1. <logic> A bound variable or formal argument in a function definition is replaced by the actual argument when the function is applied. In the lambda abstraction
\ x . Mx is the bound variable. However, x is a free variable of the term M when M is considered on its own. M is the scope of the binding of x. [FOLDOC]
2. <predicate logic> In predicate logic, an individual variable at least one of whose occurrences lies within the scope of a quantifier on the same letter. Because other occurrences may be free, a variable may be both free and bound in the same wffs.
to bind a variable to add a quantifier on an individual variable, x, to a wff so that one or more previously free occurrences of x lie inside the scope of that quantifier.
See closure, free variable
[Glossary of First-Order Logic]
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