概念空间的彻底形式化
A Thorough Formalization of Conceptual Spaces
摘要：
概念空间的高度影响力的框架提供了一个几何的方式来表示知识。在高维空间中，概念由点表示，概念由该空间中的凸区域表示。在指出概念空间的凸性要求存在的问题后，提出了一种基于模糊星形集的概念空间形式化。我们的形式化使用参数定义的概念，并通过添加手段来表示不同域之间的相关性，以几何的方式扩展了原来的框架。此外，我们定义了计算效率的概念（交集，工会，投影到一个子空间）的操作，并表明这些操作可以支持学习和推理过程。
英文摘要：
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a high-dimensional space and concepts are represented by convex regions in this space. After pointing out a problem with the convexity requirement, we propose a formalization of conceptual spaces based on fuzzy star-shaped sets. Our formalization uses a parametric definition of concepts and extends the original framework by adding means to represent correlations between different domains in a geometric way. Moreover, we define computationally efficient operations on concepts (intersection, union, and projection onto a subspace) and show that these operations can support both learning and reasoning processes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
