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.
What’s happened so far
This is just a little add-on to the former posting Concepts vs Modules for Classificationwhere remained open, if and how the relationships inside the sub-matrix ‘I’ in the figure (concept matrix) can be compatible to the concept lattice, defined by the upper right sub-matrix.
The nice case
The four cases of ‘compatible’ relationships are shown in figure (concepts and relations) up to isomorphy. The corresponding matrix views are shown in figures (a) to (d). For example, relationship (a) from concept 1 to 2, element (1,2) in the matrix, implies also the matrix element (2,2) since concept 1 is a generalisation of 2.
The not so nice case
However, sometimes the concept lattice may need some amendment. Notice, the above are the ‘compatible’ cases, where the concept lattice is in alignment with the relationships ‘seamlessly’. In other cases, like in figure (concepts and relations matrix) the concept lattice might need to be fitted correspondingly like (fitted lattice).
we’ve seen some basic cases how property structures and relational structures can fit together, more or less ‘seamlessly’.