[FOM] Logical Correctness

[Lotfi A. Zadeh]

Dear all,

In dealing witha problem in nonmonotonic reasoning, the following 
question arose. Informally, consider the sentence

        If it is impossible that p, then it is possible that p,

where p is a factual proposition. The sentence is counterintuitive. 
Could it be logically correct, considering various interpretations of 
impossible, implication, possibility and p? There are some related basic 
questions.Could the sentence be logically correct if possibility is 
allowed to take values in the unit interval? How can one deal with the 
questionunder discussion when p is a proposition such as Robert is rich, 
where rich is a multivalued(fuzzy) predicate? If it is possible that 
Robert is rich, what is the possibility that Robert is not rich? What is 
the possibility that Robert is poor? A less simple example of p: Most 
Swedes are tall. Can fuzzy 
<http://www2.iiia.csic.es/%7Efbou/LoMoReVI/Slides/Bou-FuzzyModalLogics.pdf> 
modal <http://uai.sis.pitt.edu/papers/94/p278-hajek.pdf> logic deal with 
such questions?

With warm regards

Sincerely,

Lotfi Zadeh

-- 
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
Fax (home): (510) 526-2433
URL:http://www.cs.berkeley.edu/~zadeh/

BISC Homepage URLs
URL:http://zadeh.cs.berkeley.edu/

-------------- next part --------------
An HTML attachment was scrubbed...
URL: </pipermail/fom/attachments/20121121/1cbebd57/attachment-0001.html>