Re: and then... (a curiosity)

["Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de>]

On Thu, 4 Sep 2008 14:04:10 +0200, stefan-lucks@see-the.signature wrote:

>> Well, indeed
>> 
>>     0 /\ _|_ = 0
>>     0 /\ T = 0
>> 
>> Here 0 = False, 1 = True, _|_ = Uncertain, T = Contradiction. False under
>> /\ always renders False.
>> 
>> Nevertheless Boolean logic /= Belnap logic, though the former is contained
>> in the latter. 
> 
> I never said "Boolean logic", I said "logic", which was ment to include 
> multi-valued logic. ;-)

There are many multi-valued logics. But the problem is that taking such a
logic for the base, you need to reconsider everything based on inference.
In such logics inference is sufficiently more difficult, especially when
the results need to be interpreted. The Boolean type is heavily used in the
language. As an example, consider "when others" of a case statement. It
uses the reasoning if X not in A then X in not A (not A = the complement
set of A). But when "in A" is uncertain then its counterpart is too. How
case is supposed to work, then? In fact, especially evident it becomes in
fuzzy logic, in such frameworks you need to keep track on multiple
competing alternatives, because at no point you can discard anything
different from False. On the contrary, in Boolean logic there is only one
right path.

-- 
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de