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In first-order logic [2,9,10], given an interpretation I and assignment v,  formula \(\forall xA(x)\) is true in (I, v) iff for any element \(a\in U, A(x/a)\) is true in (I, v);  and formula \(\forall xA(x)\) is false in (I, v) iff for some element \(a\in U, A(x/a)\) is false in (I, v),  where U is the universe of interpretation I.

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Binary-Valued First-Order Logic

  • 章节

  • 发表日期：

    2025年

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  • Wei Li,
  • Yuefei Sui

摘要

In first-order logic [2,9,10], given an interpretation I and assignment v,  formula \(\forall xA(x)\) is true in (I, v) iff for any element \(a\in U, A(x/a)\) is true in (I, v);  and formula \(\forall xA(x)\) is false in (I, v) iff for some element \(a\in U, A(x/a)\) is false in (I, v),  where U is the universe of interpretation I.