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Hi
Confutus wrote:
But I doubt that three value logic is useful for reasoning.
Because we can get away without, and still have undefined.
For example the empty theory neither entails p nor ~p,
so this might be interpreted as undefined.
>
The ability to deal consistently with that odious and uncomfortable
never-never land of the forbidden middle and the "unknown" and
"undefined" is precisely why it is useful in reasoning and has such
potentially broad application.
FOL or propositional logic also deals consistently with
the case that neither p nor ~p are entailed. You don't
need to switch to 3-valued logic.
2-valued logic does the job. It does the job because
consistency is not affected by undefined. Completness
is affected by undefined, but consistency is not.
Consistency is affected by over definition.
For example if you have in a theory p and ~p, you get
inconsisteny. But I said the theory contains neither
p nor ~p.
In your 3-valued logic you cannot define over definition,
or lets call it error. So arguing similar you have argued
in favor of 3-valued logic, I could argue in favor of
4-valued logic, because 3-valued logic is not able to
represent error.
There was a thread about para consistent logic in
sci.logic. But lets stick to undefined, and not confuse
it with issues of consistency.
> The modal operators of L3 have the same effect of
> limiting uncertainty and containing it within the more
> tractable 2-valued approach. That's partly why I don't
> use the constant U, because then uncertainty would
> tend to proliferate.
I showed you in another post that a constant u is not
necessary. So it is present, whether you want it or not,
as soon as you have the operator [], you can talk about
undefined.
Further I don't understand your slang, things like "limit
uncertainy" or "tendency of uncertainty proliferation"
need to be specified. Up til now, you didn't talk about
these issues.
Could you please elaborate.
Bye
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