=Paper=
{{Paper
|id=Vol-2060/aqemo1
|storemode=property
|title=Model Adequacy
|pdfUrl=https://ceur-ws.org/Vol-2060/aqemo1.pdf
|volume=Vol-2060
|authors=Bernhard Thalheim
|dblpUrl=https://dblp.org/rec/conf/modellierung/Thalheim18
}}
==Model Adequacy==
https://ceur-ws.org/Vol-2060/aqemo1.pdf
Ina Schaefer, Loek Cleophas, Michael und
Loek Cleophas Felderer (Eds.):
Michael Workshops
Felderer at Modellierung
(Hrsg.): Modellierung 2018,
2018,
Adequacy
Lecture Notes in Informatics (LNI), of Modeling
Gesellschaft Methods Bonn
für Informatik, (AQEMO)
2018 11
11
Model Adequacy
Bernhard Thalheim1
Abstract: 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.
Keywords: model notion; model adequacy; analogy; focus/truncation/abstraction; purposeful;
well-formed model; mode dependability
1 Models, Modelling Activities, Systematic Modelling
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 sub-
disciplines in a large variety of application cases with different purposes and context for
different 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 different 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 affairs (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 different
1 Christian-Albrechts University at Kiel, Department of Computer Science, D-24098 Kiel, Germany thalheim@is.
informatik.uni-kiel.de
2 The title of the book [4] has inspired this observation.
cbe
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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 The Notion of the Model
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 sufficiently
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 sufficient by its quality characterisation for internal quality, external
quality and quality in use or through quality characteristics (see [40]) such as correctness,
generality, usefulness, comprehensibility, parsimony, robustness, novelty etc. Sufficiency is
typically combined with some assurance evaluation (tolerance, modality, confidence, and
restrictions).
A well-formed instrument is called dependable if it is sufficient and is justified for some of
the justification properties and some of the sufficiency characteristics.
Model
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Adequacy 13
13
3 Adequacy as a Generalisation of Mapping, Truncation, and Prag-
matic Properties
Following H. Stachowiak (see, for instance, [33, 34]), a model is often defined in a
phenomenalistic way based on three properties:
(1) Mapping property: the model has an origin and can be based on a mapping from the
origin to the instrument.
(2) Truncation (reduction) property: the model lacks some of the ascriptions made to the
origin.
(3) 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 affairs, (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 [40]):
Adjustable selection of principles depending on modelling goals; model suites with explicit
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model association; development of a language culture; models 2.0; explicit treatment of
model value; coexistence of theory, languages, and tools; adequate representation variants
of models; compiler development for models; model families and variants. These challenges
are the background behind the consternation that has been summarised at Modellierung
208 by W. Hesse (see also [11, 12]): ... but they do not know what they do ...; Babylonian
language confusion and muddle; “it’s not a bug, it’s a feature” and other statements for
de-facto-standards and lobbyists; why I should cope with what was the state of art yesterday;
each day a new wheel, new buzzwords without any sense, and a new trend; without
consideration of the value of the model; competition is a feature, inhomogeneity; Laokoon
forever; dreams about a sound mathematical foundation; take but don’t think - take it only
without critics; academia in the ivory tower without executable models; where is the Ariadne
thread through.
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 [54]). What is the role of
languages in modelling?
• Which modelling context results in which modelling approach?
• What is the difference between the modelling process that is performed in daily
practice and systematic and well-founded modelling?
• Are we really modelling reality or are we only modelling our perception and our
agreement about reality?
• What is the influence of the modeller’s community and schools of thought?
Model
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Adequacy 15
15
5 The Storyline for this Keynote
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, farm-
ing, 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 [19, 20]. We are
going to introduce a general and formal notion of adequacy. Since adequacy cannot be
separated from dependability we have also to investigate it for the two modelling methods.
Finally, the keynote ends with a collection of open problems on adequacy of modelling
methods.
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