Say What You Mean, and Mean What You Say (Part II)

Last time I rambled on, trying to set some context for how to interpret a 3rd (or 4th) truth value of "not applicable". What I was hoping to do was to make plausible the following truth table for it's conjunction:

    P^Q | T | F | NA
    ----------------
      T | T | F |  T
    ----------------
      F | F | F |  F
    ----------------
     NA | T | F | NA

This is the plausibility argument: if a predicate does not apply, then it can be ignored. Thus, T^NA becomes simply T, since the second predicate can be ignored. Obviously, one could continue in this vein, and construct a truth table for this logic's disjunction:

    PvQ | T | F | NA
    ----------------
      T | T | T |  T
    ----------------
      F | T | F |  F
    ----------------
     NA | T | F | NA

But, if we do this, we find that the distributive law does not hold. In particular, if one considers:

     P^(QvR) = (P^Q)v(P^R)

for the truth values P=True, Q=False, and R=NULL, One finds that the left and right side both evaluate to NULL in standard SQL, but the left side evaluates to False and the right to True in my hypothetical 3 valued logic. So, this is not going to become part of SQL anytime soon.

To sum up, what is the point of all this? Here is the short answer:

• 
  Values can be missing for at least two reasons: the proper value is currently unknown, and/or the value does not apply.
  
• 
  The SQL Null is tailored for the "unknown" reason.
  
• 
  Using a Null to mean "does not apply" will produce confusing results at best, and downright wrong results at worst.