sentential function, or propositional function, n. (Logic) a well-formed expression containing a free occurrence of a variable that can be replaced by a name to yield a sentence; for example, x is wise, or x gave y to z. In a formulation of the predicate calculus in which names and atomic sentences are primitive, an open sentence is obtained from a well-formed sentence by replacing a name uniformly with a variable. An open sentence does not have a truth-value, but a sequence will satisfy it if the replacement of its variables by the respective elements of the sequence yields a true sentence; if each of the variables is bound by a quantifier, the resulting closed sentence also has truth value.