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{{short description|
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
== 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, and are often denoted using capital [[Latin script|roman letters]] such as <math>P</math>, <math>Q</math> and <math>R</math>.
;Example
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* Every propositional variable is a formula.
* Given a formula ''X'', the [[negation]] ''¬X'' is a formula.
* 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
== Predicate logic ==
Propositional variables
The internal structure of propositional variables contains [[predicate symbol|predicate letters]] such as P and Q, in association with [[bound variable|bound]] individual variables (e.g., x, ''y''), individual constants such as ''a'' and ''b'' ([[singular term]]s from a [[___domain of discourse]] D), ultimately taking a form such as P''a'', ''a''R''b''.(or with parenthesis, <math>P(11)</math> and <math>R(1, 3)</math>).<ref>{{Cite web|date=2015-06-24|title=Mathematics {{!}} Predicates and Quantifiers {{!}} Set 1|url=https://www.geeksforgeeks.org/mathematic-logic-predicates-quantifiers/|access-date=2020-08-20|website=GeeksforGeeks|language=en-US}}</ref> Propositional logic is sometimes called [[zeroth-order logic]] due to not considering the internal structure in contrast with [[first-order logic]] which analyzes the internal structure of the atomic sentences.
== See also ==
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* [[Boolean algebra (logic)]]
* [[Boolean
* [[Boolean ___domain]]
* [[Boolean function]]
* [[Logical value]]
* [[Predicate variable]]
* [[Propositional logic]]
{{div col
== References ==
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== Bibliography ==
* Smullyan, Raymond M. ''First-Order Logic''. 1968. Dover edition, 1995. Chapter 1.1: Formulas of Propositional Logic.
{{Mathematical logic}}
[[Category:Propositional calculus]]
[[Category:Concepts in logic]]
[[Category:Logic symbols]]
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