| __First order predicate calculus__ *(Site not responding. Last check: 2007-10-31)* |

| | First-order **predicate** **calculus** or first-order logic (FOL) is a theory in symbolic logic that states quantified statements such as "there existsan object such that..." or "for all objects, it is the case that...." |

| | There are two types of axioms: the logical axioms which embody the general truths about proper reasoning involving quantifiedstatements, and the axioms describing the subject matter at hand, for instance axioms describing sets in set theory or axiomsdescribing numbers in arithmetic. |

| | While the set of inference rules in first-order **calculus** is finite, the set of axioms may very well be and often is infinite.However we require that there is a general algorithm which can decide for a givenwell-formed formula whether it is an axiom or not. |

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