Abstract

We study unification and admissibility for an infinite class of modal logics. Conditions superimposed to these logics are to be decidable, Kripke complete, and generated by the classes of rooted frames possessing the greatest clusters of states (in particular, these logics extend modal logic S4.2). Given such logic \( L \) and each formula \( \alpha \) unifiable in \( L \) , we construct a unifier  \( \sigma \) for  \( \alpha \) in  \( L \) , where \( \sigma \) verifies admissibility in \( L \) of arbitrary inference rules \( \alpha/\beta \) with a switched-modality conclusions  \( \beta \) (i.e.,  \( \sigma \) solves the admissibility problem for such rules).

中文翻译：

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与 S4.2 相关的模态逻辑的可接受性和统一性

摘要

我们研究无限类模态逻辑的统一性和可接受性。叠加到这些逻辑上的条件是可判定的、Kripke 完备的，并且由拥有最大状态簇的根框架类生成（特别是，这些逻辑扩展了模态逻辑 S4.2）。给定这样的逻辑\( L \)和\( L \)中的每个公式\( \alpha \)是统一的，我们 为 \( L \)中的 \( \alpha \)构造一个统一符\( \sigma \)，其中\( \sigma \)使用切换模态结论 \( \beta \)验证任意推理规则\( \alpha/\beta \)在\( L \)中的可接受性（即 \( \sigma \)解决了此类规则的可接受性问题）。