Modal Logic for Granularity

粒度模态逻辑

• 批准号: 2834843
• 金额: --
• 依托单位: University of Leeds
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2023
• 资助国家: 英国
• 起止时间: 2023 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2834843
• 关键词: Modal; Logic; Granularity

The aim of this project is to develop a logic which allows the representation of statements such as "At all levels of detail ..." and "At some level of detail ...". The main area of application is to reasoning about spatial information, especially in a discrete space such as a graph representing a network, or an image built of pixels with a graph modelling adjacency. The project builds on work using a non-classical modal logic, BISKT, for describing spatial relations at a single level of detail in a discrete space. The project will investigate bisimulation and the Hennessy-Milner property for the BISKT logic, as this is part of the underlying modal theory that has not been explored. In order to study granularity, the perspective of co-algebras will be applied. The existing BISKT semantics can be expressed in terms of T-coalgebras for a suitable endofunctor, T, on the category of pre-ordered sets and order-preserving functions. This setting represents a very natural space to develop the BISKT semantics and opens up a new line of research where, the objective would be to provide a coalgebraic interpretation of semantic and syntactic properties of BISKT.

该项目的目的是开发一种逻辑，允许表示“在所有细节级别......”和“在某些细节级别......”等语句。主要应用领域是推理空间信息，特别是在离散空间中，例如表示网络的图，或由具有图建模邻接的像素构建的图像。该项目建立在使用非经典模态逻辑 BISKT 的基础上，用于描述离散空间中单个细节级别的空间关系。该项目将研究 BISKT 逻辑的互模拟和 Hennessy-Milner 属性，因为这是尚未探索的基础模态理论的一部分。为了研究粒度，将应用协代数的视角。现有的 BISKT 语义可以用 T 代数来表示，用于在预序集和保序函数的类别上合适的内函子 T。这种设置代表了开发 BISKT 语义的非常自然的空间，并开辟了一条新的研究路线，其目标是提供 BISKT 语义和句法属性的联合代数解释。