[FOM] Logical Correctness/ Chow

[Lotfi A. Zadeh]

Dear Tim:

Thank you for your comment. Your comment is valid if p is a crisp 
proposition. In this case, as you point out, my question has a trivial 
answer.

My question--and related questions--are non-trivial when p is a fuzzy 
proposition. In this case, my questions fall within the province of 
fuzzy modal logic, fuzzy logic and possibility theory. A point at issue 
is whether fuzzy modal logic is capable of coming up with answers to my 
questions. Vaughn thinks so, but I have doubts. There is a reason. If 
pis a fuzzy proposition, assessment of its truthvalue in a possible 
world is a non-trivial problem. Does fuzzy modal logic address this 
problem? Example. p: Robert is much richer than most of his friends. 
Representation of meaning ofpropositions of this level of complexity 
falls within the province of fuzzy logic.

When p is a fuzzy proposition, possibility ceases to be a bivalent 
concept. Can fuzzy Kripke semantics deal with sentences like: It is 
quite possible that Robert is rich. As you can see, we enter unchartered 
territory.

     It is a sobering thought that dealing with simple sentences 
drawnfrom everyday discourse may well be beyond the reach of fuzzy modal 
logic.

                            Sincerely,

                            Lotfi

-- 
Lotfi A. Zadeh
Professor Emeritus
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
Fax (office): (510) 642-1712
Tel.(home): (510) 526-2569
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BISC Homepage URLs
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