In his 1973 book “Allgemeine Modelltheorie” (General Model Theory) Herbert Stachowiak describes the fundamental properties that make a Model. Unfortunately this is still not available in english language, so I thought why not try a (quite free-style) translation of the essential bits (see here for all):
Part I: Excerpt
184.108.40.206 Preterition, Abundance and Contrastation
Three fundamental concepts (out of many) from the model theoretical apparatus are presented here (their explication is done not here).
Preteritive (= omitted, ignored) attributes are not covered by the Original-Model mapping, since they are operationally irrelevant. The preteritive class of an Original (wrt one of its Models) is the class of the preterited Original attributes (wrt this O-M mapping).
Abundant (= superfluous, redundant) attributes in the Model correspond to no attributes in the Original. This can often be found by retrospective empirical analysis of concrete Models. They constitute the abundance class of the Model wrt its Original. Abundant attributes have no direct function in the O-M mapping. They are either just ‘technical vehicles’ of Model construction or ‘hypothetical bridge-over’ constructs. As technical vehicles they are chosen by economies of efficiency, construction, but also presentation and explanation. As hypothetical bridge-overs they close a gap in the mapping, i.e. they imply imaginary attributes of the Original from which they are mapped. This may be in close conjunction with the intention to gain new insights into ‘yet unknown’ properties of the Original.
Contrastation (not in the picture) refers to the feature of many concrete Models to accentuate certain attributes or attribute classes wrt the other original attributes, i.e. to contrast with each other. (e.g. image processing like sharpening or increasing contrast)
Stachowiak, Herbert (1973) (in german (DE)). Allgemeine Modelltheorie [General Model Theory]. Springer. ISBN 3-211-81106-0.
Part II: Interpretation
From a logical point of view, I would put it like this:
An Original-Model mapping, can be seen as a homomorphism. In this case, the homomorphism preservation theorem holds, stating that just Original attributes of a certain limited expressiveness are always preserved in the Model. Others may or may not hold in the Model.
In detail: Sentences equivalent to a positive first-order existential expression are always preserved by the mapping (this also holds when restricted to finite models only). E.g. ‘my relation has a non-reflexive element’ might hold in the Original, whereas ‘all my elements are reflexive’ might hold in the model.
Thus, for non-preserved expressions from the Original, their negation might hold in the Model. The earlier could be interpreted as Preterition, the latter as Abundance. However, I don’t think, this was what Stachowiak had in mind.
Beyond these unpreserved attributes, there are cases like in figure (unpreserved colouring). The Model could be interpreted s.t. now all nodes and edges are coloured black. Alternatively the Model could be seen as not covering the concept of colour at all anymore, i.e. colour has been abstracted away. However, even in the case of a non-coloured model the nodes and edges physical have to be drawn in some colour. Thus, here black means neutral. Imho this was the kind of Abundance Stachowiak had in mind.
The book at Google books