论文标题
积极的模态逻辑超出分布
Positive Modal Logic Beyond Distributivity
论文作者
论文摘要
我们为（模态）晶格开发了二元性，不需要分配，并使用它来研究阳性（模态）逻辑超出分布式，我们称之为弱（模态）逻辑。这种二元性建立在霍夫曼（Hofmann），Mislove和stralka二元性的基础上。我们介绍了$π_1$的概念，并表明每个弱的正模态逻辑为$π_1$ - 渗透率。这种方法为弱正模态逻辑提供了一种新的关系语义，我们证明了Sahlqvist对应性结果的类似物。
We develop a duality for (modal) lattices that need not be distributive, and use it to study positive (modal) logic beyond distributivity, which we call weak positive (modal) logic. This duality builds on the Hofmann, Mislove and Stralka duality for meet-semilattices. We introduce the notion of $Π_1$-persistence and show that every weak positive modal logic is $Π_1$-persistent. This approach leads to a new relational semantics for weak positive modal logic, for which we prove an analogue of Sahlqvist correspondence result.
