Substitution and instantiation - sql, PL-SQL Programming

Substitution and Instantiation - SQL

It shows how NULL might appear in substitution for a parameter of a predicate and how it might thus participate in instantiation of that predicate to yield a proposition. Now consider instantiations of the dyadic predicate a < b. As well as instantiations such as 5 < 10 (a true one) and 9 < 6 (a false one), we now have to entertain the possibility of instantiations such as 5 < NULL, NULL < 6, and NULL < NULL.

In SQL these comparisons evaluate to that intrusive truth value, unknown. It goes on to explain that the extension of a predicate consists exactly of those instantiations of it that evaluate to true, from which we can conclude, of every instantiation that does not appear in the extension, that it is false, in which case it must appear instead in the extension of the negation of that predicate. In SQL, then, the instantiation 5 < NULL, for example, cannot be considered to appear in either the extension of a < b or NOT (a < b). Or so it would appear.

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