锥形矫正器
Orthologics for Cones
摘要：
在使用知识表示（KR）技术的应用中，特别是那些结合数据驱动和逻辑方法的应用中，对象的域不是抽象的非结构化域，而是呈现出几何对象的专用的深层结构。一个例子是用于在概念空间中对自然概念建模的凸集类，它也通过凸优化技术与机器学习联系起来。在本文中，我们研究这种几何结构的逻辑。使用机器的格理论，我们描述了一个扩展的最小正交与部分模块规则，适用于封闭凸锥。该逻辑将可行的数据结构（利用凸性/圆锥性）与足够的表达性（包括完全正交负性（利用圆锥性））相结合。
英文摘要：
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).
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