Triune continuum paradigm

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The Triune continuum paradigm is a paradigm for general system modeling published in 2002.[1] The paradigm allows for building of rigorous conceptual frameworks employed for systems modeling in various application contexts (highly tailored as well as interdisciplinary).


As it is defined in the Cambridge Dictionary of Philosophy:[2] "Paradigm, as used by Thomas Kuhn (The Structure of Scientific Revolutions, 1962), a set of scientific and metaphysical beliefs that make up a theoretical framework within which scientific theories can be tested, evaluated and if necessary revised."

The Triune continuum paradigm holds true to this definition by defining a set of scientific principles within which conceptual frameworks used for system modeling in different contexts can be built, tested, evaluated and revised.[3]

For existent modeling framework, the paradigm allows the framework to be tested against its principles, showing framework deficiencies, if any, explaining how to fix the deficiencies in a possible revision of the framework. When building a new system modeling framework, the paradigm provides guidelines on how to do so, assuring the resulting quality of the framework.

According to Herrera et al.,[4] Triune Continuum Paradigm is a complete theoretical base that can be used for building or for improvement of modern modeling frameworks that are employed for system modeling in different contexts, in particular in software development and in the engineering of enterprise information systems.

Foundations and their implications[edit]

The Triune continuum paradigm is based on the three theories: on Tarski's theory of truth, on Russell's theory of types and on the Theory of Triune Continuum.[5] The theories, when applied to general system modeling, produce three principles:[3]

  • The first principle assures coherency and unambiguity within modeling interpretations of a single modeling framework.
  • The second principle assures internal consistency of descriptions and specifications that are constructed with the aid of a modeling framework.
  • The third principle allows to introduce and to justify the minimal set of modeling concepts that is necessary and sufficient to cover the representation scope of a modeling framework on the most abstract level (on the level that corresponds to the first order propositions in Russell's theory of types).

Applications of the paradigm[edit]

The Triune continuum paradigm can be applied in practice either to improve an existing system modeling framework or to design a new system modeling framework for a given purpose.

  • RM-ODP
The paradigm was applied in the domain of software and systems engineering, to formalize foundations of Reference Model of Open Distributed Processing (RM-ODP) conceptual framework.[6] As described by Dijkman,[7] Naumenko in 2002 defined an abstract syntax for RM-ODP in a language called Alloy that uses a set theoretic formal semantics.
  • UML
The paradigm was applied to define a formal metamodel for UML.[8] According to Lano,[9] the lack of grounded interpretation for UML concepts was identified in this application. As explained by Broy and Cengarle,[10] this application of the Triune continuum paradigm:
  • showed deficits of UML (e.g. circular and contradictory definitions);
  • introduced an option that has an internally consistent structure supported by Russell’s theory of types;
  • defined declarative semantics à la Tarski;
  • was justified on the basis of philosophical and natural science foundations (in contrast to UML which is a result of tries, failures and successes that were never theoretically justified).
  • SEAM
The application for RM-ODP was employed in the definition of SEAM method for Enterprise Architecture, allowing for enterprise modeling in which all the systems are systematically represented with the same modeling ontology.[11]
  • UFO
A new framework, "Unit - Function - Object" (UFO) approach,[12] was designed for business modeling[13] based on the ontology that was provided by the Triune continuum paradigm.


  1. ^ A. Naumenko. Triune Continuum Paradigm: a paradigm for general system modeling and its applications for UML and RM-ODP, Doctoral thesis 2581, Swiss Federal Institute of Technology – Lausanne. EPFL, June 2002.
  2. ^ R. Audi (general editor). The Cambridge Dictionary of Philosophy, second edition; Cambridge University Press 1999.
  3. ^ a b A. Naumenko. "Triune Continuum Paradigm", in Encyclopedia of Information Science and Technology, second edition, Vol. VIII, pp. 3821–3825; M. Khosrowpour (Ed.), Information Science Reference, IGI Global, September 2008. ISBN 978-1-60566-026-4.
  4. ^ S.I. Herrera, M.M. Clusella, G.N. Tkachuk, P.A. Luna. "How System Models Contributes to the Design of Information Systems", Proceedings of the First World Congress of the International Federation for Systems Research (IFSR 2005): The New Roles of Systems Sciences For a Knowledge-based Society; Kobe, Japan, November 2005.
  5. ^ A. Naumenko. "A report on the Triune Continuum Paradigm and on its foundational theory of Triune Continuum", PHISE'05, the 1-st International Workshop on Philosophical Foundations of Information Systems Engineering. Proceedings of the CAiSE'05 Workshops, Vol. 2, pp. 439–450; J. Castro, E. Teniente (Eds.); Porto, Portugal, June 2005. FEUP edições. ISBN 972-752-077-4.
  6. ^ A. Naumenko, A. Wegmann. "Formalization of the RM-ODP foundations based on the Triune Continuum Paradigm", Computer Standards & Interfaces, Volume 29, Issue 1, pp. 39–53, Elsevier B.V., 2007. ISSN 0920-5489. doi:10.1016/j.csi.2005.10.001
  7. ^ R.M. Dijkman. Consistency in multi-viewpoint architectural design. PhD thesis 06-80, Centre for Telematics and Information Technology, University of Twente, 2006. Page 16.
  8. ^ A. Naumenko, A. Wegmann. "A Metamodel for the Unified Modeling Language". "UML" 2002 – The Unified Modeling Language: Model Engineering, Concepts, and Tools. The 5th International Conference; pp. 2–17.; J.-M. Jézéquel, H. Hussmann, S. Cook (Eds.); Dresden, Germany, September/October 2002. LNCS 2460. Springer-Verlag 2002. ISBN 3-540-44254-5. doi:10.1007/3-540-45800-X_2
  9. ^ K. Lano. "Using B to verify UML Transformations", Proceedings of the 3rd Workshop on Model design and Validation (MODEVA 2006), B. Baudry, D. Hearnden, N. Rapin, J. G. Süß (Eds.), pp. 46–61; Genova, Italy, October 2006.
  10. ^ M. Broy, M. V. Cengarle. "UML formal semantics: lessons learned". Software & Systems Modeling, Volume 10, Number 4, pp. 441–446, Springer-Verlag, 2011. ISSN 1619-1366. doi:10.1007/s10270-011-0207-y
  11. ^ A. Wegmann, L.-S. Lê, G. Regev, B. Wood. "Enterprise modeling using the foundation concepts of the RM-ODP ISO/ITU standard". Information Systems and E-Business Management, Volume 5, Issue 4, pp. 397–413, Springer Berlin/Heidelberg, 2007. ISSN 1617-9846. doi:10.1007/s10257-007-0051-3
  12. ^ O. Ukrainets. "UFO-element presentation in metamodel structure of Triune Continuum Paradigm", Proceedings of the international conference on Computer Science and Informational Technologies (CSIT'2006), pp. 107–108; Lviv, Ukraine, September 2006.
  13. ^ K. Vanhoof, M. Bondarenko, K. Solovyova, O. Ukrayinets. "Systemological Language for Intelligence Business Modelling". Intelligent Decision Making Systems. Proceedings of the 4th International ISKE Conference; pp. 439–444.; K. Vanhoof, D. Ruan, T. Li, G. Wets (Eds.); Hasselt, Belgium, November 2009. World Scientific Publishing Co. Singapore, 2010. ISBN 981-4295-05-1. doi:10.1142/9789814295062_0068

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