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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