Foundations of Science

, Volume 23, Issue 2, pp 297–321 | Cite as

Impure Systems and Ecological Models (I): Axiomatization

  • José-Luis Usó-Doménech
  • Josué-Antonio Nescolarde-Selva
  • Miguel Lloret-Climent


Building models as a practical aspect of ecological theory has as a principal purpose the determination of relations in formal (mathematical) language. In this paper, the authors provide a formalization of ecological models based on impure systems theory. Impure systems contain objects and subjects: subjects are human beings. We can distinguish a person as an observer (subjectively outside the system) that by definition is the subject himself and part of the system. In this case he acquires the category of object. Objects (relative beings) are significances, which are the consequence of perceptual beliefs on the part of the subject about material or energetic objects (absolute beings) with certain characteristics. The impure system approach is as follows: objects are perceptual significances (relative beings) of material or energetic objects (absolute beings). The set of these objects will form an impure set of the first order. The existing relations between these relative objects will be of two classes: transactions of matter and/or energy and inferential relations. Transactions can have alethic modality: necessity, possibility, impossibility and contingency. In this work we define measures which let us choose the more suitable variables to relate both the model with the ecosystem and with different models. In this way we define different comparison indexes.


Behaviors Ecosystem Impure sets Impure systems Mathematical model System-linkage Variable 


