Definition. FOL - Quantifiers and Scoping [000x]

  • November 22, 2025

For quantifiers:

\[ \forall x.\ F \quad \exists x.\ F \]

Each variable occurring within the formula \(F\) known as the scope is either:

  • bound: if it is within the scope of a quantifier that binds it. E.g., in \(\forall x.\ P(x, y)\), the variable \(x\) is bound.
  • free: if it is not bound by any quantifier within the formula. E.g., in \(\forall x.\ P(x, y)\), the variable \(y\) is free.