including probability theory.

     Regards to all,

     Lotfi

-- 
Lotfi A. Zadeh
Professor in the Graduate School
Director, Berkeley Initiative in Soft Computing (BISC)

Address:
729 Soda Hall #1776
Computer Science Division
Department of Electrical Engineering and Computer Sciences
University of California
Berkeley, CA 94720-1776
zadeh at eecs.berkeley.edu
Tel.(office): (510) 642-4959
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BISC Homepage URLs
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