[FOM] Logical Correctness/ Friedman

Lotfi A. Zadeh zadeh at eecs.berkeley.edu
Thu Nov 22 01:13:45 EST 2012

Dear Joel Friedman,

     Thank you for your constructive comment. A problem with your 
reasoning is that it applies only when p is a crisp proposition. When p 
is a fuzzy proposition such as Robert is rich, or Most Swedes are tall, 
classical material implication does not apply. As a test, consider the 
conditional statement:

        If it is impossible that Robert is rich, then it is possible
        that Robert is rich.

     In this case, the issue is not logical correctness but the 
truth-value of the conditional statement, with the understanding that 
rich, most and tall are labels of fuzzy sets. How would you compute the 
truth-value of the conditional statement?


     Lotfi Zadeh

Lotfi A. Zadeh
Professor Emeritus
Director, Berkeley Initiative in Soft Computing (BISC)

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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