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# Tag Archives: refinement

## Reflections on Abstractions: Joining Classification by Relationships and Properties

How does classification based on properties go together with relationship based classes? In addition to the former posting “Concepts vs Modules for Classification”, the fit of concept lattices and relationship graphs is examined in more detail. Continue reading

Posted in Mathematics, Reflections on Abstractions
Tagged abstraction, abstraction awareness, Class, classification, classifier, component, concept analysis, formal concept analysis, formal methods, Graph Theory, model, modeling, modeling theory, module, refinement, reflections on abstractions, ROA
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## Reflections on Abstractions: Concepts vs Modules for Classification

A Concept (as in Formal Concept Analysis) and a Module (as in Graph Theory) both cover the notion of Classification. Although they share the same basic idea, they reveal differences in detail. Continue reading

## Reflections on Abstractions in Relational Structures. The very basic Setting.

Abstractional concepts can be found in the very basics of Graph Theory and Formal Concept Analysis. They provide the basic elements of Classification, Aggregation and Generalisation for a deeper rigorous analysis of Abstractions. Continue reading

Posted in Mathematics, Reflections on Abstractions
Tagged abstraction, abstraction awareness, aggregation, classification, component, concept analysis, connectivity, formal concept analysis, formal methods, generalisation, Graph Theory, model, modeling, modeling theory, module, refinement, reflections on abstractions, ROA
2 Comments

## Reflections on Abstractions: Cases vs Models

We describe by simple means of basic Finite Model Theory a very important principle in software engineering: modelling properties is more expressive than just collecting cases. This, for example, is the reason why test cases can be derived from specifications but not vice versa. Continue reading

Posted in Mathematics, Reflections on Abstractions
Tagged abstraction, abstraction awareness, axiomatizable, Case, Finite Model Theory, finite models, formal methods, intentional programming, model, model theory, modeling, modeling theory, refinement, reflections on abstractions, ROA, specification, Test
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## Reflections on Abstractions: Generalisation and Aggregation

Abstraction Awareness is about gaining a deeper understanding of abstraction. With basic means of Graph Theory we diff among two kinds of abstraction: abstraction wrt. generalisation and aggregation. Continue reading