[FOM] Fuzziness

[Kreinovich, Vladik]

There are several aspects of fuzzy logic research:

* there is pragmatic fuzzy logic, motivated by applications, this is probably the farthest away from FOM

* there is mathematical research of fuzzy logic structures, this is often very much related to FOM, since it extended the usual logical results to different multi-valued logics

* there is also a general philosophical idea that, in the words of Zadeh, "everything is a matter of degree"; many concepts of logic and FOM are attempts to formalize semi-intuitive ideas; these ideas are rarely black-and-white, often, we can perceive different degrees: e.g., in physics, there is a causality relation, but in reality, some events A can barely influence events  while others are strongly influencing; 

similarly, in logic, traditional implication includes both cases when a mathematician would agree that a theorem A indeed follows from theorem B and the general pairs caused by the fact that every two statements imply each other

In such situations, fuzzy is a heuristic idea that motivates us to replace the original black-and-white formalization with a more degreed one. For example, if we fix an inference system, then we can say that A truly implies B if the shortest proof of B from the axioms is longer than the shortest proof in which we add A as one of the axioms, and the difference between the two shortest lengths can be viewed as a degree to which A implies B
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From: fom-bounces at cs.nyu.edu <fom-bounces at cs.nyu.edu> on behalf of Harvey Friedman <hmflogic at gmail.com>
Sent: Tuesday, June 21, 2016 7:07 PM

Except that the very idea of doing "fuzzy logic" is deeply
foundational, and it could be of great interest for the FOM to see a
modern account of the basics of fuzzy logic and fuzzy mathematics and
fuzziness from the ground up. it would seem likely that f.o.m. people
who have not been informed much about it would have something
interesting and/or useful to say about it.

Also, how does it relate to recent breakthroughs in machine learning,
deep leaning, etcetera?

Harvey Friedman
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