- Propositional variable
In

mathematical logic , a**propositional variable**(also called a**sentential variable**or**sentential letter**) is avariable which can either be**true**or**false**. Propositional variables are the basic building-blocks ofpropositional formula s, used inpropositional logic and higher logics.Formulas in logic are typically built up recursively from some propositional variables, some number of

logical connective s, and somelogical quantifier s. Propositional variables are theatomic formula s of propositional logic. For example, in a given propositional logic, we might define a formula as follows:*Every propositional variable is a formula.

*Given a formula "X" thenegation "¬X" is a formula.

*Given two formulas "X" and "Y", and abinary connective "b" (such as thelogical conjunction ∧), then "(X b Y)" is a formula. (Note the parentheses.)In this way, all of the formulas of propositional logic are built up from propositional variables as a basic unit.

**ee also***

Boolean algebra (logic)

*Boolean datatype

*Boolean domain

*Boolean function

*Logical value

*Propositional logic **References***Smullyan, Raymond M. "First-Order Logic". 1968. Dover edition, 1995. Chapter 1.1: Formulas of Propositional Logic.

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