Modelling Theory and Practice/Models and Abstraction

Models

Herbert Stachowiak, 1973

Fundamental Properties of the general Concept of Models

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

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

[[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]]

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

Stachowiak, Herbert (1973). Allgemeine Modelltheorie [General Model Theory] (in german (DE)). Springer. ISBN ISBN 3-211-81106-0. {{cite book}}: Check |isbn= value: invalid character (help)CS1 maint: unrecognized language (link)
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