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一階述語論理

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[数学]

一階述語論理

  • 一階述語論理
    • 全称量化記号 (universal quantifier) と呼ぶ記号 ∀
    • 存在量化記号 (existential quantifier) と呼ぶ記号 ∃

  Bill is a student.

\( student\left( Bill\right) \)

  Bill takes analysis either geometry

\( takes (Bill, Analysis) \lor takes (Bill, Geometry) \)

  Bill takes analysis and geometry

\( takes (Bill, Analysis) \land takes (Bill, Geometry) \)

  Some students loves Bill

\( \exists_x student(x) \land love (x, Bill) \)

  No students loves Bill

  All students are smart

\( \forall_x student(x) \to smart (x) \)

  All graduating people are happy

\( \forall_x g(x) \to h (x) \)

  All happy people smile

\( \forall_x h(x) \to s (x) \)

  Someone is graduating

\( \exists_x g(x) \)

  Someone is smiling

\( \exists_x s(x) \)