text: **First-order logic**
  
  First-order logic includes the same propositional connectives as 
  propositional logic but differs from it because it articulates the 
  internal structure of propositions. This happens through devices 
  such as singular terms, which refer to particular objects, 
  predicates, which refer to properties and relations, and quantifiers, 
  which treat notions like "some" and "all".[123] For example, to 
  express the proposition "this raven is black", one may use the 
  predicate 
  . To express that 
  referring to the raven to form the expression 
   is combined 
  some objects are black, the existential quantifier 
  with the variable 
  . First-order logic contains various rules of inference 
  that determine how expressions articulated this way can form valid arguments, for example, that one may 
  infer 
  
  Gottlob Frege's*Begriffschrift*
  introduced the notion of quantifier in 
  a graphical notation, which here 
  represents the judgment that 
  
   for the property "black" and the singular term 
   is true. 
  
  .[124]   from 