Monadic predicate calculus

<p>In <a href="/facts/Logic/8JnpJLtt">logic</a>, the monadic predicate calculus (also called monadic first-order logic) is the fragment of <a href="/facts/First-order_logic/lcISqWIg">first-order logic</a> in which all relation symbols in the <a href="/facts/Signature_(mathematical_logic)/C0YQCuce">signature</a> are <a href="/facts/Monadic_(arity)/zSVuwHvP">monadic</a> (that is, they take only one argument), and there are no function symbols. All <a href="/facts/Atomic_formula/s9WMnbqT">atomic formulas</a> are thus of the form 
  
    
      
        P
        (
        x
        )
      
    
    {\displaystyle P(x)}
  
, where 
  
    
      
        P
      
    
    {\displaystyle P}
  
 is a relation symbol and 
  
    
      
        x
      
    
    {\displaystyle x}
  
 is a <a href="/facts/Variable_(mathematics)/VbQlrvKz">variable</a>.
</p><p>Monadic predicate calculus can be contrasted with polyadic predicate calculus, which allows relation symbols that take two or more arguments.
</p>

Monadic predicate calculus open-in-new

Monadic predicate calculus