Individual km#FOL__first-order_logic__firstorderlogic__first-order_predicate_calculus__predicate_logic__predicatelogic  FOL is distinguished from HOL in that it does not allow statements such as "for every property, it is the case that..." or "there exists a set of objects such that..."; it is a stronger theory than sentential logic, but a weaker theory than arithmetic, set theory, or second-order logic; it is strong enough to formalize all of set theory and thereby virtually all of mathematics
  >part:  PCEF_logic
  >part of:  predicate_logic__predicatelogic__predicate_calculus  permits the formulation of quantified statements such as "there is at least one X such that..." or "for any X, it is the case that...", where X is an element of a set called the domain of discourse
     >part of:  mathematical_logic__symbolic_logic__metamathematics__metamathematic
        >part of:  formal_logic
           >part of:  logic.philosophy  the branch of philosophy that analyzes inference
              >part of:  philosophy  the rational investigation of questions about existence and knowledge and ethics
        >part of:  abstract_algebra

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