Triune Continuum Paradigm is a new paradigm for general system modeling that allows for building of rigorous conceptual frameworks employed for system modeling in diverse contexts (highly tailored as well as interdisciplinary). The paradigm supports efficient information management in application domains belonging to various disciplines. In particular, it was successfully applied for Software Engineering and for the design of Enterprise Information Systems.

Triune Continuum Paradigm was defined and presented in the following doctoral thesis:

A. Naumenko. "Triune Continuum Paradigm: a paradigm for General System Modeling and its applications for UML and RM-ODP", Ph.D. thesis number 2581, Swiss Federal Institute of Technology - Lausanne. EPFL, June 2002.

This dissertation contains all of the technical details related to the paradigm definition. The following two articles familiarize the audience with the Triune Continuum Paradigm and with several of the existing paradigm's applications:

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.
 
A. Naumenko. "A report on the Triune Continuum Paradigm and on its foundational theory of Triune Continuum"; in 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.

The following article introduces the paradigm to the Russian-speaking audience:

Науменко А. А. "Введение в Парадигму Триединого Континуума, парадигму для общего системного моделирования"; Економiка: проблеми теорiї та практики, выпуск 220, том 2, стр. 513-530. Днепропетровск, издательство «Наука и образование», Октябрь 2006. ISSN: 1561-6908.
 

A brief introduction to the
Triune Continuum Paradigm

Reference: "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." - this quote from the Cambridge Dictionary of Philosophy [1] is explaining the meaning of the word "paradigm".

A paradigm is usually defined for a collection of sciences. In this context a paradigm introduces and justifies a set of basic assumptions and principles on which any of the sciences from the collection can rely as on their foundations.  Then, starting from the principles provided by a paradigm, different sciences build their specific frameworks of knowledge. And if some sciences share the same paradigm then they can bind and synchronize their specific frameworks of knowledge. By doing so they can mutually enrich each other with the knowledge obtained from the different (but consistent with regard to the basic principles) points of view.

Triune Continuum Paradigm (defined in [4], later presented in [3] and in [2]) is a paradigm for general system modeling. Thus the Triune Continuum Paradigm serves the sciences that have diverse interests in system modeling. As any paradigm, it introduces and justifies a set of principles that provide the sciences with the necessary starting points for building their diverse conceptual frameworks of scientific knowledge; in our case - the principles that are necessary for building modeling frameworks.

Triune Continuum Paradigm is composed of three principles.

The first principle is the result of an application of Tarski's Theory of Truth [8] for the case of general system modeling. This application allows to define coherent semantics for the concepts of a modeling framework. This is done by constructing formal descriptions for the relations between the subjects that are interesting to be modeled on one side, and the concepts that have to represent these subjects on the other side. This principle is necessary to assure the coherency and unambiguity within modeling interpretations of a single framework.

The second principle is the result of an application of Russell's Theory of Types [7] for the case of general system modeling. This application defines the way to categorize concepts of a modeling framework so that within the applications of this framework the concepts make up the internally consistent structures of propositions. Thus this principle is necessary to assure the consistency of descriptions and specifications that are constructed with the aid of the modeling frameworks.

The third principle is the result of an application of the theory of Triune Continuum that was defined in [4] and later presented in [2]. In its application for the case of general system modeling this theory allowed for an introduction and justification of the minimal set of modeling concepts that is necessary and sufficient to cover the representation scope of the general system modeling domain on the most abstract level. This principle is necessary for different system modeling frameworks to justify the existence of their basic modeling concepts.

The paper [5] provides an elaborated analysis on the usefulness of the first principle of Triune Continuum Paradigm. The paper [6] explains application of the second principle for the case of RM-ODP conceptual framework. And the paper [2] explains the theory of Triune Continuum - the foundation for the third paradigm's principle. More detailed explanations about the theory of Triune Continuum can be found in the dissertation [4]. Basics of the theory of Triune Continuum (without implications) are briefly explained on this web site under the following hyperlink.

References:

[1] R. Audi (general editor). The Cambridge Dictionary of Philosophy, second edition; Cambridge University Press 1999.

[2] A. Naumenko. A report on the Triune Continuum Paradigm and on its foundational theory of Triune Continuum, in 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 ediзхes. ISBN 972-752-077-4.

[3] A. Naumenko. Basics of the Triune Continuum Paradigm, in Encyclopedia of Information Science and Technology; M. Khosrowpour (Ed.), Idea Group Inc., January 2005. ISBN: 1-59140-553-X.

[4] A. Naumenko. Triune Continuum Paradigm: a paradigm for General System Modeling and its applications for UML and RM-ODP, Ph.D thesis number 2581, Swiss Federal Institute of Technology - Lausanne. EPFL, June 2002.

[5] A. Naumenko, A. Wegmann, C. Atkinson. The Role of Tarski’s Declarative Semantics in the Design of Modeling Languages, Technical report No. IC/2003/43, Swiss Federal Institute of Technology - Lausanne. EPFL, April 2003.

[6] A. Naumenko, A. Wegmann. A Formal Foundation of the RM-ODP Conceptual Framework, Technical report No. DSC/2001/040, Swiss Federal Institute of Technology - Lausanne. EPFL, July 2001.

[7] B. Russell. Mathematical logic as based on the theory of types, American Journal of Mathematics, 30, 1908, pp. 222-262.

[8] A. Tarski. Logic, Semantics, Meta-mathematics. Oxford University Press, 1956.