Formal properties and rules of concept algebra
Mehrdad Valipour, Yingxu Wang · 2015
Concept algebra is a denotational mathematics for rigorously manipulating formal concepts and their algebraic operations in knowledge representation, semantic analyses, and machine learning. Properties of concept algebra are formally studied in order to elaborate the nature of formal concepts and their algebraic operations. This leads to a set of algebraic rules in the categories of relational, reproductive, and compositional operations on formal concepts. Relationship between algebraic operations of concept algebra is rigorously described. Proofs are provided for the algebraic rules of concept algebra elaborated by examples. This work enables a rigorous implementation of concept algebra in cognitive knowledge base manipulations and cognitive machine learning.