Algorithms for determining semantic relations of formal concepts by cognitive machine learning based on concept algebra

It is recognized that the semantic space of knowledge is a hierarchical concept network. This paper presents theories and algorithms of hierarchical concept classification by quantitative semantic relations via machine learning based on concept algebra. The equivalence between formal concepts are analyzed by an Algorithm of Concept Equivalence Analysis (ACEA), which quantitatively determines the semantic similarity of an arbitrary pair of formal concepts. This leads to the development of the Algorithm of Relational Semantic Classification (ARSC) for hierarchically classify any given concept in the semantic space of knowledge. Experiments applying Algorithms ACEA and ARSC on 20 formal concepts are successfully conducted, which encouragingly demonstrate the deep machine understanding of semantic relations and their quantitative weights beyond human perspectives on knowledge learning and natural language processing.