Propositional Formula

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 FormulaPropositions, 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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