English Dictionary

valuation function

名詞

(logic) A function which assigns a truth value to every well-formed formula, which is identical to the model's interpretation function when applied to atomic propositions, and which otherwise assigns a truth value recursively depending on the formula's top logical connective and the truth values of the subformulae surrounding that logical connective.

日本語の意味

（論理学において）すべての整形式文に対して真偽値を割り当てる関数。原子命題に対してはモデルの解釈関数と一致し、それ以外の場合は、文の最上位の論理結合子と周囲の部分式の真偽値に基づいて再帰的に真偽値を決定する関数。

In propositional semantics, a valuation function assigns a truth value to every well-formed formula, coincides with the model's interpretation on atomic propositions, and determines the truth of complex formulas recursively based on their top logical connective and the truth values of their subformulae.

命題論理の意味論において、真理値割当関数はすべての構成式に真理値を割り当て、原子命題に関してはモデルの解釈関数と一致し、その他の場合はその式の最上位の論理結合子と部分式の真理値に基づいて再帰的に真理値を決定します。

意味（1）

(logic) A function which assigns a truth value to every well-formed formula, which is identical to the model's interpretation function when applied to atomic propositions, and which otherwise assigns a truth value recursively depending on the formula's top logical connective and the truth values of the subformulae surrounding that logical connective.

Say that a model's interpration assigns true to A and false to B. Then the valuation function assigns false to not A, true to not B, false to A implies B, false to A and B, and true to A or B.

valuation functions （ plural ）