Reflections on Abstractions

1. Inroduction

reflections on abstractionsRelational structures like (simple) are quite ‘friendly’ and easy to ‘handle’ in any way. However, if structures become more ‘nasty’ as in (hard), one must think of ways to make them understandable and easier to deal with. The world is full of structures like (hard), in the professional world, like software architecture or business analysis, as well as in our thinking and communication in everyday life.

Here the approach considered for handling such structures is abstraction. Where abstraction is understood in a common sense meaning, roughly indicated in (abstract), based of the Stachowiakian model-properties: mapping (from original to model), reduction (of the original by the model), and pragmatism (such that the model makes ‘sense’). ( -> General Model Theory)

A key to contemplate abstraction is the choice of a suitable abstraction level/ view. This approach here is restricted to finite relational structures. Judging by practical experience, mainly from software engineering and business analysis, finite relational structures are of considerable relevance.

A rigorous treatment of abstraction comprises more that sole formalisation. The justification for dealing with abstraction is its ubiquity. Thus, it should be present in relevant mathematical structures as well. So, in finite relational structures first class candidates for a formal underlying of abstraction are Graph Theory, Formal Concept Analysis, Finite Model Theory and others as appropriate. Notice, the focus here is on applying existing mathematical theories, not on proving theorems.

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