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SQL and Relational Theory, 2nd Edition by C.J. Date

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SIMPLE AND COMPOUND PREDICATES

Consider the following statements:[139]

  1. x is a star

  2. x has two moons

  3. x has m moons

  4. x is between Earth and y

  5. x is between y and z

Here x, y, z, and m are parameters or placeholders. As a consequence, the statements aren’t propositions (i.e., they aren’t unequivocally either true or false), precisely because they do involve such parameters. For example, the statement “x is a star” involves the parameter x, and we can’t say whether it’s true or false unless and until we’re told what that x stands for—at which point we’re no longer dealing with the given statement anyway but a different one instead, as the paragraph immediately following makes clear.

Now, we can substitute arguments for the parameters and thereby obtain propositions from those parameterized statements. For example, if we substitute the argument the sun for the parameter x in “x is a star,” we obtain “the sun is a star.” And this statement is indeed a proposition, because it’s unequivocally either true or false (in fact, of course, it’s true). But the original statement as such (“x is a star”) is, to say it again, not itself a proposition. Rather, it’s a predicate, which—as you’ll recall from Chapter 5—is a truth valued function; that is to say, it’s a function that, when invoked, returns a truth value. Like all functions, a predicate has a set of parameters; when it’s invoked, arguments are substituted for the parameters; substituting arguments for the parameters effectively converts the predicate ...

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