Propositional formula

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A propositional formula (also called a propositional expression, a sentence, or a sentential formula) is a syntactic expression that is formed from the elements in a given alphabet A of propositional variables, say, A = {p, q, r, …}, together with the elements in a given set of k-adic operator symbols from propositional logic, typically, the 0-adic operator symbols in {false, true}, the 1-adic symbol ¬, plus some subset of the 2-adic symbols in {∧, ∨, →, ↔}. Other collections of operator symbols may be used, depending on the particular formal language that is in play.

In contexts of discussion that involve little risk of confusion, a propositional formula may be more briefly referred to as a "proposition", but the distinction between a proposition, a formal object under discussion, and a propositional formula, a formal expression that denotes it, must be maintained.