section_path: Systems of logic/Classical/First-order logic
section_name: First-order logic
paragraph_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". For example, to express the proposition "this raven is black", one may use the predicate B {\displaystyle B} for the property "black" and the singular term r {\displaystyle r} referring to the raven to form the expression B (r) {\displaystyle B(r)}. To express that some objects are black, the existential quantifier ∃ {\displaystyle \exists } is combined with the variable x {\displaystyle x} to form the proposition ∃ x B (x) {\displaystyle \exists xB(x)}. 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 ∃ x B (x) {\displaystyle \exists xB(x)} from B (r) {\displaystyle B(r)}.