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Models and Modelling in Computer Science

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Logic, Computation and Rigorous Methods

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12750))

Abstract

Models are a universal instrument of mankind. They surround us our whole lifespan and support all activities even in case we are not aware of the omnipresence. They are so omnipresent that we don’t realise their importance. Computer Science is also heavily using models as companion in most activities. Meanwhile, models became one of the main instruments. The nature and anatomy of models is not yet properly understood.

Computer Science research has not yet been properly investigating its principles, postulates, and paradigms. The well-accepted three dimensions are states, transformation, and collaboration. An element of the fourth dimension is abstraction. The fourth dimension is modelling. We review here the fourth dimension.

Dedicated to Egon Börger

Remark: See too the presentations in https://vk.com/id349869409 or in the youtube channel “Bernhard Thalheim” for the theory and practice of modelling.

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Notes

  1. 1.

    The oldest mention we acknowledge is the usage in Ancient Egypt with the use of models as moulds, models as representations, and models of the right order (’maat’). The first explicit notion of model is ‘metron’ in Ancient Greece and ‘modulus’ in Roman time, i.e. at least 40BC. The wide use of this word came with engineering in the 16th century and with sciences in the 19th century.

  2. 2.

    A description of Computer Science has been given in [12]:

    “Computer Science and engineering is the systematic study of algorithmic processes – their theory, analysis, design, efficiency, implementation and application – that describe and transform information. The fundamental question underlying all of computing is, What can be (efficiently) automated.”.

  3. 3.

    Computer Science can be divided into kernel CS and applied CS. The first subdiscipline spans theoretical, practical and technical CS.

  4. 4.

    We do not know a commonly accepted description of this subdiscipline.

    Essentially, applied CS has two branches: specific application-oriented CS and engineering of solutions in applications. The first branch has led to a good number of so-called ‘hyphen’ CS such as business informatics, biomedical informatics, and geoinformatics. The second branch is engineering of work systems [2], i.e. systems “in which humans or machines perform processes and activities using resources to produce specific products or services for customers”. It spans topics such as information systems, information science, information theory, information engineering, information technology, information processing, or other application fields, e.g. studying the representation, processing, and communication of information in natural and engineered systems. It also has computational, cognitive and social aspects.

  5. 5.

    A dimension that has not found its proper entry into our discipline is approximation. Approximation is the fifth dimension orthogonal to states, transformation, and collaboration.

  6. 6.

    We expect that modern applications such as internet technology have to use humanisation as the sixth dimension in order to cope with modern interdisciplinary tasks.

  7. 7.

    See below: adequate and justified, sufficient internal and external quality.

  8. 8.

    Donald Knuth followed this meaning by calling his four volumes: ‘The art of programming’ [24].

  9. 9.

    A mould is a distinctive form in which a model is made, constructed, shaped, and designed for a specific function a model has in a scenario.

    It is similar to mechanical engineering where a mould is a container into which liquid is poured to create a given shape when it hardens. In Mathematics, it is the general and well-defined, experienced framework how a problem is going to be solved and faithfully mapped back to the problem area.

  10. 10.

    A model and modelling science consists of a system of knowledge that is concerned with models, modelling and their phenomena. It entails unbiased observations and systematic experimentation. It involves a pursuit of model and modelling knowledge covering general truths or the operations of fundamental laws.

  11. 11.

    Culture combines approaches, attitudes, behaviour, conventional conducts, codes, traditions, beliefs, values, customs, thought styles, habits, the system comprising of the accepted norms and values, goals, practices, and manners that are favored by the community of practice. It is a characteristic of this community and includes all the knowledge and values shared by the community of practice.

    Culture of modelling is a highly developed state of perfection that has a flawless or impeccable quality.

  12. 12.

    Objects can be developed for usage. At a later stage, they were exhibited and become models used for explanation, e.g. about culture. See for instance, Ancient Egyptian objects in modern museums. We also may observe the opposite for the model-being of object, e.g. see [8].

  13. 13.

    The earliest source of systematic model consideration we know is Heraclitus (see [26] for a systematic and commented re-representation of Heraclitus fragments) with his concept of \(\lambda \) ó\(\gamma o \varsigma \) (logos).

  14. 14.

    Mathematician often claim that they are the only ones who know what is a model and what is modelling. We notice, however, that modelling is typically performed outside Mathematics.

  15. 15.

    The notion

    “A model is a simplified reproduction of a planned or real existing system with its processes on the basis of a notational and concrete concept space. According to the represented purpose-governed relevant properties, it deviates from its origin only due to the tolerance frame for the purpose.” [44]

    is a typical example of this parametrisation. The origin is the system and the inherited concept space. Analogy is essentially a mapping. Focus is simplification. Purpose is reproduction or documentation. The justification is inherited from the system and its processes. Sufficiency is based on tight mapping with some tolerated deviation.

    In a similar form we use parameters for the definition in [1]:

    “A model is a mathematical description of a business problem.”.

  16. 16.

    See http://bernhard-thalheim.de/ModellingToProgram/.

  17. 17.

    Engineering is the art of building with completely different success criteria (see [33]: “Scientists look at things that are and ask ‘why’; engineers dream of things that never were and ask ‘why not’.” (Theodore von Karman)).

    “Engineers use materials, whose properties they do not properly understand, to form them into shapes, whose geometries they cannot properly analyse, to resist forces they cannot properly assess, in such a way that the public at large has no reason to suspect the extent of their ignorance.” (John Ure 1998, cited in [33]).

  18. 18.

    Well-formedness is often considered as a specific modelling language requirement.

  19. 19.

    The criteria for adequacy are analogy (as a generalisation of the mapping property that forms a rather tight kind of analogy), being focused (as a generalisation of truncation or abstraction), and satisfying the purpose (as a generalisation of classical pragmatics properties).

  20. 20.

    The model has another constituents that are often taken for granted. The model is based on a background, represents origins, is accepted by a community of practice, and follows the accepted context. The model thus becomes dependable, i.e. it is justified or viable and has a sufficient quality.

    Most notions assume dependability either as a-priori given or neglect it completely.

  21. 21.

    The word fields in German and English languages are different.

  22. 22.

    The software crisis has been a crisis 1.0. Nowadays we have a data crisis, a (large and embedded) system crisis, an infrastructure crisis, and an energy crisis. For instance, it is estimated that one third of the world-wide produced electro energy is consumed by computers by 2025.

  23. 23.

    Culture is a “a collective phenomenon, which is shared with people who live or lived within the same social environment, which is where it was learned; culture consists of the unwritten rules of the social game; it is the collective programming of the mind that separates the member of one group or category of people from others.” [19].

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Authors and Affiliations

  1. Department of Computer Science, Christian-Albrechts University at Kiel, 24098, Kiel, Germany

    Bernhard Thalheim

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  1. Institut für Softwaretechnik und Programmiersprachen, University of Ulm, Ulm, Germany

    Alexander Raschke

  2. Dipartimento di Informatica, Università degli Studi di Milano, Crema, Italy

    Elvinia Riccobene

  3. UIUC Institute, Zhejiang University, Haining, China

    Klaus-Dieter Schewe

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Thalheim, B. (2021). Models and Modelling in Computer Science. In: Raschke, A., Riccobene, E., Schewe, KD. (eds) Logic, Computation and Rigorous Methods. Lecture Notes in Computer Science(), vol 12750. Springer, Cham. https://doi.org/10.1007/978-3-030-76020-5_17

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