The logic UBiSKt is a bi-intuitionistic modal logic with universal modalities having a semantics in which formulae are interpreted as subgraphs. We use the logic to formalize the idea of looking at subgraphs at different levels of detail. We show how the logic can be used to define various spatial relations between subgraphs. These relations are considered with respect to change in level of detail. We use an existing formulation of generalized partitions on graphs and hypergraphs in terms of relations to give a novel generalization of the classical modal logic S5 to a bi-intuitionistic modal logic we call UBiSKtS5.

中文翻译：

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在粒度下表达离散的空间关系

逻辑UBiSKt是一种具有通用模态的双直觉模态逻辑，具有一种将公式解释为子图的语义。我们使用逻辑来规范化以不同细节级别查看子图的想法。我们展示了如何使用逻辑来定义子图之间的各种空间关系。考虑到这些关系的详细程度的变化。我们使用关系图在图和超图上使用广义分区的现有表示形式，以将经典模态逻辑S5新颖地推广为称为UBiSKtS5的双直觉模态逻辑。