Scope (logic)  

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In logic, the scope of a quantifier or a quantification is the range in the formula where the quantifier "engages in". It is put right after the quantifier, often in parentheses. Some authors describe this as including the variable put right after the forall or exists symbol. In the formula Template:Math, for example, Template:Math (or Template:Math) is the scope of the quantifier Template:Math (or Template:Math).

A variable in the formula is free, if and only if it does not occur in the scope of any quantifier for that variable. A term is free for a variable in the formula (i.e. free to substitute that variable that occurs free), if and only if that variable does not occur free in the scope of any quantifier for any variable in the term.

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Unless indicated otherwise, the text in this article is either based on Wikipedia article "Scope (logic)" or another language Wikipedia page thereof used under the terms of the GNU Free Documentation License; or on research by Jahsonic and friends. See Art and Popular Culture's copyright notice.

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