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Assignment

SEMANTICS: the function which assigns a reference to a variable. The truth-value of quantified formulas is determined with respect to a given assignment. EXAMPLE: in order to determine whether All(v)[P] is true with respect to an assignment g we have to check whether P is true for every assignment g' differing at most from g in the value it assigns to v. Exists(v)[P] is true with respect to an assignment g when P is true for at least one assignment g' which may only differ from g in the value it assigns to v. The use of assignments to variables makes it possible to interpret multiply quantified formulas in a compositional way.

LIT.	Gamut, L.T.F. (1991)