Propositional variable: Difference between revisions

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Revision as of 04:45, 26 November 2014

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In [[mathematical logic]], a '''propositional variable''' (also called a '''sentential variable''' or '''sentential letter''') is a [[Variable (mathematics)|variable]] which can either be '''true''' or '''false'''. Propositional variables are the basic building-blocks of [[propositional formula]]s, used in [[propositional logic]] and higher logics.

==Uses==

Formulas in logic are typically built up recursively from some propositional variables, some number of [[logical connective]]s, and some [[logical quantifier]]s. Propositional variables are the [[atomic formula]]s of propositional logic. For example, in a given propositional logic, we might define a formula as follows:

;Example

Formulas in logic are typically built up recursively from some propositional variables, some number of [[logical connective]]s, and some [[logical quantifier]]s. Propositional variables are the [[atomic formula]]s of propositional logic. For example, in a given propositional logic, we might define a formula as follows:

In a given propositional logic, we might define a formula as follows:

*Every propositional variable is a formula.

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In this way, all of the formulas of propositional logic are built up from propositional variables as a basic unit. Propositional variables should not be confused with the [[metavariable]]s which appear in the [[Propositional_logic#Example_1._Simple_axiom_system|typical axioms of propositional calculus]]; the latter effectively range over well-formed formulae.

==In first order logic==

Propositional variables are represented as nullary [[Predicate (mathematical logic)|predicates]] in [[first order logic]].