Fuzzy logic can be emulated with standard logic

lennybogzy
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fuzzy logic can be emulated with "standard logic"

if fuzzy logic can be emulated with "standard logic" then how can it be fundamentally different?

shouldnt any newly proposed logic system, by definition, be impossible to model with another logic system? If you can emulate it then its not fundamentally different...
 
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lennybogzy said:
if fuzzy logic can be emulated with "standard logic" then how can it be fundamentally different?

shouldnt any newly proposed logic system, by definition, be impossible to model with another logic system? If you can emulate it then its not fundamentally different...

Sounds reminiscent of Turing-completeness. Once you have a logical system capable of representing number theory, you have reached the top (as far as anyone has ever seen). Your system can emulate any other system with finite complexity. Some systems are more succinct and expressive. Others rely on fewer axioms. But other than that, it's all the same.
 


if fuzzy logic can be emulated with "standard logic" then how can it be fundamentally different?

It isn't. The only ones that boast the "fundamental differences" are its proponents, but their arguments don't go much beyind that statement.

The fact is that the so-called "fuzzy logic" is just another way to perform calculations that are completey consistent with classical logic. The only advantage is that using fuzzy simplifies some things, but it's ultimately based on classical logic (consider this: if it's so fundamentally different, why almost every application of FL needs a "defuzzification" step?).
 
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The following is more or less taken from page 6 of C. Smorynski's "Self-Reference and Modal Logic". (Springer, 1985) (I couldn't get raised brackets to indicate codification (Gödel numbering), so I use a box. The overline is assigning a name. The detail I would like clarification on is in the second step in the last line, where we have an m-overlined, and we substitute the expression for m. Are we saying that the name of a coded term is the same as the coded term? Thanks in advance.

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