On concept algebra and knowledge representation

A concept is a basic unit of cognition that carries certain meanings. In cognitive informatics, a concept is formally modeled as an abstract and dynamic mathematical structure that encapsulates attributes, objects, and relations. The most important feature of an abstract concept is its networking capability, or the adaptive capability to interrelate itself to other concepts. This paper presents a formal theory for abstract concepts and knowledge manipulation known as concept algebra. The mathematical models of concepts and knowledge are developed based on the object-attribute-relation (OAR) theory. The formal methodology for manipulating knowledge as a concept network is described. Case studies demonstrate that the concept network and concept algebra provide a generic and formal knowledge manipulation means that are capable to deal with complex knowledge structures and their algebraic operations.