A truth-function of a number of propositions or sentences is a function of them that has a definite truth-value, dependent only on the truth-values of the constituents. Thus (p & q ) is a combination whose truth-value is true when p is true and q is true, and false otherwise. ¬ p is a truth-function of p, false when p is true and true when p is false. The way in which the value of the whole is determined by the combinations of values of constituents is presented in a truth-table. The propositional calculus is the standard treatment of truth-functional combinations. Its constants, &, ∨ , ¬, →, and ↔, are all truth-functors, i.e. expressions standing for truth-functions.

Philosophy dictionary. . 2011.

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