“commutativity”的概念、定义、翻译、参考文献-科学参考

commutativity

Logic

单词	commutativity
释义	commutativity Logic 1. The property that holds of certain binary connectives $\circ$ in a deductive system $L$ when they commute, that is, when $φ \circ ψ$ and $ψ \circ φ$ are logically equivalent in $L$ . 2. The rules of inference for conjunction ( $\land$ ) and disjunction ( $\lor$ ) that capture the commutativity of the operations. $\frac{φ \land ψ}{ψ \land φ} \frac{φ \lor ψ}{ψ \lor φ}$ Sometimes the rule of permutation, i.e., $\frac{φ \to (ψ \to ξ)}{ψ \to (φ \to ξ)}$ is introduced as a property of commutativity as well. 3. In a multi-modal logic with two operators $□_{0}$ and $□_{1}$ , the equivalence of formulae $□_{0} □_{1} φ$ and $□_{1} □_{0} φ$ and any rule of inference corresponding to this logical equivalence.
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