论文标题
锥形的矫形学
Orthologics for Cones
论文作者
论文摘要
在使用知识表示（KR）技术的应用程序中，尤其是结合数据驱动和逻辑方法的应用程序，对象的域不是抽象的非结构域，而是表现出几何对象的专用，深层结构。一个示例是用于在概念空间中建模自然概念的一类凸组集，该凸空间还通过凸优化技术链接到机器学习。在本文中，我们研究了这种几何结构的逻辑。使用晶格理论的机制，我们描述了最小直接学的扩展，其部分模块化规则适用于封闭凸锥。该逻辑结合了可行的数据结构（利用凸/锥度）的表现力，包括完整的矫形性（利用锥度）。
In applications that use knowledge representation (KR) techniques, in particular those that combine data-driven and logic methods, the domain of objects is not an abstract unstructured domain, but it exhibits a dedicated, deep structure of geometric objects. One example is the class of convex sets used to model natural concepts in conceptual spaces, which also links via convex optimization techniques to machine learning. In this paper we study logics for such geometric structures. Using the machinery of lattice theory, we describe an extension of minimal orthologic with a partial modularity rule that holds for closed convex cones. This logic combines a feasible data structure (exploiting convexity/conicity) with sufficient expressivity, including full orthonegation (exploiting conicity).
