*Abstraction Awareness is about deeper understanding of abstraction, a concept so basic to human thinking. Subsequently abstraction is discussed by the means of basic graph theory and formal concept analysis.
*

Lets bring the definition of abstraction by subsumption, i.e. of not always lhs-unique mappings, to life.** We want to detect complete subgraphs in graphs and build an abstract graph (model) from them.** Think of this as building components, where their elements are extremely tightly bound. Notice that this is stronger than ‘connected components’ of graph theory.

### Abstraction by ‘Siamese’ Edge

**(rhs-unique)** gives a pretty nice example of abstraction by subsumption, where rhs-uniqueness holds. We get two rhs nodes with an edge amongst them, that ‘survived’ the mapping.

**(not-rhs-unique)** – a kind of ‘siamese graph’ – leaves us with the choice to simply map the middle node to two different nodes, and then introduce an additional type of **edge for ‘having common node’** (e.g. meaning ‘these two rooms have a common wall’) or to introduce any other kind of construct.

### Abstraction by Concept Lattice

**There is an elegant construct for bi-partite graphs **(that correspond to an object – attribute, or extension – intension situation)** from formal concept analysis:**

**(bi-partite)** shows an example where nodes 1 and 2 together with a and b are ‘as complete as possible’ since they have all connections allowed amongst them in a bi-partite graph. This kind of completeness corresponds to a ‘concept’ in formal concept analysis. Thus we can draw a **concept lattice** as in (bi-partite), with 1-3 as objects and a-c as attributes. Notice that the edges here are read from bottom to top as generalisations, i.e. we can completely refrain from object-attribute edges here (no mesh up as by the ‘having common node’ edge above).

So long

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