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# Category Archives: Mathematics

## Reflections on Abstractions: From ‘Siamese’ Graphs to Concept Lattices

There is an elegant construct of dealing with ‘Siamese’ abstractions for object-attribute situations, from formal concept analysis. Where ‘Siamese’ means not-rhs-unique mapping of complete subgraphs. Continue reading

## Reflections on Abstractions: Subsumptions and Omissions

In addition to the recent posting ‘Abstractive and Functional Mappings’ we provide a simple visualisation of subsuming and omitting abstractions. Continue reading

Posted in Mathematics, Reflections on Abstractions
Tagged abstraction, Graph, left-total, left-unique, lhs, Mapping, model, modeling, omission, reflections on abstractions, Relation, rhs, ROA, subsumption
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## Reflections on Abstractions: Abstractive vs Functional Mappings

We introduce the concepts of subsuming and omitting mappings, and see how they are better suited for abstraction and modelling than the classical mathematical concept of functions. Continue reading

Posted in Mathematics, Reflections on Abstractions
Tagged abstraction, bijection, function, Graph, left-total, left-unique, lhs, Mapping, model, modeling, reflections on abstractions, Relation, rhs, ROA, total, unique
3 Comments

## Reflections on Abstractions: The Use Case trade-off

Based on the elementary terms of relational structures, this little example shows the basic trade-off of Use Cases: understandability vs redundancy. Continue reading

## 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: 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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## Models: Correct, Complete, Consistent, Unambiguous

**How do you judge how ‘good’ or ‘bad’ a model is?** I mean models like we use them in **software requirements specification** or **business analysis**. On this, one can find criteria in literature like BABOK, Wikipedia, IEEE, research papers, or textbooks. However, for some reason these criteria sets are quite different in each case. I’ve tried to get the things a little straighter, starting with the ‘big four’ quality characteristics of software requirements specifications … Continue reading

Posted in Mathematics, Requirements
Tagged abstraction, Complete, completeness, consistency, Consistent, Correct, correctness, IEEE 830, incomplete, incorrect, incosistent, logic, model, model quality, model theory, Modelling, quality criteria, Requirements, software requirements specification, specification, Unambiguous, venn diagram
1 Comment