- This article is a technical mathematical article in the area of predicate logic. For the ordinary English language meaning see Sentence (linguistics), for a less technical introductory article see Statement (logic).
In
mathematical logic, a
sentence of a
predicate logic is a boolean-valued
well-formed formula with no
free variables. A sentence can be viewed as expressing a
proposition, something that may be true or false. The restriction of having no free variables is needed to make sure that sentences can have concrete, fixed
truth values: As the free variables of a (general) formula can range over several values, the truth value of such a formula may vary.