Well-Formed Formulas

Atomic formula: an n-ary predicate symbol followed by n terms in parentheses:

e.g., P(x, f(x, a, y))

If F is an atomic formula, then it is a well-formed formula (WFF).

Compound formula: a statement formed from one or more WFFs using logical connectives.

If F is a compound formula, then it is a WFF.

e.g., P(x, f(x, a, y)) v (Q -> R(x))

Quantified formula: a statement formed from a WFFs by prefixing it with a quantifier and a variable.

e.g., (Forall x) (P(x, f(x, a, y)) v (Q -> R(x))) (Exists y) Q(y)

If F is a quantified formula, then it is a WFF.