Godel's Theorem under Fuzzy Logic?

greenrd@hotmail.com
Tue, 24 Mar 1998 00:53:21 +0100 (MET)

Can Godel's Incompleteness Theorem be extended to formal systems based on
fuzzy logic?

This is a crucial question, IMO, with regard to Artificial Intelligence,
because as I understand it, Roger Penrose's whole argument in his book
"Shadows of the Mind" that convincingly attempts to show that AI is
in principle unachievable on any algorithmic computer, assumes that the
posited machine intelligence thinks in terms of either-or (Aristotlean) logic
rather than fuzzy logic. Surely fuzzy logic would invalidate Godel's Theorem
and hence his whole argument? - therefore AI might in fact be possible after
all.

However, I wonder whether Godel's Theorem can be extended to formal systems
based on fuzzy logic. In this case, Penrose might be correct after all!

I am only a first-year mathematics student, so please try to keep your replies
as simple as possible.

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