Predicate variable

<p>In <a href="/facts/Mathematical_logic/SaI7Y3wN">mathematical logic</a>, a predicate variable is a <a href="/facts/Predicate_(mathematical_logic)/5WazAvKF">predicate</a> letter which functions as a "placeholder" for a <a href="/facts/Finitary_relation/JkNnVYNj">relation</a> (between terms), but which has not been specifically assigned any particular relation (or meaning). Common symbols for denoting predicate variables include capital <a href="/facts/Latin_script/7EWeJjUV">roman letters</a> such as 
  
    
      
        P
      
    
    {\displaystyle P}
  
, 
  
    
      
        Q
      
    
    {\displaystyle Q}
  
 and 
  
    
      
        R
      
    
    {\displaystyle R}
  
, or lower case roman letters, e.g., 
  
    
      
        x
      
    
    {\displaystyle x}
  
. In <a href="/facts/First-order_logic/lcISqWIg">first-order logic</a>, they can be more properly called <a href="/facts/Metalinguistic_variable/oP8MLX0F">metalinguistic variables</a>. In <a href="/facts/Higher-order_logic/hdUhry6m">higher-order logic</a>, predicate variables correspond to <a href="/facts/Propositional_variable/NtAz1rfI">propositional variables</a> which can stand for <a href="/facts/Well-formed_formula/YpTVlzuj">well-formed formulas</a> of the same logic, and such variables can be quantified by means of (at least) second-order <a href="/facts/Quantifier_(logic)/bgmvwxoo">quantifiers</a>.
</p>

Predicate variable open-in-new

Predicate variable