Free Variable (First-Order Logic)

Definition

Free Variable (First-Order Logic)

For a term $t$ , the set $free (t)$ of free variables is:
$t = x \in V t a constant t = f (t_{1}, \dots, t_{n}) : free (t) = {x} : free (t) = \emptyset : free (t) = i = 1 ⋃ n free (t_{i})$
For a formula $φ$ , the set $free (φ)$ of free variables is:
$φ = P (t_{1}, \dots, t_{n}) φ = \neg ψ φ = (ψ ⊙ ψ^{'}), ⊙ \in {\land, \lor, \to} φ = (\forall x ψ), (\exists x ψ) : free (φ) = i = 1 ⋃ n free (t_{i}) : free (φ) = free (ψ) : free (φ) = free (ψ) \cup free (ψ^{'}) : free (φ) = free (ψ) ∖ {x}$

Lukas' Notes

Free Variable (First-Order Logic)

Definition

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