Abstract

We consider products of modal logics in topological semantics and prove that the topological product of S4.1 and S4 is the fusion of logics S4.1 and S4 plus one extra asiom. This is an example of a topological product of logics that is greater than the fusion but less than the semiproduct of the corresponding logics. We also show that this product is decidable.

中文翻译：

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模态逻辑与麦肯锡公理的拓扑积

摘要

我们在拓扑语义中考虑模态逻辑的乘积，并证明S4.1和S4的拓扑乘积是逻辑S4.1和S4的融合加上一个额外的asiom。这是逻辑的拓扑乘积大于融合但小于相应逻辑的半积的示例。我们还表明该产品是可判定的。