well-formed formula a grammatically wellformed sentence or (structured) predicate of an artificial language of the sort studied by logicians. A well-formed formula is sometimes known as a wff (pronounced ‘woof’) or simply a formula. Delineating the formulas of a language involves providing it with a syntax or grammar, composed of both a vocabulary (a specification of the symbols from which the language is to be built, sorted into grammatical categories) and formation rules (a purely formal or syntactical specification of which strings of symbols are grammatically well-formed and which are not). Formulas are classified as either open or closed, depending on whether or not they contain free variables (variables not bound by quantifiers). Closed formulas, such as (x) (Fx / Gx), are sentences, the potential bearers of truth-values. Open formulas, such as Fx / Gx, are handled in any of three ways. On some accounts, these formulas are on a par with closed ones, the free variables being treated as names. On others, open formulas are (structured) predicates, the free variables being treated as place holders for terms. And on still other accounts, the free variables are regarded as implicitly bound by universal quantifiers, again making open formulas sentences. See also FOR- MAL LOGIC , LOGICAL CONSTANT , LOGICAL SYNTAX , QUANTIFICATIO. G.F.S.