Set-theoretical approach to defining of terms “classification”, “taxonomy” and “ontology”

Hryhoriy Kravtsov, Oleksandr Dolhorukov, Volodymyr Koshel


The authors have analyzed terminology usage of words ”taxonomy” and ”classification” and found that classification is reflection of system of mereologic and taxonomic divides. The mereologic dividing is oriented for separation of term about subject in accordance to relation ”whole – part”. In the same time for taxonomic dividing between term and its members the relation “genius-spaces” must exist. Using terms taxonomy and classification as synonyms leads to incorrect understanding and future misusing these terms. It can be explained because taxonomy like hierarchical structure is subset of classification. Term ontology has been studied separately and was done emphasis on usage of formal ontologies for development of the global semantic network. Ontology creates taxonomy from classes and set of relations between them. Ontology usage must be accompanied the definition on the space. From this view of point a simple ontology is a taxonomy without relations. It permits us to define any complex ontology through set of it’s abilities and relations. This fact gives the right to research taxonomy, ontology and classification based on the set theory. The research results show that the taxonomy set is a subset of classifications, classification set is a subset of the ontology set. The result is new for science and is in conflict with existing scientific views. But the obtained results based on the set theory are correct.


Classification; ontology; taxonomy; set; relation; mereologic dividing; taxonomic dividing; set-theoretical approach.


T. Gruber, and R. Gruber, “A translation approach to portable Ontology Specifications”. [Online]. Available: Accessed on: Aug. 19, 2017.

H.A. Kravtsov, “Measure of difference between classifications”, Electronic modeling, vol. 38, no. 4, pp. 81-99, 2016.

Iu.V. Ivlev, Logic. Moscow, Russian Federation: publishing house “Prospect”, 2008.

M.M. Kovbliuk, Fundamentals of zoological nomenclature and taxonomy, Simferopol, Ukraine: DIAIPI, 2008.

S. Lesnevskii, “On the foundations of mathematics”, in Philosophy and logic of the Lviv-Warsaw School, V. Smirnov V. Vasiukov, Eds. Moscow, Russian Federation: ROSSPEN, 1999, pp. 262-280.

V.I. Hlushchenko, A.Y. Akulov, D.V. Leontiev, and S.Y. Utevskyi, Fundamentals of general systematics: Kharkiv, Ukraine: V.N. Karazin Kharkiv national university, 2004.

A.I. Shatalkin, Taxonomy. Foundations, principles and rules, Moscow, Russian Federation: Association of scientific publications of KMK, 2012.

I.Y. Khalymon, and S.I. Shevchenko, “Bloom's taxonomy and its application in studies in country studies”, Scientific blog of the National university of Ostroh Academy, 2015. [Online]. Available: Accessed on: Aug. 25, 2017.

Reinout van Rees, “Clarity in the usage of the terms ontology, taxonomy and classification”. [Online]. Available: Accessed on: Aug. 25, 2017.

O.V. Palahin, M.H. Petrenko, V.Yu. Velychko, K.S. Malakhov, and O.V. Karun, “Principles of design and software development models of ontological-driven computer systems”, Problems of Informatization and Management, № 2 (34), pp. 96-101, 2011.

Semantic Web: Linked Data on the Web. [Online]. Available: 0130-sb-W3CTechSemWeb/#(24) . Accessed on: Aug. 25, 2017.

H. Paulheim, and F. Probst, “W3C. Why UI standards should come together with formal ontologies”. [Online]. Available: Accessed on: Aug. 25, 2017.

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ISSN 2411-1031 (Print), ISSN 2518-1033 (Online)