**SQL and Logic**

*Logic takes care of itself;**all we have to do is look and see how it does it.*

—Ludwig Wittgenstein: *Tractatus Logico-Philosophicus* (1922)

As I mentioned in Chapter 1, there’s an alternative to the relational algebra called the relational calculus. What this means is that queries, constraints, view definitions, and so forth can all be formulated in calculus terms as well as algebraic ones; sometimes, in fact, it’s easier to come up with a calculus formulation than an algebraic one, though the opposite can also be true.

What is the relational calculus? Essentially, it’s an applied form of predicate calculus (also known as predicate logic), tailored to the needs of relational databases. So the aims of this chapter are to introduce the relevant features of predicate logic (hereinafter abbreviated to just *logic*); to show how those features are realized in concrete form in the relational calculus; and, of course, to consider the relevant features of SQL as we go.

Incidentally, it follows from the above that a relational language can be based on either the algebra or the calculus. For example, **Tutorial D** is based on the algebra (which is why there aren’t many references to **Tutorial D** in this chapter), and Query-By-Example and QUEL (see Appendix G) are both based on the calculus. So which is SQL based on? The answer, regrettably, is partly both and partly neither ... When it was first designed, SQL was specifically intended to be different from both the algebra ...

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