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c# barcode generator open source IF t a f in Font
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With these definitions, the expressions IF p THEN p, p IF AND ONLY IF p, and ( p IFF q ) IFF ( ( IF p THEN q ) AND ( IF q THEN p ) ) are indeed all tautologies, as required. Sadly, however, this one isn t: ( IF p THEN q ) IFF ( ( NOT p ) OR q ) What are the consequences of this state of affairs One is that users are likely to make mistakes in formulating queries (because they probably think that this last expression is a tautology, or in other words that the identity does hold). Another is that the optimizer is likely to make incorrect expression transformations, for essentially the same reason. Either way, the system is likely to deliver wrong answers. Note: As you might be aware, I ve made the foregoing point in different ways in many other writings. I could sum it up by saying that the pragmatic problem with threevalued logics in general is not that they can t be defined and implemented in a consistent way, but rather that the answers they say are correct are not always correct in the real world. A couple of simple examples are discussed in my book Database in Depth: Relational Theory for Practitioners (O Reilly Media Inc., 2005), pages 54 56. What s more, a literally infinite number of analogous examples can be constructed to illustrate the same overall point. The nub of the matter is this: All bets are off! You can never trust a system that s based even if, unlike today s SQL systems, it s correctly based on some 3VL, because you never know whether what the system is telling you is true. In my view, this state of affairs is a complete showstopper.

