propositional function

n. Logic
An expression having the form of a proposition but containing undefined symbols for the substantive elements and becoming a proposition when appropriate values are assigned to the symbols.

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In programming, a statement that evaluates an expression and provides a true or false answer based on the condition of the data.

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The concept introduced by Frege of a function taking a number of names as arguments, and delivering one proposition as the value. The idea is that ‘x loves y’ is a propositional function, which yields the proposition ‘John loves Mary’ for those two arguments (in that order). A propositional function is therefore roughly equivalent to a property or relation. In Principia Mathematica, Russell and Whitehead take propositional functions to be the fundamental functions, since the theory of descriptions could be taken as showing that other expressions denoting functions are incomplete symbols.