In this paper, we investigate neighbourhood semantics for modal extensions of relevant logics. In particular, we combine the neighbourhood interpretation of the relevant implication (and related connectives) with a neighbourhood interpretation of modal operators. We prove completeness for a range of systems and investigate the relations between neighbourhood models and relational models, setting out a range of augmentation conditions for the various relations and operations.

中文翻译：

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模态相关逻辑的邻域语义

在本文中，我们研究了相关逻辑模态扩展的邻域语义。特别是，我们将相关含义（和相关连接词）的邻域解释与模态算子的邻域解释结合起来。我们证明了一系列系统的完整性，并研究了邻域模型和关系模型之间的关系，为各种关系和操作设置了一系列增强条件。