论文标题
分析邻里空间上的空间特性
Analysing Spatial Properties on Neighbourhood Spaces
论文作者
论文摘要
我们提出了邻里空间的分配关系，这是拓扑空间的概括。我们表明，这种概念保留了双仿真，保留了空间逻辑SLC的公式。然后，我们使用此保存结果表明SLC无法表达标准的拓扑特性，例如分离和连接性。此外，我们将双仿真关系与标准模态仿真和模态仿真与匡威进行比较，并证明它与后者一致。
We present a bisimulation relation for neighbourhood spaces, a generalisation of topological spaces. We show that this notion, path preserving bisimulation, preserves formulas of the spatial logic SLCS. We then use this preservation result to show that SLCS cannot express standard topological properties such as separation and connectedness. Furthermore, we compare the bisimulation relation with standard modal bisimulation and modal bisimulation with converse on graphs and prove it coincides with the latter.
