The definition of institution formalizes the intuitive notion of logic in a category-based setting. Similarly, the concept of stratified institution provides an abstract approach to Kripke semantics. This includes hybrid logics, a type of modal logics expressive enough to allow references to the nodes/states/worlds of the models regarded as relational structures, or multi-graphs. Applications of hybrid logics involve many areas of research, such as computational linguistics, transition systems, knowledge representation, artificial intelligence, biomedical informatics, semantic networks, and ontologies. The present contribution sets a unified foundation for developing formal verification methodologies to reason about Kripke structures by defining proof calculi for a multitude of hybrid logics in the framework of stratified institutions . To prove completeness, the article introduces a forcing technique for stratified institutions with nominal and frame extraction and studies a forcing property based on syntactic consistency. The proof calculus is shown to be complete and the significance of the general results is exhibited on a couple of benchmark examples of hybrid logical systems.

中文翻译：

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混合逻辑的强制和演算

的定义机构在基于类别的设置中形式化了直观的逻辑概念。同样，概念分层机构为 Kripke 语义提供了一种抽象方法。这包括混合逻辑，一种模态逻辑，其表达方式足以允许引用被视为关系结构或多图的模型的节点/状态/世界。混合逻辑的应用涉及许多研究领域，例如计算语言学、转换系统、知识表示、人工智能、生物医学信息学、语义网络和本体。目前的贡献为开发形式验证方法论奠定了统一的基础，通过在分层机构. 为了证明完整性，文章引入了一个强迫技术具有名义和框架提取的分层机构并研究一个强制财产基于句法一致性。证明演算被证明是完整的，并且在混合逻辑系统的几个基准示例中展示了一般结果的重要性。