On the Translation of Qualitative Spatial Reasoning Problems into Modal Logics
On the Translation of Qualitative Spatial Reasoning Problems into Modal Logics
复制标题
论定性空间推理问题到模态逻辑的转化
DOI：
--
复制
发表时间：
1999
期刊：
影响因子：
--
通讯作者：
W. Nutt
中科院分区：
文献类型：
--
作者：
W. Nutt
我们引入拓扑集约束来表达区域之间的定性空间关系。在拓扑空间上解释约束。我们展示了如何将我们的约束转换成多模态命题逻辑的公式，并给出了这种转换保持可满足性的严格证明。因此，已知的模态逻辑推理算法可以应用于定性空间推理。我们的研究结果为Bennett、Nebel、Renz等人在RCC8形式主义中的空间推理工作奠定了正式的基础。
We introduce topological set constraints that express qualitative spatial relations between regions. The constraints are interpreted over topological spaces. We show how to translate our constraints into formulas of a multimodal propositional logic and give a rigorous proof that this translation preserves satisfiability. As a consequence, the known algorithms for reasoning in modal logics can be applied to qualitative spatial reasoning. Our results lay a formal foundation to previous work by Bennett, Nebel, Renz, and others on spatial reasoning in the RCC8 formalism.