First-Order Logic System

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A First-Order Logic System is a Predicate Logic System that allows the representation of logic terms, predicate symbols, function symbols, constant symbols, and of Quantification over Variables.







    • A first-order theory is a theory that can be axiomatised as an extension of first-order logic by adding a recursive set of first-order sentences as axioms.
    • Permits the formulation of quantified statements such as "there exists an x such that..." () or "for any x, it is the case that...", where x is a member of the domain of discourse.
  • CYC Glossary
    • first-order predicate calculus (FOPC): A formal language incorporating predicate symbols, function symbols, constant symbols, variables, logical connectives and quantifiers, which can be used to express facts about a world. Unlike propositional logic, FOPC can express general statements or statements about existence, by using quantified variables. "First-order" means that statements which quantify over predicate and function symbols are not allowed.