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# Category Archives: Reflections on Abstractions

## Reflections on Abstractions: Classification and Generalisation by Conceptualisation

It is demonstrated how the basic notion of Concept in Formal Concept Analysis covers two of the fundamental notions of Abstraction: Classification and Generalisation. This is why conceptualisation is so highly valuable in examining entities and their properties. Continue reading

## Reflections on Abstractions: Correctness and Completeness

An earlier post on quality properties of models is compared to basic concepts of mathematical logic, in strive for rigour. What does a formal system of mathematical logic has in common with a modelling situation as in requirements analysis? It depends … Continue reading

Posted in Mathematics, Reflections on Abstractions
Tagged abstraction, axiom, Complete, completeness, consistency, Consistent, Correct, correctness, formal system, incomplete, incorrect, incosistent, logic, model, model quality, model theory, Modelling, Requirements, resolution, software requirements specification, specification, Unambiguous, venn diagram
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## 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