First-order logic – also known as first-order predicate calculus and predicate logic – is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects and allows the use of sentences that contain variables, so that rather than propositions such as Socrates is a man one can have expressions in the form “there exists X such that X is Socrates and X is a man” where there exists is a quantifier and X is a variable.This distinguishes it from propositional logic, which does not use quantifiers.
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