In propositional logic, a **propositional formula** is a type of syntactic formula which is well formed and has a truth value. If the values of all variables in a propositional formula are given, it determines a unique truth value. A propositional formula may also be called a **propositional expression**, a **sentence**, or a **sentential formula**.

A propositional formula is constructed from simple propositions, such as "*x* is greater than three" or propositional variables such as *P* and *Q*, using connectives such as NOT, AND, OR, and IMPLIES; for example:

- (
*x*= 2 AND*y*= 4) IMPLIES*x*+*y*= 6.

In mathematics, a propositional formula is often more briefly referred to as a "**proposition**", but, more precisely, a propositional formula is not a proposition but a formal expression that *denotes* a proposition, a formal object under discussion, just like an expression such as "*x* + *y*" is not a value, but denotes a value. In some contexts, maintaining the distinction may be of importance.

Read more about Propositional Formula: Propositions, An Algebra of Propositions, The Propositional Calculus, Propositional Connectives, More Complex Formulas, Inductive Definition, Parsing Formulas, Well-formed Formulas (wffs), Reduced Sets of Connectives, Normal Forms, Impredicative Propositions, Propositional Formula With "feedback", Historical Development

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