First-order logic is a type of Predicate Logic in which predicates take only individuals as arguments and quantifiers only bind individual variables. 

'' First-order logic is distinguished from propositional logic by its use of quantifiers; each interpretation of first-order logic includes a domain of discourse over which the quantifiers range. Briefly, first-order logic is distinguished from higher-order logics in that quantification is allowed only over atomic entities (individuals but not sets).''
* http://en.wikipedia.org/wiki/First-order_logic

Related:
* PredicateLogic
* BooleanLogic 
* FuzzyLogic 
* ProofTheory 
* SymbolicLogic.

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CategoryLogic