Propositional variable: Difference between revisions

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== 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>.<ref name=":0">{{Cite web|date=2020-04-06|title=Comprehensive List of Logic Symbols|url=https://mathvault.ca/hub/higher-math/math-symbols/logic-symbols/|access-date=2020-08-20|website=Math Vault|language=en-US}}</ref><ref>{{Cite web|title=Predicate Logic {{!}} Brilliant Math & Science Wiki|url=https://brilliant.org/wiki/predicate-logic/|access-date=2020-08-20|website=brilliant.org|language=en-us}}</ref>
 
;Example
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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_1._Simple_axiom_system|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>.<ref name=":0" />
 
== Predicate logic ==