  1. Beaugrande, R. A., & Dressler, W. U. (1997). Einführung in die Textlinguistik. (Spanish Trad., Introducción a la lingüística del texto). Barcelona: Ariel.Google Scholar
  2. Benacerraf, P. (1973). Mathematical truth. Journal of Philosophy, 19, 661–679.CrossRefGoogle Scholar
  3. Cale, W. G., Jr., & Odell, P. L. (1979). Concerning aggregation in ecosystems modelling. In E. Halfon (Ed.), Theoretical systems ecology. Advances and case studies. Cambridge: Academic Press.Google Scholar
  4. Chandler, D. (2004). Semiotics. The basis. London: Routledge.Google Scholar
  5. Colgate, S. A., & Ziock, H. (2011). A definition of information, the arrow of information, and its relationship to life. Complexity, 16(5), 54–62.CrossRefGoogle Scholar
  6. Eco, U. (1976). El signo. Barcelona: Editorial Labor (in Spanish).Google Scholar
  7. Febres, G., Jaffé, K., & Gershenson, C. (2015). Complexity measurement of natural and artificial languages. Complexity, 20(6), 25–48.CrossRefGoogle Scholar
  8. Field, H. (1980). Science without numbers: A defense of nomilanism. Pricenton: Princeton University Press.Google Scholar
  9. Field, H. (1989). Realism, mathematics and modality. Oxford: Basil Blackwell.Google Scholar
  10. Gell-Mann, M., & Lloyd, S. (1996). Information measures, effective complexity, and total information. Complexity, 2(1), 44–52.CrossRefGoogle Scholar
  11. Gershenson, C. (2001). Comments to neutrosophy. In Proceedings of the first international conference on neutrosophy, neutrosophic logic, set, probability and statistics, University of New Mexico, Gallup, December 1–3, 2001.Google Scholar
  12. Gershenson, C., & Fernández, N. (2012). Complexity and information: Measuring emergence, self-organization, and homeostasis at multiple scales. Complexity, 18(2), 29–44.CrossRefGoogle Scholar
  13. Hempel, C.G. (1945). On the nature of mathematical truth. American Mathematical Monthly 52. Reprinted in H. Feigl, & W. Sellars (eds.) Readings in philosophical analysis. New York: Appleton-Century-Crofts, 1949. Reprinted in J. R. Newman (ed.) The world of mathematics, vol. III. New York: Simon and Shuster, 1956. Transcribed into hypertext by Andrew Chrucky, Feb. 4, 2001.Google Scholar
  14. Higashi, M., & Burns, T. P. (1991). Enrichment of ecosystem theory. In Theorical studies of ecosystems. Cambridge, NY: Cambridge University Press.Google Scholar
  15. Jorgënsen, S. E. (1988). Fundamentals of ecological modelling. Amsterdam: Elsevier.Google Scholar
  16. Kun, W., & Brenner, J. E. (2015). An informational ontology and epistemology of cognition. Foundations of Science, 20(3), 249–279.CrossRefGoogle Scholar
  17. Lincoln, R. J., Boxshall, G. A., & Clark, P. F. (1982). A dictionary of ecology, evolution and systematics. Cambridge, NY: Cambridge University Press.Google Scholar
  18. Lloret, M., Villacampa, Y., & Usó, J. L. (1998). System-linkage: Structural functions and hierarchies. Cybernetics and Systems, 29, 29–39.Google Scholar
  19. Locker, M. (2016). Blindness and seeing in systems epistemology: Alfred locker’s trans-classical systems theory. Foundations of Science. doi: 10.1007/s10699-016-9502-y.Google Scholar
  20. Lombardi, O. (2004). What is information? Foundations of Science, 9(2), 105–134.CrossRefGoogle Scholar
  21. MacCallum, D. (2000). Conclusive reasons that we perceive sets. International Studies in the Philosophy of Science., 14(1), 26–42.CrossRefGoogle Scholar
  22. Maddy, P. (1990). Realism in mathematics. Oxford: Clarendon Press.Google Scholar
  23. Maddy, P. (1996). Set theoretic naturalism. Journal of Symbolic Logic, 61, 490–514.CrossRefGoogle Scholar
  24. Margalef, R. (1995). Ecología. Barcelona: Omega (in Spanish).Google Scholar
  25. Markushevich, A. (1978). Teoría de las funciones Analíticas (Vol. I). Moscow: Editorial Mir (in Spanish, translated from Russian).Google Scholar
  26. Nescolarde-Selva, J., & Usó-Domènech, J. L. (2014a). Semiotic vision of ideologies. Foundations of Science, 19(3), 263–282.CrossRefGoogle Scholar
  27. Nescolarde-Selva, J., & Usó-Domènech, J. L. (2014b). Reality, systems and impure systems. Foundations of Science, 19(3), 289–306.CrossRefGoogle Scholar
  28. Nescolarde-Selva, J., Usó-Doménech, J. L., & Gash, H. (2015a). A logic-mathematical point of view of the truth: Reality, perception, language. Complexity, 20(4), 58–67.CrossRefGoogle Scholar
  29. Nescolarde-Selva, J., Usó-Doménech, J. L., Lloret- Climent, M., & González-Franco, L. (2015b). Chebanov law and Vakar formula in mathematical models of complex systems. Ecological Complexity, 21, 27–33.CrossRefGoogle Scholar
  30. Nescolarde-Selva, J., Usó-Doménech, J. L., & Sabán, M. J. (2015c). Linguistic knowledge of reality: A metaphysical impossibility? Foundations of Science, 20(1), 27–58.CrossRefGoogle Scholar
  31. Nescolarde-Selva, J., Vives-Macía, F., Usó-Doménech, J. L., & Berend, D. (2012a). An introduction to alysidal algebra (I). Kybernetes, 41(1/2), 21–34.CrossRefGoogle Scholar
  32. Nescolarde-Selva, J., Vives-Macía, F., Usó-Domènech, J. L., & Berend, D. (2012b). An introduction to alysidal algebra (II). Kybernetes, 41(5/6), 780–793.CrossRefGoogle Scholar
  33. Peirce, C. S. (1931–1958). In C. Hartshorne, P. Weiss, & A. W. Burks (Eds.) Collected papers of charles sanders peirce (vol. 1–8). Cambridge, MA: Cambridge University Press.Google Scholar
  34. Quine, W. V. O. (1969). Epistemology naturalized. In Ontological relativity. New York: Columbia University Press.Google Scholar
  35. Usó-Domènech, J. L., Mateu, J., & Lopez, J. A. (1997). Mathematical and statistical formulation of an ecological model with applications. Ecological Modelling, 101, 27–40.CrossRefGoogle Scholar
  36. Usó-Doménech, J. L., & Nescolarde-Selva, J. (2012). Mathematic and semiotic theory of ideological systems. Sarrebruck: Editorial LAP.Google Scholar
  37. Usó-Doménech, J. L., Nescolarde-Selva, J. A., & Lloret-Climent, M. (2016a). Complex impure systems: Sheaves, freeways, and chains. Complexity, 21(S1), 387–400.CrossRefGoogle Scholar
  38. Usó-Doménech, J. L., Nescolarde-Selva, J. A., Lloret-Climent, M., & Gash, H. (2016b). Semantics of language for ecosystems modelling: A model case. Ecological Modelling, 328, 85–94.CrossRefGoogle Scholar
  39. Usó-Domènech, J. L., Villacampa, Y., Mateu, J., & Sastre-Vazquez, P. (2000). Uncertainty and complementary principles in flow equations of ecological models. Cybernetics and Systems, 31(2), 137–160.CrossRefGoogle Scholar
  40. Villacampa, Y., Usó-Domènech, J. L., Mateu, J., & Sastre, P. (1999). Generative and recognoscitive grammars in ecological models. Ecological Modelling, 117, 315–332.CrossRefGoogle Scholar
  41. Yang, Z. B. (1989). A new model of general systems theory. Cybernetic and Systems, 20, 67–76.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  • José-Luis Usó-Doménech
    • 1
  • Josué-Antonio Nescolarde-Selva
    • 1
  • Miguel Lloret-Climent
    • 1
  1. 1.Department of Applied MathematicsUniversity of AlicanteAlicanteSpain

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