Propositional variable: Difference between revisions

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{{short description|Variable that can either be true or false}}

In [[mathematical logic]], a '''propositional variable''' (also called a '''sentence letter,<ref name=":13">{{Cite book |last=Howson |first=Colin |author-link=Colin Howson |title=Logic with trees: an introduction to symbolic logic |date=1997 |publisher=Routledge |isbn=978-0-415-13342-5 |___location=London; New York |pages=5}}</ref>''' '''sentential variable,''' or '''sentential letter''') is an input [[variable (mathematics)|variable]] (that can either be '''true''' or '''false''') of a [[truth function]]. Propositional variables are the basic building-blocks of [[propositional formula]]s, used in [[propositional logic]] and [[higher-order logic]]s.

== Uses ==

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* Given two formulas ''X'' and ''Y'', and a [[binary connective]] ''b'' (such as the [[logical conjunction]] ∧), the expression ''(X b Y)'' is a formula. (Note the parentheses.)

Through this construction, all of the formulas of propositional logic can be 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|typical axioms of [[propositional calculus]]; the latter effectively range over well-formed formulae, and are often denoted using lower-case greek letters such as <math>\alpha</math>, <math>\beta</math> and <math>\gamma</math>.

== Predicate logic ==

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* [[Boolean algebra (logic)]]

* [[Boolean datatypedata type]]

* [[Boolean ___domain]]

* [[Boolean function]]

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[[Category:Concepts in logic]]

[[Category:Logic symbols]]

{{logic-stub}}