Thread:Demetrick7/@comment-5761448-20130418020616/@comment-26160254-20130422001743

that is, a term is recursively defined to be a constant c (a named object from the domain of discourse), or a variable x (ranging over the objects in the domain of discourse), or an n-ary function f whose arguments are terms tk. Functions map tuples of objects to objects.

Propositions: that is, a proposition is recursively defined to be an n-ary predicate P whose arguments are terms tk, or an expression composed of logical connectives (and, or) and quantifiers (for-all, there-exists) used with other propositions.

An atomic formula or atom is simply a predicate applied to a tuple of terms; that is, an atomic formula is a formula of the form P (t1, …, tn) for P a predicate, and the tk terms.

All other well-formed formulae are obtained by composing atoms with logical connectives and quantifiers.

For example, the formula ∀x. P (x) ∧ ∃y. Q (y, f (x)) ∨ ∃z. R (z) contains the atoms