Towards a General Theory of Classifications

This book provides an original and progressive introduction to the main questions of the theory of classification. It makes connections between previously separate domains of classification theory in applied mathematics, computer science and pure mathematics.

This book is an essay on the epistemology of classifications. Its main purpose is not to provide an exposition of an actual mathematical theory of classifications, that is, a general theory which would be available to any kind of them: hierarchical or non-hierarchical, ordinary or fuzzy, overlapping or non-overlapping, finite or infinite, and so on, establishing a basis for all possible divisions of the real world. For the moment, such a theory remains nothing but a dream. Instead, the authors essentially put forward a number of key questions. Their aim is rather to reveal the state of art of this dynamic field and the philosophy one may eventually adopt to go further. To this end they present some advances made in the course of the last century, discuss a few tricky problems that remain to be solved, and show the avenues open to those who no longer wish to stay on the wrong track. Researchers and professionals interested in the epistemology and philosophy of science, library science, logic and set theory, order theory or cluster analysis will find this book a comprehensive, original and progressive introduction to the main questions in this field.

Takes a comprehensive and historical approach to classification problems Is first in making a connection between previously seperate domains of classification theory in applied mathematics, computer science and pure mathematics Provides an original and progressive introduction to the main questions Attempts to present and comment the idea of a general theory of classifications Includes supplementary material: sn.pub/extras

Inhalt
Foreword.- 1 Philosophical problems.- 2 Information data structures.- 3 Empirical Clustering and classic hierarchies.- 4 Algebra of trees.- 5 Generalized Classifications.- 6 Topology of generalized classifications.- 7 Meta-classification.- 8 For an axiomatic theory of classifications.- 9 Alternative theories and higher infinite.- 10 Postscript.- Bibliography.