Meanings of “Model”

Becoming aware of Finite Model Theory. Part 2 of n.

Just a word on the different usages of ‘model’ in (Software) Engineering and mathematical Model Theory.

Consider a (finite) hotel with a room schedule, i.e. a table Room X Day where a “x” stands for “this room is occupied that day”, O(room, day) for short. Moreover a field without a “x” means “this room is available that day”, what requires that the schedule is maintained properly, i.e. each time someone books a room it is actually marked in the table. Here the schedule table is expressed in a formalized language, so we can call it a model, in the sense of Business Process Model or Entity Relationship Model.

Such a schedule table can be seen as partially isomorphic to reality, i.e. certain parts of the real world have just been extracted, without any change. Furthermore, the schedule defines a structure which can assumed to be finite, since one cannot book a room say two years in advance. Thus the schedule can be described in a single statement like O(24, 10th Nov) AND O(24, 11th Nov) AND O(32, 9th Nov) and so on. Also negations on an atomic level can be expressed by empty fields, e.g. NOT O(24, 12th Nov). Thus there is an extract of reality that is a model for the schedule, in the sense of Model Theory.

Thus the schedule is a model of reality as well the reality provides (by extraction) a model of the schedule. Notice that statements true for the schedule do not have to be true in reality, what we leave to be examined later.

About modelpractice

Modeling Theory and Abstraction Awareness in strive for scientific rigour and relevance to information systems engineering.
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8 Responses to Meanings of “Model”

  1. TY says:

    Interesting thought. What do models mean? it seems need more exact answer…
    hope to read your next.

    • Hi TY

      thanks for your opinion. An outlook in brief:

      In this blog I will goon, with focus solely on model in the 2nd, the model theoretic sense. The general debate about definition of model (or abstraction) in the 1st sense is sth I’m interested in too, (like the great work of Herbert Stachowiak – as cited on your blog) but this would be out of the scope of this blog.

      so, more to come …

  2. TY says:

    Well, it’s saw little of the discussion under model theoretic sense … (at least, for me)

    By the way, I have only read a bit of piece of the Herbert Stachowiak’ s “General Model Theory” in English via internet. Would you know where can I find more by internet? (but I don’t know any German)

    • Herbert Stachowiak: I know that even in german language his main book (Allgemeine Modelltheorie) is not available any more. That’s really a shame! Has it been published in English at all?

  3. mbrambil says:

    extremely interesting post.
    Let me add one question (more at the philosophical level maybe): what about the observer that because of the observation itself (you may read observation as modeling in this case) modifies the reality?
    Let me point also to some additional discussion of the roles and objectives of modeling (maybe more at a pragmatic level) on my blog:
    I would be glad to get the viewpoint of a more theory-oriented expert.

  4. Hi Marco, thanks for your comment.

    Indeed, think this is a big issue in Analysis: through the deeper understanding provided by a good requirements model the expert changes its mind. (sth like ‘Convergent Modelling’)

    I’m very interested in basic modeling principles/ issues (like in “Are your requirements complete”) and their formalisation. This sounds like a very promising one. Will have to meditate about it …

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