Towards a General Theory of Classifications
Springer Science & Business Media, May 14, 2013 - Mathematics - 304 pages
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.
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Aronszajn tree associahedron associated axiom binary called cardinal cells chains of partitions Chap classification theory clique clustering complex concept lattice condition construction contains continuum countable defined Definition dendrogram dissimilarity domain elements equivalent example exists fact field of sets finite set Formal Concept Analysis formal concepts formal ontology formula function functor Galois connection graph hierarchical classifications hierarchy hypergraph infinite classifications intersection isomorphic k-classifications kind Kurepa tree logic mapping mathematical mereology metaclassification method minimal covers morphism non-associative nonempty notion objects one-to-one ordered set p-adic pair Parrochia partially ordered partition lattice permutohedron planary possible predicate Proof properties real numbers relational structure satisfies Sect sequence set theory subsets Suslin tree system of classes taxonomists Theorem theory of classifications tion topological space ultrametric weakly compact cardinal