A Mathematical Model for Knowledge Acquisition

The way in which we acquire and organize knowledge to construct our perception of the world is a fascinating and little understood phenomenon. Cognitive scientists have proposed and studied a wide variety of models for learning and understanding. Most of these models are inspired by the physical characteristics and biological processes that we have observed in thinking beings. Though great strides have been made in the study of the workings of the brain, we are still far from a complete understanding. Naturally occurring phenomena have consistently proven to be a much harder study than anything man has ever created. This work proposes an abstract model of knowledge acquisition that is not based on cognitive science nor the biology of the brain. The model is instead a purely abstract model which is built out of the notion of concept lattices and the mathematical theory of closure spaces. The model is explored and compared with our intuitive understanding of how we acquire and organize knowledge. It is our hope that such a model could prove useful for further study and understanding of the phenomenon of knowledge acquisition [3, 7–9, 15].