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).

In science and philosophy, a paradigm is a distinct set of concepts or thought patterns, including theories, research methods, postulates, and standards for what constitutes legitimate contributions to a field.

In the context of systems science and systems philosophy, systemics is an initiative to study systems. It is an attempt at developing logical, mathematical, engineering and philosophical paradigms and frameworks in which physical, technological, biological, social, cognitive and metaphysical systems can be studied and modeled.

Systems modeling conceptual mode that describes and represents a system

Systems modeling or system modeling is the interdisciplinary study of the use of models to conceptualize and construct systems in business and IT development.



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."

<i>The Structure of Scientific Revolutions</i> book

The Structure of Scientific Revolutions is a book about the history of science by the philosopher Thomas S. Kuhn. Its publication was a landmark event in the history, philosophy, and sociology of scientific knowledge. Kuhn challenged the then prevailing view of progress in "normal science". Normal scientific progress was viewed as "development-by-accumulation" of accepted facts and theories. Kuhn argued for an episodic model in which periods of such conceptual continuity in normal science were interrupted by periods of revolutionary science. The discovery of "anomalies" during revolutions in science leads to new paradigms. New paradigms then ask new questions of old data, move beyond the mere "puzzle-solving" of the previous paradigm, change the rules of the game and the "map" directing new research.

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]

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 conceptual frameworks capture something real and do this in a way that is easy to remember and apply.

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.

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 is a process of writing and maintaining the source code, but in a broader sense, it includes all that is involved between the conception of the desired software through to the final manifestation of the software, sometimes in a planned and structured process. Therefore, software development may include research, new development, prototyping, modification, reuse, re-engineering, maintenance, or any other activities that result in software products.

Foundations and their implications

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]

A semantic theory of truth is a theory of truth in the philosophy of language which holds that truth is a property of sentences.

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.

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.
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).
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]
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.

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A modeling language is any artificial language that can be used to express information or knowledge or systems in a structure that is defined by a consistent set of rules. The rules are used for interpretation of the meaning of components in the structure.

Model-driven architecture (MDA) is a software design approach for the development of software systems. It provides a set of guidelines for the structuring of specifications, which are expressed as models. Model-driven architecture is a kind of domain engineering, and supports model-driven engineering of software systems. It was launched by the Object Management Group (OMG) in 2001.

The Open Group Architecture Framework TOGAF

The Open Group Architecture Framework (TOGAF) is a framework for enterprise architecture that provides an approach for designing, planning, implementing, and governing an enterprise information technology architecture. TOGAF is a high level approach to design. It is typically modeled at four levels: Business, Application, Data, and Technology. It relies heavily on modularization, standardization, and already existing, proven technologies and products.


A metamodel or surrogate model is a model of a model, and metamodeling is the process of generating such metamodels. Thus metamodeling or meta-modeling is the analysis, construction and development of the frames, rules, constraints, models and theories applicable and useful for modeling a predefined class of problems. As its name implies, this concept applies the notions of meta- and modeling in software engineering and systems engineering. Metamodels are of many types and have diverse applications.

Domain-specific modeling (DSM) is a software engineering methodology for designing and developing systems, such as computer software. It involves systematic use of a domain-specific language to represent the various facets of a system.

Executable UML is both a software development method and a highly abstract software language. It was described for the first time in 2002 in the book "Executable UML: A Foundation for Model-Driven Architecture". The language "combines a subset of the UML graphical notation with executable semantics and timing rules." The Executable UML method is the successor to the Shlaer–Mellor method.


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, platform and technology independence, and portability, together with an enterprise architecture framework for the specification of ODP systems.

Generic Eclipse Modeling System (GEMS) is a configurable toolkit for creating domain-specific modeling and program synthesis environments for Eclipse. The project aims to bridge the gap between the communities experienced with visual metamodeling tools like those built around the Eclipse modeling technologies, such as the Eclipse Modeling Framework (EMF) and Graphical Modeling Framework (GMF). GEMS helps developers rapidly create a graphical modeling tool from a visual language description or metamodel without any coding in third-generation languages. Graphical modeling tools created with GEMS automatically support complex capabilities, such as remote updating and querying, template creation, styling with Cascading Style Sheets (CSS), and model linking.

Enterprise modelling

Enterprise modelling is the abstract representation, description and definition of the structure, processes, information and resources of an identifiable business, government body, or other large organization.

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The Business Process Definition Metamodel (BPDM) is a standard definition of concepts used to express business process models, adopted by the OMG. Metamodels define concepts, relationships, and semantics for exchange of user models between different modeling tools. The exchange format is defined by XSD and XMI, a specification for transformation of OMG metamodels to XML. Pursuant to the OMG's policies, the metamodel is the result of an open process involving submissions by member organizations, following a Request for Proposal (RFP) issued in 2003. BPDM was adopted in initial form in July 2007, and finalized in July 2008.

The Semantics of Business Vocabulary and Business Rules (SBVR) is an adopted standard of the Object Management Group (OMG) intended to be the basis for formal and detailed natural language declarative description of a complex entity, such as a business. SBVR is intended to formalize complex compliance rules, such as operational rules for an enterprise, security policy, standard compliance, or regulatory compliance rules. Such formal vocabularies and rules can be interpreted and used by computer systems. SBVR is an integral part of the OMG's model-driven architecture (MDA).

Enterprise engineering is defined as the body of knowledge, principles, and practices to design all or part of an enterprise. An enterprise is a complex, socio-technical system that comprises interdependent resources of people, information, and technology that must interact with each other and their environment in support of a common mission. According to Kosanke, Vernadat and Zelm, enterprise engineering is an enterprise life-cycle oriented discipline for the identification, design, and implementation of enterprises and their continuous evolution, supported by enterprise modelling. Enterprise engineering is a subdiscipline of industrial engineering / systems engineering. The discipline examines each aspect of the enterprise, including business processes, information flows, material flows, and organizational structure. Enterprise engineering may focus on the design of the enterprise as a whole, or on the design and integration of certain business components.

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A view model or viewpoints framework in systems engineering, software engineering, and enterprise engineering is a framework which defines a coherent set of views to be used in the construction of a system architecture, software architecture, or enterprise architecture. A view is a representation of a whole system from the perspective of a related set of concerns.

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OntoUML is a ontologically well-founded language for Ontology-driven Conceptual Modeling. OntoUML is built as a UML extension based on the Unified Foundational Ontology (UFO). The foundations of UFO and OntoUML can be traced back to Giancarlo Guizzardi's Ph.D. thesis "Ontological foundations for structural conceptual models". In his work, he proposed a novel foundational ontology for conceptual modeling (UFO) and employed it to evaluate and re-design a fragment of the UML 2.0 metamodel for the purposes of conceptual modeling and domain ontology engineering.


  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. 1 2 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