# Modelling Theory and Practice/Models and Abstraction

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## Models[edit | edit source]

Herbert Stachowiak, 1973

### Fundamental Properties of the general Concept of Models[edit | edit source]

**Mapping**: Models are always models__of something__, i.e. mappings from, representations of natural or artificial originals, that can be models themselves.**Reduction**: Models in general capture__not all__attributes of the original represented by them, but rather only those seeming relevant to their model creators and/ or model users.**Pragmatism**: Models are not uniquely assigned to their originals per se. They fulfill their replacement function a) for__particular__- cognitive and/ or acting, model using__subjects__, b) within__particular time intervals__and c) restricted to__particular mental or actual operations__.

### Remarks[edit | edit source]

- Of particular importantance is the aspect of pragmatism: "Beyond mapping and reduction the general notion of model needs to be relativised in three ways. Models are not only models
__of something__. They are also models__for someone__, a human or an artificial model user. At this, they fulfill they function__over time__, within a time interval. Finally, they are models__for a certain purpose__. Alternatively this could be expressed as: a pragmatic complete determination of the notion of model has not only to consider the question '__what of__' something is a model, but also '__whom for__',__when__, and '__what for__' it is a model, wrt. its specific function." - Moreover Stachowiak provides a more formal explication of the concept of model. For our purposes the above colloquial description is sufficient.
- For example ...
- This book relates to the above properties in the following way:
**Mapping**: This book in the first place covers the right hand side of the mapping, i.e. the structures one might map to. The structures presented start from very basic ones, becoming more and more complex in a (hopefully) systematic way. Thus it provides the modeler with a basic repertoire for mapping its originals to. Of course the underlying assumption is, that the simple strcutures are more relevant than the more complex ones ...**Reduction**: The book is purely structural, i.e. it is not about any concrete area of knowledge, it's like mathematics: one cow plus another one make two cows, as well as one electron plus another one make two electrons. In terms of maths it's 1+1. Thus, the structures in this book contain no semantics from any kind of application domain.**Pragmatism**is difficult to approach, since it is a quite 'soft' aspect, relative to the eyes of every beholder. The approach of this book to pragmatism is case based, i.e. providing empirical cases on a restricted subject area and in a systematic way, s.t. they can be fit by a modeller for its purposes. See Case-based reasoning.

## Abstraction[edit | edit source]

[[File:|600px|alt=A map made of brightly coloured lines weaving a pattern between stations.|Zone 1 (central zone) of the Underground (and DLR) network in a geographically more accurate layout than the usual Tube map, using the same style]]

## Literature[edit | edit source]

- Stachowiak, Herbert (1973) (in german (DE)).
*Allgemeine Modelltheorie [General Model Theory]*. Springer. ISBN ISBN 3-211-81106-0. - Translation by modelpractice