The Triune Continuum Paradigm is a

paradigm In science and philosophy, a paradigm () is a distinct set of concepts or thought patterns, including theories, research methods, postulates, and standards for what constitute legitimate contributions to a field. Etymology ''Paradigm'' comes f ...

for general system modeling published in 2002.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. The paradigm allows for building of rigorous conceptual frameworks employed for

systems modeling Systems modeling or system modeling is the interdisciplinary study of the use of models to conceptualize and construct systems in business and IT development.Cambridge Dictionary of Philosophy ''The Cambridge Dictionary of Philosophy'' (1995; second edition 1999; third edition 2015) is a dictionary of philosophy published by Cambridge University Press and edited by the philosopher Robert Audi Robert N. Audi (born November 1941) is an ...

'':R. Audi (general editor). The Cambridge Dictionary of Philosophy, second edition; Cambridge University Press 1999. "Paradigm, as used by Thomas Kuhn (''

The Structure of Scientific Revolutions ''The Structure of Scientific Revolutions'' (1962; second edition 1970; third edition 1996; fourth edition 2012) is a book about the history of science by philosopher Thomas S. Kuhn. Its publication was a landmark event in the history, philosophy ...

'', 1962), refers to 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 framework A conceptual framework is an analytical tool with several variations and contexts. It can be applied in different categories of work where an overall picture is needed. It is used to make conceptual distinctions and organize ideas. Strong conceptu ...

s used for system modeling in different contexts can be built, tested, evaluated, and revised.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. . For an 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.,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. the Triune Continuum Paradigm is a complete theoretical base that can be used for building or for improving modern modeling frameworks that are employed for system modeling in different contexts, in particular in

software development Software development is the process of conceiving, specifying, designing, programming, documenting, testing, and bug fixing involved in creating and maintaining applications, frameworks, or other software components. Software development invol ...

and in the engineering of enterprise information systems.

Foundations and their implications

The Triune Continuum Paradigm is based on three theories: on

Tarski's theory of truth A semantic theory of truth is a theory of truth in the philosophy of language which holds that truth is a property of sentences. Origin The semantic conception of truth, which is related in different ways to both the correspondence and deflation ...

, on Russell's theory of types, and on the theory of the triune continuum.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. . The theories, when applied to general system modeling, produce three principles: * 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

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 Software is a set of computer programs and associated documentation and data. This is in contrast to hardware, from which the system is built and which actually performs the work. At the lowest programming level, executable code consists ...

and

systems engineering Systems engineering is an interdisciplinary field of engineering and engineering management that focuses on how to design, integrate, and manage complex systems over their enterprise life cycle, life cycles. At its core, systems engineering util ...

, to formalize foundations of Reference Model of Open Distributed Processing (

RM-ODP Reference Model of Open Distributed Processing (RM-ODP) is a reference model in computer science, which provides a co-ordinating framework for the standardization of open distributed processing (ODP). It supports distribution, interworking, plat ...

) conceptual framework.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. . doibr>10.1016/j.csi.2005.10.001
/ref> As described by Dijkman,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. Naumenko in 2002 defined an abstract syntax for RM-ODP in a language called

Alloy An alloy is a mixture of chemical elements of which at least one is a metal. Unlike chemical compounds with metallic bases, an alloy will retain all the properties of a metal in the resulting material, such as electrical conductivity, ductility, ...

that uses a set theoretic formal semantics. *UML :The paradigm was applied to define a formal metamodel for

UML The Unified Modeling Language (UML) is a general-purpose, developmental modeling language in the field of software engineering that is intended to provide a standard way to visualize the design of a system. The creation of UML was originally m ...

.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. . doibr>10.1007/3-540-45800-X_2
/ref> According to Lano, 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. the lack of grounded interpretation for UML concepts was identified in this application. As explained by Broy and Cengarle, M. Broy, M. V. Cengarle. "UML formal semantics: lessons learned". ''Software & Systems Modeling'', Volume 10, Number 4, pp. 441–446, Springer-Verlag, 2011. . doibr>10.1007/s10270-011-0207-y
/ref> 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. 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. . doibr>10.1007/s10257-007-0051-3
/ref> *UFO :A new framework, "Unit - Function - Object" (UFO) approach,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. was designed for

business modeling Business process modeling (BPM) in business process management and systems engineering is the activity of representing processes of an enterprise, so that the current business processes may be analyzed, improved, and automated. BPM is typically ...

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. . doibr>10.1142/9789814295062_0068
/ref> based on the ontology that was provided by the Triune continuum paradigm.

References

External links

at triunecontinuum.com. {{Systems 2002 introductions Systems engineering