The Triune continuum paradigm is a paradigm

Paradigm

The word paradigm has been used in science to describe distinct concepts. It comes from Greek "παράδειγμα" , "pattern, example, sample" from the verb "παραδείκνυμι" , "exhibit, represent, expose" and that from "παρά" , "beside, beyond" + "δείκνυμι" , "to show, to point out".The original Greek...

 for general system modeling

Systemics

In the context of systems science and systems philosophy, the term systemics refers to an initiative to study systems from a holistic point of view...

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

Systems modeling

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

 in various application contexts (highly tailored as well as interdisciplinary).

Introduction

As it is defined in the Cambridge Dictionary of Philosophy

The Cambridge Dictionary of Philosophy

The Cambridge Dictionary of Philosophy is a dictionary of philosophical terms published by Cambridge University Press and edited by Robert Audi. The dictionary, having been in publication since 1995, is now in its second edition. There are 28 members on the Board of Editorial Advisors and 440...

: "Paradigm, as used by Thomas Kuhn (The Structure of Scientific Revolutions

The Structure of Scientific Revolutions

The Structure of Scientific Revolutions , by Thomas Kuhn, is an analysis of the history of science. Its publication was a landmark event in the history, philosophy, and sociology of scientific knowledge and it triggered an ongoing worldwide assessment and reaction in — and beyond — those scholarly...

, 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 is a paradigm for general system modeling in the sense of this definition. The paradigm defines a set of scientific foundations (principles) within which conceptual frameworks

Conceptual framework

A conceptual framework is used in research to outline possible courses of action or to present a preferred approach to an idea or thought. For example, the philosopher Isaiah Berlin used the "hedgehogs" versus "foxes" approach; a "hedgehog" might approach the world in terms of a single organizing...

 used for system modeling in different contexts can be built, tested, evaluated and if necessary revised.

Thus, for an existent modeling framework, the paradigm allows to test the framework against its principles and to show the framework's deficiencies (if any), explaining how to fix the deficiencies in a possible revision of the framework. And if the goal is to build a new system modeling framework, then the paradigm provides its guidelines on how to do it assuring the resulting quality of the framework.

According to Herrera et al., 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

Software development

Software development is the development of a software product...

 and in the engineering of enterprise information systems.

Foundations and their implications

The Triune continuum paradigm is based on the three theories: on Tarski's theory of truth

Semantic 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 deflationary conceptions, is due to work published by Polish...

, on Russell's theory of types and on the Theory of Triune Continuum. The three theories were applied for the case of general system modeling, which produced the corresponding three principles that compose the paradigm:

• 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 engineering

Software Engineering is the application of a systematic, disciplined, quantifiable approach to the development, operation, and maintenance of software, and the study of these approaches; that is, the application of engineering to software...

 and systems engineering

Systems engineering

Systems engineering is an interdisciplinary field of engineering that focuses on how complex engineering projects should be designed and managed over the life cycle of the project. Issues such as logistics, the coordination of different teams, and automatic control of machinery become more...

, in particular, to formalize foundations of RM-ODP

RM-ODP

Reference Model of Open Distributed Processing is a reference model in computer science, which provides a co-ordinating framework for the standardization of open distributed processing...

 conceptual framework. As it was described by Dijkman, Naumenko in 2002 defined an abstract syntax for RM-ODP in a language called Alloy

Alloy (specification language)

In computer science and software engineering, Alloy is a declarative specification language for expressing complex structural constraints and behavior in a software system. Alloy provides a simple structural modeling tool based on first-order logic...

 that uses a set theoretic formal semantics.

• UML

The paradigm was applied to define a formal metamodel for UML

Unified Modeling Language

Unified Modeling Language is a standardized general-purpose modeling language in the field of object-oriented software engineering. The standard is managed, and was created, by the Object Management Group...

. According to Lano, the lack of grounded interpretation for UML concepts was identified in this application. As it was explained by Broy and Cengarle, 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 and, moreover, 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

Enterprise architecture

An enterprise architecture is a rigorous description of the structure of an enterprise, which comprises enterprise components , the externally visible properties of those components, and the relationships between them...

 allowing for enterprise modeling in which all the systems are systematically represented with the same modeling ontology.

• UFO

A new framework, "Unit – Function – Object" (UFO) approach, was designed for business modeling based on the ontology that was provided by the Triune Continuum Paradigm.

External links

• Triune Continuum Enterprise: About the Triune Continuum Paradigm at triunecontinuum.com.