# 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.

### Other articles related to "formulas, propositional, propositional formula":

Substitution (logic) - Definition
... Where Ψ and Φ represent formulas of propositional logic, Ψ is a substitution instance of Φ if and only if Ψ may be obtained from Φ by substituting formulas for symbols in Φ, always replacing ... A) is a substitution instance of (A A) In some deduction systems for propositional logic, a new expression (a proposition) may be entered on a line of a derivation if it is a substitution instance of a previous ... In first-order logic, every closed propositional formula that can be derived from an open propositional formula by substitution is said to be a substitution instance of ...
Boolean Algebra (logic) - Propositional Logic
... Propositional logic is a logical system that is intimately connected to Boolean algebra ... Many syntactic concepts of Boolean algebra carry over to propositional logic with only minor changes in notation and terminology, while the semantics of propositional ... Syntactically, every Boolean term corresponds to a propositional formula of propositional logic ...
Propositional Formula - Historical Development
... Although a propositional calculus originated with Aristotle, the notion of an algebra applied to propositions had to wait until the early 19th century ... It is here that what we consider "modern" propositional logic first appeared ... connective, the "stroke"

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