Re: 1 NF

On 2007-02-28, V.J. Kumar wrote:

> Leaving aside arguably dubious utility of fuzzy logic, could you show
> how fuzzy logic "can be handled on the latter, classical terms" ?

As I understand it, fuzzy logic as a whole can be grounded in fuzzy set theory. That in case is founded in real membership functions in orthodox sets. The theory of real functions, measures and the like is then formulated on top of normal ZFC axiomatics. As such, all of fuzzy logic can be reduced to orthodox mathematics. I don't think I've even bumped into a fuzzy result relying on the "C" (Choice) part, yet.

> All of them?

Yes. As I understand it, anything going outside of something embeddable into the monotone reasoning, real-valued, set membership function, etc. framework shouldn't be called "fuzzy".

> So your claim is that paraconsistent logics are even easier to handle
> "on the classical terms"?

I thought I just stated the precise opposite.

> If you know at least a little bit about paraconsistent logics, you
> should be aware that some of them do not even have the modus ponens
> rule so they can hardly be even counted as logics. Fuzzy logic(s) by
> the way does/do have the rule.

My point exactly. Fuzzy logic is trivial to the point of being useless, especially given that I've never seen a result in fuzzy logic that couldn't be equally formulated in classical probability, modulo interpretational difficulties. (Nowadays I'm a full blown formalist, and mostly interpret math from a constructivist viewpoint.)

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Sampo Syreeni, aka decoy - mailto:decoy_at_iki.fi, tel:+358-50-5756111
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