In 2003 Zia Movahed pointed to a passage of Avicenna, written probably in 1022, which Movahed claimed anticipated the modal formula of Barcan (that ‘For every $x$ necessarily $\phi $’ entails ‘Necessarily for every $x$$\phi $’), and its converse. Since 2003, examination of early logical writings of Avicenna has clarified how he understood entailments between modal sentences, using his own new temporal language to provide a kind of semantics. In the light of that, Movahed’s claim for the Barcan formula needs some tidying up but is basically correct. But by his semantics Avicenna should not have claimed the converse Barcan formula and probably didn’t claim it.

中文翻译：

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阿维森纳是如何理解巴肯公式的？

2003 年，Zia Movahed 指出了可能写于 1022 年的 Avicenna 的一段，Movahed 声称这预测了 Barcan 的模态公式（“对于每个 $x$ 必然 $\phi $”意味着“对于每个 $x$$\phi $')，以及它的反面。自 2003 年以来，对阿维森纳早期逻辑著作的考察已经阐明了他如何理解情态句之间的蕴涵，使用他自己的新时态语言来提供一种语义。鉴于此，Movahed 对 Barcan 公式的主张需要一些整理，但基本上是正确的。但根据他的语义，阿维森纳不应该声称逆巴坎公式，也可能没有声称它。