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«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «NAUKI O ZEMLE»
«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «EARTH SCIENCES»
ISSN 2073-3402 (Print)

List of issues > Series «Earth Sciences». 2023. Vol 43

Classification of Geosystems: Axiomatic Approach

Author(s)
A. K. Cherkashin
Abstract
Using the experience of solving classification problems in quantum mechanics and biology, the basic principles (axioms) that the natural classification of geosystems should satisfy are formulated. The science resolutes research problems from three independent positions: describing phenomena, highlighting fundamental laws and classifying objects. Classification is the relation structure of various types of objects (taxa), usually in the form of a graph. Geography classifies not territorial objects, but varieties of the environment (geomers) in which these objects manifest themselves to varying degrees. The classification theory is an intertheory that describes processes and phenomena in nature and society in a through way. Mathematical methods of feature space bundle, group theory and functional spaces are used to model the structure of typology and classification. The intertheory is created on the general theory of systems at various levels of formalization: from systems of quantum numbers, eigenvalues and variables to systems of geoinformation functions, probability estimation functionals, function transformation operators for describing states (taxonomic positions) and their quantum transitions. At the lower level of quantization, the axiomatization scheme assumes the existence of a universal facet space of series of integers of the classification code, restrictions on the length of the series and rules for changing the numbers of the code during quantum transitions. Triangular classification structures satisfying these requirements were identified at the systematics of the facies of the southern taiga of the Lower Angara region.
About the Authors
Cherkashin Alexander Konstantinovich, Doctor of Sciences (Geography), Professor, Head, Laboratory of Theoretical Geography, V. B. Sochava Institute of Geography SB RAS, 1, Ulan-Batorskaya st., Irkutsk, 664033, Russian Federation, e-mail: akcherk@irnok.net
For citation
Cherkashin A. K. Classification of Geosystems: Axiomatic Approach. The Bulletin of Irkutsk State University. Series Earth Sciences,, 2023, vol. 43, pp. 102–126. https://doi.org/10.26516/2073-3402.2023.43.102 (in Russian)
Keywords
classification theory, axioms of theory, typological bundle, principal bundle, grouptheoretic relations, facies classification, southern taiga of the Lower Angara region.
UDC
911.5:168.2:51–7(571.53)
DOI
https://doi.org/10.26516/2073-3402.2023.43.102
References

Varlamov V.V. Teoretiko-gruppovoe opisanie periodicheskoj sistemy` e`lementov [Grouptheoretic description of the periodic system of elements]. Matematicheskie struktury i modelirovanie [Mathematical structures and modeling], 2018, no. 2(46), pp. 5-23. (in Russian)

Grigor'ev A.A., Budyko M.I. O periodicheskom zakone geograficheskoj zonalnosti [On the periodic law of geographical zoning]. Doklady AN SSSR [Reports of the USSR Academy of Sciences], 1956, vol. 110, no. 1, pp. 129-132. (in Russian)

Frolova N.L., Kireeva M.B., Harlamov M.A., Samsonov T.E., Entin A.L., Lur'e I.K. Kartografirovanie sovremennogo sostoyaniya i transformacii vodnogo rezhima rek Evropejskoj territorii Rossii [Mapping of the current state and transformation of the water regime of the rivers of the European territory of Russia]. Geodeziya i kartografiya [Geodesy and cartography], 2020, no. 7, pp.14-26. (in Russian)

Krauklis A.A. Naturnaya model' [Natural model]. Prirodnye rezhimy i topogeosistemy Priangarskoj tajgi [Natural regimes and topogeosystems of the Angara taiga]. Novosibirsk, Nauka Publ., 1975, pp. 28-49. (in Russian)

Krauklis A.A. Problemy eksperimentalnogo landshaftovedeniya [Problems of experimental landscape studies]. Novosibirsk, Nauka Publ., 1979, 233 p. (in Russian)

Miheev V.S., Ryashin V.A. Landshafty Yuga Vostochnoj Sibiri. Karta. M 1: 1 500 000 [Landscapes of the south of Eastern Siberia. Map. M 1:1 500 000]. Ed. V.B. Sochava. Moscow, GUGK Publ., 1977. (in Russian)

L'vovich M.I. Opyt klassifikacii rek SSSR [Experience of classification of rivers of the USSR]. Publications of GGI, 1938, iss. 6, pp. 58-104. (in Russian)

Pavlinov I.Ya. Osnovaniya biologicheskoj sistematiki: istoriya i teoriya. Sbornik trudov Zoologicheskogo muzeya MGU [The foundations of biological systematics: history and theory. Collection of works of the Zoological Museum of Moscow State University]. Moscow, Association of Scientific Publications KMK Publ., 2018, vol. 55, 786 p. (in Russian)

Pozdnyakov A.A. Ontologicheskij status taksonov s tradicionnoj tochki zreniya [Ontological status of taxa from the traditional point of view]. Linneevskij sbornik [The Linnean Collection]. Moscow, MGU Publ., 2007, vol. 48, pp. 261-304. (in Russian)

Rozov M.A. Klassifikaciya i teoriya kak sistemy znaniya [Classification and theory as systems of knowledge]. Na puti k teorii klassifikacii [On the way to the theory of classification]. Novosibirsk, NGU Publ., 1995, pp. 81-127. (in Russian)

Rozova S.S. Klassifikacionnaya problema v sovremennoj nauke [Classification problem in modern science]. Novosibirsk, Nauka Publ., 1986, 223 p. (in Russian)

