模态逻辑的半积与积的一些前景
Some prospects for semiproducts and products of modal logics
AI总结：
研究命题模态逻辑L与S5的积和半积，给出新的可最小公理化且有积（或半积）有限模型性质的例子，通过双模拟博弈证明相关局部有限性，得出谓词模态逻辑单变量片段可判定性，还给出不可最简单公理化的反例。
AI中文摘要：
我们考虑命题模态逻辑L与S5的积和半积，给出以最小方式公理化且具有积（或半积）有限模型性质的积逻辑和半积逻辑的新例子。证明的关键部分是这些（半）积对于有限深度L的局部有限性，通过双模拟博弈得到。这些结果意味着谓词模态逻辑QL和QL+巴肯公式的单变量片段的可判定性。我们还给出了新的反例，即不能以最简单方式公理化的（半）积。
英文摘要：
We consider products and semiproducts of propositional modal logics L with S5 and present new examples of product and semiproduct logics axiomatized in the minimal way and enjoying the product (or semiproduct) FMP. An essential part of the proof is local tabularity of these (semi)products for L of finite depth; it is obtained by using bisimulation games. These results readily imply decidability for 1-variable fragments of predicate modal logics QL and QL+Barcan formula. We also present new counterexamples, i.e. (semi)products not axiomatizable in the simplest way.
