SQL and Relational Theory, 2nd Edition

WHAT’S WRONG WITH NULLS?

The opening paragraph from the section WHAT’S WRONG WITH DUPLICATES? applies equally well here, with just one tiny text substitution, so I’ll basically just repeat it: There are numerous practical arguments in support of the position that nulls should be prohibited. Here I want to emphasize just one—but I think it’s a powerful one. But it does rely on certain notions I haven’t discussed yet in this book, so I need to make a couple of preliminary assumptions:

1. I assume you know that any comparison in which at least one of the comparands is null evaluates to the UNKNOWN truth value instead of TRUE or FALSE. The justification for this state of affairs is the intended interpretation of null as value unknown: If the value of A is unknown, then it’s also unknown whether, for example, A > B, regardless of the value of B (even—perhaps especially—if the value of B is unknown as well). Note: That same state of affairs is also the source of the term three-valued logic (3VL). That is, the notion of nulls, as understood in SQL, inevitably leads to a logic in which there are three truth values instead of the usual two. (The relational model, by contrast, is based on conventional two-valued logic, 2VL.)

2. I assume you’re also familiar with the 3VL truth tables for the familiar logical operators—also known as connectives—NOT, AND, and OR (T = TRUE, F = FALSE, U = UNKNOWN):

   

   Observe ...