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Stachowiak’s <M, O, K, t, Z>: a case for model as use

In the General Model Theory[1] Stachowiak defined a n-tuple with model[2]. It appears that very consistent with the definition on model as use.

Stachowiak defined <M, O, K, t, Z> as a n-tuple of five parameters (of which) comprising an object O and a model M representing the functional operation F, M= F(O). The object M is a model of object O at time interval t and in reference to the objective Z for a K-system K. [2]

Understanding by Niemeyer’s paper, the M is model; O is the original of the model, i.e., the object the model modeled; K is the system using the model as a substitute of the O at time interval t with Z; Z is the goal or purpose for K.

It seems very close to the situation in model as use: “where the role carries certain properties of a thing directly or indirectly and works by the properties“. I see this is a certain case of the situation in Model as Use, and I think, is it the case that suitable for all uses of model? The functional operation F, M = F(O), of course, is a mapping. This implies that the model in the Stachowiak’s 5-tuple is one of the types of model in my thoughts, but not all.


[1] I know a book Allgemeine Modelltheorie (General Model Theory) by Herbert Stachowiak, Wien: Springer, 1973. Unfotunately, so far, I’ve only seen some of fragments by the citations in some literature in English.

[2] Quotes from: Niemeyer, K. (2007). A Contribution to Model Theory, volume 12 of NATO Science for Peace and Security Series – D: Information and Communication Security. IOS Press.


About TY

interested in models & modeling, software, information systems, applications & engineering for enterprises


14 thoughts on “Stachowiak’s <M, O, K, t, Z>: a case for model as use

  1. Hi TY
    is this “Niemeyer, K. (2007). A Contribution to Model Theory” available somewhere on the internet?

    Posted by modelpractice | July 6, 2012, 22:32
  2. Just discovered the following passage in Stachowiak’s “explication”: “Notice, that also the Reduction property is satisfied [by ] …” then he describes how his 12 rules* belonging to achieve this.

    i.e. as it seems doesn’t correspond to “Model as use”

    *The rules are quite complex, with lots of new defined concepts he introduces before


    Posted by modelpractice | July 7, 2012, 05:01
    • tech note the lt and gt symbols seem to disappear, thus < M, O, K, t, Z > is missing above after “by …” and “seems …”

      Posted by modelpractice | July 7, 2012, 05:04
    • “Model as use” emphasized that a thing (anything) can be a model in (just) the situation, as a fashion model is played a model only in the T-stage, rather than in their daily lives.
      I see the situation is general and suitable for all types of model; the Stachowiak’s 5-tuple as a use case to model consistent to the situation, too. Model-as-use does not exclude reduction, it seems suitable to all the types of models I see, so far :-)

      Posted by TY | July 7, 2012, 11:49
      • yes, thus we have the “Model as use”(1) as a generalisation of “Model by Stachowiak”(2). I would call (1) an analogy – right? Like the analogy of the Higgs boson and the celebrity entering a party.

        Posted by modelpractice | July 7, 2012, 17:22
        • It seems that I don’t quite understanding your metaphor …
          I see the Stachowiak’s models seems is clearly denoted to the >mapping<, but some models, such as so-called linguistic models (the models expressed in language), I prefer do not call that mapping.

          Posted by TY | July 7, 2012, 18:00
          • Stachowiak assumes that an original as well as a model is described by attributes (that can be complex expressions). thus, they can be expressed in natural as well as in formal languages, and thus can also be mapped.
            As far as I understood it.

            Posted by modelpractice | July 8, 2012, 00:03
          • this is a very clear thinking.

            Posted by TY | July 8, 2012, 08:16
  3. what I would like to understand: if you take Stachowiak’s definition, and leave out either Mapping, Reduction, Pragmatism, what do you get? The above is perhaps an idea on this …

    Posted by modelpractice | July 9, 2012, 03:53


  1. Pingback: Stachowiak’s K-System | modelpractice - July 8, 2012

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