L. Biacino and G. Gerla, Decidability, recursive enumerability and Kleene
Hierarchy for L-subsets, Z. Math. Logik Grund. Math. 35 1989.
where some limitative theorem is given. ù
See also
L. Biacino and G. Gerla, Fuzzy sets: a constructive approach. Fuzzy Sets and
Systems 45 (1992).
At 04.02 06/04/98 +0200, you wrote:
>Christian Borgelt <borgelt@iws.cs.uni-magdeburg.de> writes:
>
> >Completeness means that starting from the axioms and applying only
> >the allowed inference rules you can, in principle, prove any true
> >formula of the formal system.
>
> No it doesn't. Completeness is a syntactic concept: for every A,
>A or the negation of A is provable in T.
>
> >Another difficulty, which is not limited to fuzzy logic, is whether
> >G"odel's proof is actually a proof. To prove incompleteness, we have
> >to interpret the formula and have to understand that what it says is
> >true. That is, the result is not achieved by formal reasoning, but
> >by some meta-reasoning done from outside the system.
>
> This is a misunderstanding. Godel's theorem for a theory T is
>an ordinary mathematical theorem, provable (for standard theories
>T) in T itself.
>
>