Models, modeling languages, modeling frameworks and their background have dominated research on information systems engineering for last four decades. Models are mainly used as mediators between the application world and the implementation or system world. Modelling is still conducted as the work of an artisan and workmanship. While a general notion of the model and of the conceptual model has already been developed, the modelling process is not investigated so well. Modelling has to be based on principles and a general theory of modelling activities. One of the lacunas is still a proper understanding of adequacy of models, adequacy of modelling and deployment methods, and a theory of adequacy. We will concentrate on the first issue. Models are principle and central instruments in mathematics, data analysis, modern computer engineering (CE), in teaching any kind of computer technology, and also modern computer science (CS). They are built, applied, revised and manufactured in many CE&CS subdisciplines in a large variety of application cases with diferent purposes and context for diferent communities of practice. CE&CS expressively use the conception of model for daily work. Modelling is one of their four central paradigms beside structures (in the small and large), evolution or transformation (in the small and large), and collaboration (based on communication, cooperation, and coordination). It is now well understood that models are something diferent from theories. They are often intuitive, visualisable, and ideally capture the essence of an understanding within some community of practice and some context. At the same time, they are limited in scope, context and the applicability. Models have been considered to be somewhere in the middle between the perception and understanding of the state of afairs (world, situations, data etc.) and theories (concepts and conceptions, statements, beliefs, etc.) since they may describe certain aspects of a situation and may represent parts of a theory. Models should thus be considered to be the third dimension of science [2, 50, 52]2. Other disciplines (see for instance [50]) have developed a diferent
c b e understanding of the notion of model, of the function of models in scientific research and of the purpose of the model. Models are often considered to be artifacts where also virtual models are considered beside real one. Models might also be mental models and thought concepts. Models are used as instruments in utilisation scenarios. They function in these scenarios. 2
There is however a general notion of a model and of a conception of the model: A model is a well-formed, adequate, and dependable instrument that represents origins. (see [8, 45, 47]) Its criteria of well-formedness, adequacy, and dependability must be commonly accepted by its community of practice within some context and correspond to the functions that a model fulfills in utilisation scenarios.
The model should be well-formed according to some well-formedness criterion. As an instrument or more specifically an artifact a model comes with its background, e.g. paradigms, assumptions, postulates, language, thought community, etc. The background its often given only in an implicit form. The background is often implicit and hidden.
A well-formed instrument is adequate for a collection of origins if it is analogous to the origins to be represented according to some analogy criterion, it is more focused (e.g. simpler, truncated, more abstract or reduced) than the origins being modelled, and it suficiently satisfies its purpose.
Well-formedness enables an instrument to be justified by an empirical corroboration according to its objectives, by rational coherence and conformity explicitly stated through conformity formulas or statements, by falsifiability or validation, and by stability and plasticity within a collection of origins.
The instrument is suficient by its quality characterisation for internal quality, external
quality and quality in use or through quality characteristics (see [
A well-formed instrument is called dependable if it is suficient and is justified for some of the justification properties and some of the suficiency characteristics.
3
Adequacy as a Generalisation of Mapping, Truncation, and
Pragmatic Properties
Following H. Stachowiak (see, for instance, [
Mapping property: the model has an origin and can be based on a mapping from the origin to the instrument.
Truncation (reduction) property: the model lacks some of the ascriptions made to the origin.
Pragmatic property: the model use is only justified for particular model users, the tools of investigation, and the period of time.
We observe however that these properties do not qualify a representation as a model. The mapping and truncation properties are far too strict and need further investigation. A model must not be a mapping from some origin. Homomorphism is a nice property but far too strict in most applications. We might use representations that are not images of mappings such as a Turing machine, a system architecture, or development strategies. Furthermore, we might use representations that are not reducts of origins such as (conceptual) information system models for the variety of viewpoints users of databases might have. Truncation (or abstraction) considers a model to be an Aristotelian one by abstraction by disregarding the irrelevant. The relevance criterion is based on the purpose (or goal or function) of a model. So, truncation is far too fuzzy. Models are developed by a community of practice for utilisation by a community of practice and in a context. The utilisation depends on the intentions of users and their context. So, we observe that the utilisation of models determines (a) the kind of model, (b) the governing purposes or goals of utilisation of the model, (c) the properties of a model, (d) the amplification a model provides with extensions, (e) the idealisation by scoping the model to the ideal state of afairs, (f) the divergence by deliberately diverging from reality in order to simplify salient properties of interest, and (g) the added value of a model. The seven additional statements are combined in the mission a model has. The mission clarifies how the model functions well within its intended scenarios of usage according to its capacity and potential. The mission must be coherent with the context, the determination or specific basis of conduct or utilisation of the model, and must be acceptable for the users or – more concrete – the community of practice. Therefore, the mission clarifies the functions (and anti-functions or forbidden ones), purposes and goals of the utilisation, the potential and the capacity of the model. 4
An Agenda: Towards Adequacy of Modelling Methods
The theory of modelling is still struggling with a number of research challenges (see [
This consternation and the challenges can be summarised by a research agenda, e.g. with the following problems: • • • • • • • • • • •
Can be develop a simple notion of adequateness that still covers the approaches we
are used in our subdiscipline?
Do we need this broad coverage for models? Or is there any specific treatment of
dependability for subdisciplines or specific deployment scenarios?
Which modelling methods are purposeful within which setting?
Which model deployment methods are properly supporting the function of a model
within a utilisation scenario?
How does the given notion of model match with other understandings and approaches
to modelling in computer science and engineering?
What is the background of modelling, especially the basis that can be changed
depending on the function that a model plays in some utilisation scenario?
Language matters, enables, restricts and biases (see [
5
In this keynote we discuss mainly the first element of the research agenda: adequateness of
models, modelling methods, and modelling as a systematic activity. So far, the adequateness
notion is far too fuzzy and too wide. The keynote is based on a large body of knowledge
developed on models, modelling activities, and systematic modelling3 The basis of our
understanding of adequacy and dependability is the case study in the Kiel compendium of
models, modelling activities and systematic modelling (see [50]). This MMM approach
to modelling has been investigated for models in agriculture, archaeology, arts, biology,
chemistry, computer science, economics, electrotechnics, environmental sciences,
farming, geosciences, historical sciences, languages, mathematics, medicine, ocean sciences,
pedagogical science, philosophy, physics, political sciences, sociology, and sports.
The introduction is based on a discussion of adequacy for two modelling methods widely
used in our area. The specific utility of models follow the line given in [
For details on language theory we refer to [3, 18, 27, 28, 7, 36, ?, 43, 56].
For details of design science research we refer to [
Formalisation also includes approaches to a general theory of modelling such as [
For details of our work we refer to [
Challenges. Springer, 2011. [9] U. Frank and S. Strecker. Open Reference Models - Community-driven collaboration to promote development and dissemination of reference models. Enterprise Modelling and Information Systems Architectures, 2(2):32–41, 2007. [16] R. Kaschek. Konzeptionelle Modellierung.
Habilitationsschrift.