“De Morgan negation”的概念、定义、翻译、参考文献-科学参考

De Morgan negation

Logic

In a deductive system $L$ with conjunction and disjunction connectives $\land$ and $\lor$ , respectively, a unary connective that is involutive and satisfies De Morgan’s laws. Formally, in a deductive system $L$ , a negation $\neg$ is De Morgan when for all formulae $φ$ and $ψ$ , the following equivalences are admissible:
$\frac{φ}{\bar{\neg \neg φ}} \frac{\neg (φ \land ψ)}{\bar{\neg φ \lor \neg ψ}} \frac{\neg (φ \lor ψ)}{\bar{\neg φ \land \neg ψ}}$
Notably, De Morgan negation is not required to satisfy the principle of explosion or the law of excluded middle.

单词	De Morgan negation
释义	De Morgan negation Logic In a deductive system $L$ with conjunction and disjunction connectives $\land$ and $\lor$ , respectively, a unary connective that is involutive and satisfies De Morgan’s laws. Formally, in a deductive system $L$ , a negation $\neg$ is De Morgan when for all formulae $φ$ and $ψ$ , the following equivalences are admissible: $\frac{φ}{\bar{\neg \neg φ}} \frac{\neg (φ \land ψ)}{\bar{\neg φ \lor \neg ψ}} \frac{\neg (φ \lor ψ)}{\bar{\neg φ \land \neg ψ}}$ Notably, De Morgan negation is not required to satisfy the principle of explosion or the law of excluded middle.
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