Truth Or Consequences

Two-valued (Boolean) logic is easy.  We recognise the basics of it from our everyday lives, and even if we can't immediately grasp some complex logical expression, we can work up to it from basic principles.

But when you start introducing more values, things get weird.

Take the simple if - then - else statement:

if a=b then:
  print "A = B".
else:
  print "A <> B".
end.

With two-valued logic, it couldn't be simpler.  If the expression is true, then you do the first bit, else you do the second bit.  But introduce null values, and hence logical nulls as a result of logical comparisons, and it starts to go pear-shaped.  If A is 1 and B is null, we find that this:

if a=b then:
  print "A = B".
else:
  print "A <> B".
end.

Prints A <> B, which is true from a two-valued perspective.  But this:

if a<>b then:
  print "A <> B".
else:
  print "A = B".
end.

Prints A = B, which is not true from a two-valued perspective.  What's going on?

What's going on is that the answer to the question, does A equal B, is neither true nor false.  It's null.  And so is the answer to the question, does A not equal B.  Since the then clause is taken if the if is true, either way, we take the else clause instead.

The problem is that if - then - else is implicitly two-valued.  What we need is a three-valued branch:

if A = B then:
  print "A = B".
else:
  print "A <> B".
otherwise:
  print "You have a null value somewhere".
end.

Yes, an if - then - else - otherwise structure will make any moderately experienced programmer choke on his cornflakes, but it's the logical consequence of the database null.

Well, that's ternary logic dealt with.  But what about yesterday's topic, quaternary logic?  Now we have four states: true, false, any, and none.  How should our if - then - else behave now?

Well, we can clarify that by looking at yet another variation on the names for the quaternary values: true, false, both and neither.  So the clear way to handle neither is not to take either of the branches - neither then nor else.

And the way to handle both is, well, to take both.

I can hear the anguished screams from here.

Posted by: Pixy Misa at 07:35 PM | Comments (8) | Add Comment | Trackbacks (Suck)
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