PROPOSITIONAL FUNCTION

in logic, a statement expressed in a form that would take on a value of true or false were it not for the appearance within it of a variable x (or of several variables), which leaves the statement undetermined as long as no definite values are specified for the variables. Denoted as a mathematical function, A(x) or A(x1, x2, , xn), the propositional function is an abstraction from propositional forms (or predicates). For example, x is small, x ist klein, and x is not large are all propositional forms. The substitution of some noun (or value) for x yields a specific proposition that is either true or false, but x is small itself has no truth-value. Abstracting from these three propositional forms yields a propositional function A(x), which has, for example, the value true when x takes the value mouse and has the value false when x is elephant. Propositional functions permit the treatment in symbolic logic of propositions the truth of which is contingent upon variable components.