Formal properties and rules of concept algebra

Author

Valipour, Mehrdad ; Wang, Yingxu

Author_Institution

International Institute of Cognitive Informatics and Cognitive Computing (ICIC), Laboratory for Computational Intelligence and Software Science, Dept. of Electrical and Computer Engineering, Schulich School of Engineering and Hotchkiss Brain Institute, Un

fYear

2015

fDate

6-8 July 2015

Firstpage

128

Lastpage

135

Abstract

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.

Keywords

Algebra; Artificial intelligence; Indexes; Concept Algebra; algebraic properties; cognitive machine learning; denotational mathematics; formal concept; knowledge manipulation;

fLanguage

English

Publisher

ieee

Conference_Titel

Cognitive Informatics & Cognitive Computing (ICCI*CC), 2015 IEEE 14th International Conference on

Conference_Location

Beijing, China

Print_ISBN

978-1-4673-7289-3

Type

conf

DOI

10.1109/ICCI-CC.2015.7259376

Filename

7259376