Table Represents an Extension - SQL
It describes how each tuple in a relation represents a true instantiation of some predicate and each true instantiation is represented by some tuple in that relation. Thus, a relation represents an extension, its body containing exactly one tuple corresponding to each element of the extension. It is true that some SQL tables can be interpreted in this way but it is also true that some SQL tables cannot. In fact there are at least two distinct ways in which an SQL table cannot be thus interpreted:
a) In SQL it is possible for the same row to appear more than once in a table. Moreover, if tables t1 and t2 differ only in the number of appearances of some row, then that difference is significant-they are not the same table.
b) Although I have noted that in SQL the instantiation 5 < NULL cannot be considered to appear in either the extension of a < b or NOT (a < b), the row (5, NULL) can appear in a table. What could be the corresponding predicate? It would have to be some dyadic predicate, P (a, b) say, such that P (5, NULL) is true. But if NULL stands for "some value but we don't know which", how could that row appear in the same table as, say, (6, 12)? If (6, 12) means "6 is related to 12" then (5, NULL), in relational theory, would have to mean that 5 is related to NULL in that same way. But it can't, because NULL doesn't designate anything. If instead it means "5 is related to something whose identity is unknown", then we have a sentence in which nothing appears in substitution for the parameter b.