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# Tag Archives: Mapping

## 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
1 Comment

## 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

## Stachowiak on Preterition and Abundance in Modelling

In his 1973 book “Allgemeine Modelltheorie” Herbert Stachowiak discusses the concepts of Preterition, Abundance and Contrastation of Original-Model mappings. This can be interpreted using homomorphism preservation and other logical concepts. Continue reading

Posted in Epistemology, Herbert Stachowiak
Tagged Abduction, abstraction, Allgemeine Modelltheorie, Contrastation, Definition, General Model Theory, Herbert Stachowiak, Homomorhism, Homomorphism preservation theorem, logic, Mapping, model, model theory, Modelling, original, Preteritition, Stachowiak
10 Comments

## General Model Theory by Stachowiak

In his 1973 book “Allgemeine Modelltheorie” (General Model Theory) Herbert Stachowiak describes the fundamental properties that make a Model: Mapping, Reduction, and Pragmatism. Continue reading