satisfaction an auxiliary semantic notion introduced by Tarski in order to give a recursive definition of truth for languages containing quantifiers. Intuitively, the satisfaction relation holds between formulas containing free variables (such as ‘Building(x) & Tall(x)’) and objects or sequences of objects (such as the Empire State Building) if and only if the formula ‘holds of’ or ‘applies to’ the objects. Thus, ‘Building(x) & Tall(x)’, is satisfied by all and only tall buildings, and ‘-Tall(x1) & Taller(x1, x2)’ is satisfied by any pair of objects in which the first object (corresponding to ‘x1’) is not tall, but nonetheless taller than the second (corresponding to ‘x2’). Satisfaction is needed when defining truth for languages with sentences built from formulas containing free variables, because the notions of truth and falsity do not apply to these ‘open’ formulas. Thus, we cannot characterize the truth of the sentences ‘Dx (Building(x) & Tall(x))’ (‘Some building is tall’) in terms of the truth or falsity of the open formula ‘Building(x) & Tall(x)’, since the latter is neither true nor false. But note that the sentence is true if and only if the formula is satisfied by some object. Since we can give a recursive definition of the notion of satisfaction for (possibly open) formulas, this enables us to use this auxiliary notion in defining truth. See also SEMANTIC PARADOXES , TARSKI, TRUT. J.Et.