Sochava V.B. K teorii klassifikacii geosistem s nazemnoj zhiznyu [On the theory of classification of geosystems with terrestrial life]. Reports of the Institute of geography of Siberia and the Far East., 1972, vol. 34, pp. 3-14. (in Russian)

Sochava V.B. Vvedenie v uchenie o geosistemah [Introduction to the doctrine of geosystems]. Novosibirsk, Nauka Publ., 1978, 318 p. (in Russian)

Subbotin A.L. Klassifikaciya [Classification]. Moscow, IF RAN Publ., 2001, 94 p. (in Russian)

Suhanov L.P. Lekcii po kvantovoj mekhanike [Lectures on quantum mechanics]. Moscow, MFTI Publ., 2016, 181 p. Available at: https://mipt.ru/drec/forstudents/study/studyMaterials/4kurs/kvant_mech.pdf (date of access: 21.03.2022). (in Russian)

Tahtadzhyan A.L. Sistema magnoliofitov [Magnoliophyte system]. Leningrad, Nauka Publ., 1987, 440 p. (in Russian)

Tikunov V.S. Klassifikacii v geografii: renessans ili uvyadanie? (Opyt formalnyh klassifikacij) [Classifications in geography: Renaissance or withering? (Experience of formal classifications)]. Moscow, Smolensk, SGU Publ., 1997, 367 p. (in Russian)

Fet A.I. Gruppa simmetrii himicheskih elementov [Symmetry group of chemical elements]. Novosibirsk, Nauka Publ., 2010, 238 p. (in Russian)

Cherkashin A.K. Estestvennaya klassifikaciya geograficheskih sistem: modeli predstavleniya znanij [Natural classification of geographical systems: knowledge representation models]. The Bulletin of Irkutsk State University. Series Earth Science, 2020, vol. 31, pp. 69-87. (in Russian)

Cherkashin A.K. Ierarhicheskaya klassifikaciya geograficheskih sistem [Hierarchical classification of geographical systems]. The Bulletin of Irkutsk State University. Series Earth Science, 2021, vol. 35, pp. 125-153. (in Russian)

Shatalkin A.I. Taksonomiya. Osnovaniya, principy i pravila [Taxonomy. Foundations, principles and rules]. Moscow, Association of Scientific Publications KMK Publ., 2012, 600 p. (in Russian)

Shipunov A.B. Osnovy teorii sistematiki [Fundamentals of the theory of taxonomy]. Moscow, Dialog-MGU Publ., 1999, 56 p. (in Russian)

Epshtejn V.M. Versiya sovremennoj teorii evolyucionnoj sistematiki [Version of the modern theory of evolutionary systematics. Appendix N 1]. Trudy Zoologicheskogo instituta RAN [Proceedings of the Zoological Institute of the Russian Academy of Sciences], 2009, pp. 272-293. (in Russian)

Broughton V. The need for a faceted classification as the basis of all methods of information retrieval. New Information Perspectives, 2006, vol. 58 (1/2), pp. 49-72.

Cherkashin A.K. Polysystem modelling of geographical processes and phenomena in nature and society. Mathematical modelling of natural phenomena, 2009, vol. 4, no. 5, pp. 4-20.

Frolof A.A., Cherkashin A.K. Altitudinal gradient as a complex factor for formation of landscape microzonality and geosystem serialness. Geography and Natural Resources, 2012, vol. 33, no. 1, pp. 10-18.

Hall M.Jr. The group theory. New York, MacMillan. Co., 1959, 13+434 p. Husemöller D. Fibre bundles, New York, Springer, 2013, 356 p.

Mayr E., Ashlock P.D. Principles of systematic zoology. New York, McGraw-Hill College, 1991, 475 p.

Mirkin B. Mathematical classification and clustering. Dordrecht, Kluwer Academic Publishers, 1996, 580 p.

Nakahara M. Geometry, topology and physics. Bristol, Philadelphia, Institute of physics publishing, 2003. 584 p.

Nelson G. Cladistics and evolutionary models. Cladistics, 1989, no. 5, pp. 275-289.

Parrochia D. Mathematical theory of classification. In Encyclopedia of knowledge organization. Eds. B. Hjørland, C. Gnoli 2020. Available at: https://www.isko.org/cyclo/mathematical_theory_of_classification#8 (date of access: 02.03.2022).

Parrochia D., Neuville P. Towards a general theory of classifications. Basel, Heidelberg, New York, Dordrecht, London, Springer, 2013, 304 p.

Pavlinov I.Ya. Biological systematics: History and Theory. New York, CRC Press, 2021, 270 p.

Restrepo G. Pachón L. A. Mathematical aspects of the periodic law. Foundations of Chemistry, 2007, vol. 9, pp. 189-214.

Rieppel O. The taxonomic hierarchy. The systematist. Newsletter of the Systematic Association, 2006, vol. 26, pp. 5-9.

Rosindell J., Harmon L.J. OneZoom: a fractal explorer for the tree of life. PLoS Biology, 2012, vol. 10, no. 10, pp. 1-5.

Rozhkov V.A. Classiology and soil classification. Eurasian soil science, 2012, vol. 45, no. 3, pp. 221-230.

Simpson G.G. Principles of animal taxonomy. New York, Columbia Univ. Press, 1961, 247 p.

Tikhonov A.N., Samarskii A.A. Equations of mathematical physics. New York, Dover Publications Inc., 2011, 800 p.

Wheeler W. C. Systematics. A course of lectures. Oxford, Wiley-Blackwell, John Wiley & Sons Ltd, 2012, 426 p.


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