1. Re: 'Unknown' and three-valued logic
Well, 3 is not a computer-world number, while 4 is. Actually, most of
our modelling of unknown values could be represented as two booleans:
- b1=0 and b2=0 --> can't decide (undecidable)
- b1=0 and b2=1 --> unknown, but could decide, have idea on how to
decide (decidable)
- b1=1 --> decision made, b2 is ordinary true/false boolean
So, if x and y are two such pairs of booleans:
- not x=x if b1=0, otherwise the expected thing;
- x and y will have b1=0 if x.b1 or y.b1 is;
- and then b2=1 only if x.b2 and y.b2 are 1.
Why separate decidable and undecidable? Just because it leads you to
different courses of action in real life. "Decidable" means you may
start and find extra data to make the decision and set the relevant b1
to 1. "Undecidable" means you won't because you have no clue (could fit
somebody on this list, :)) and you either raise a logical error, don't
return a decision, return a random decision, whatever.
And also because 3-state hardware is expensive if it ever exists, while
pairs of booleans can be handled neatly by any language on standard
hardware.
Getting uninitialised variables contents falls in the (0,0) case: raise
an error (Euphoria), return whatever rubbish is there (most others). Not
finding a file, or finding unexpected syntax, is rather (0,1), because
the most logical approach is to search extra information, for instance
in a plugin handling extended syntax, in a user-filled form or box,...
(hint, hint, Rob).
Have a nice day!
CChris
>
> But I digress. I think the key point is that you *can* in fact represent
> information like "we don't know" as a boolean fact, and it doesn't
> necessitate the creation of a third logic value.
>
> -- David Cuny
>
