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Data structures, orderings and applied classifications are generally defined on finite sets or sets of relations, which supposes that we know what are such entities (Sect. 2.3). But a part of classification research deals with data mining and the constitution of structured domains of concepts or objects. The fact that a mathematical structure, the Galois connection, contains a quasi-exhaustive information about the correspondence of two sets (Sect. 2.4) has suggested to use this structure in association with an order relation (Sect. 2.5) to initiate formal conceptual analysis (Sect. 2.6). But formal concepts are not real concepts. The exploration of concrete structures of objects has then led to the construction of formal (Sect. 2.7) and regional (Sect. 2.8) ontologies, using sometimes, as Barry Smith does, non-classical logics (the mereology of Lesniewski). In all this chapter, we study these models in relation to the main problems of classification and, finally, discuss (Sect. 2.9) the theories and results that have been introduced.

DOI: 10.1007/978-3-0348-0609-1_2

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