Predicate logic

Japanese: 述語論理学 - じゅつごろんりがく

A branch of symbolic logic that extends propositional logic and uses two quantifiers, the universal quantifier ∀ and the existential quantifier ∃, in addition to the five logical symbols. Here, ∀xF(x) represents the universal proposition that "for all x, the proposition F(x) holds," and ∃xF(x) represents the existential proposition that "there exists an x such that the proposition F(x) holds." When the variable x on which the quantifiers ∀ and ∃ act has a domain that is a fixed, non-empty set, this is called first-order predicate logic, and is what is usually referred to as predicate logic.

Source : Heibonsha Encyclopedia About MyPedia Information

Japanese:

命題論理学を拡張し，その五つの論理記号のほかに全称記号∀と存在記号∃の二つの限定記号を用いる記号論理学の一分野。ここで∀xF（x）は〈すべてのxに対し命題F（x）が成立する〉という全称命題を，∃xF（x）は〈命題F（x）が成立するようなxが存在する〉という存在命題を表す。限定記号∀，∃が作用する変数xが，空でない一定の集合を変域とする場合が１階の述語論理で，ふつう述語論理といえばこれをさす。

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