Abstract

We study two kinds of combined modal logics, semiproducts and products with \({\mathbf{S5}}\), and their connection with modal predicate logics. We present examples of propositional modal logics, for which semiproducts or products with \({\mathbf{S5}}\) are axiomatized in the minimal way (they are called semiproduct- or product-matching with \({\mathbf{S5}}\)) and also present counterexamples for these properties. The finite model property for (semi)products, together with (semi)product-matching, allow us to obtain decidability of corresponding 1-variable modal predicate logics.

中文翻译：

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半产品、产品和模态谓词逻辑：一些示例

摘要

我们研究两种组合模态逻辑，半积和带\({\mathbf{S5}}\)的积，以及它们与模态谓词逻辑的联系。我们提出了命题模态逻辑的例子，其中具有\({\mathbf{S5}}\)的半积或乘积以最小方式公理化（它们被称为与\({\mathbf{S5}\)的半积或乘积匹配}\)）并提供这些属性的反例。（半）乘积的有限模型属性以及（半）乘积匹配使我们能够获得相应的 1 变量模态谓词逻辑的可判定性。