TypesOfHierarchies (ThoughtStorms)

I use the word hierarchy too easily. And make general inferences about all hierarchies. Let's try to distinguish ...


Now, of course we can see many interactions between these :

etc.

But sometimes we should think about the differences too.


Isn't it that all the examples here are just partial order? So you could define hierarchy as a POSet.--ZbigniewLukasiak

Excellent point. This just made me realize that I do use the word "hierarchy" both for tree-shaped things like XML docs and OrgCharts, and for posets / semi-lattices, things which just have different levels or orderings. So let's think which are real trees and which posets?

: But trees are isomorphic with posets, aren't they?. --ZbigniewLukasiak

: Erm ... my maths is pretty bad, and my memory of partial orders has just gone out of the window. I'm definitely sure that there's a distinction between trees and semi-lattices, but whether partial-orders / posets are like trees, or semi-lattices I don't remember. -- PhilJones

: Ah so, I can't remember the axioms for semi-lattices and tress, but partial orders are the most basic and all semi-lattices, lattices and trees are for sure posets (that is there is an injection, not surjection). -- ZbigniewLukasiak

|| || Trees || Semi-lattices ||

|| Scale || Artificial political regions and organizations [1] || Module composition (has-a) in complex systems like cities and programs ||

|| Classification || Inheritance in Java / Smalltalk, broader and narrower terms in thesauri, all the book libraries I've ever used || Inheritance in Python / C++, FacetedClassification in thesauri ||

|| Power and control || Traditional org-chart. || CasteSystems, DominanceHierarchy ||

|| Time || || ShearingLayers in EcoSystems ||

|| Information storage || XML, file system || None [2] ||

Notes

[1] Maybe there are cities on borders between two countries? But I think most political regions are parts of larger political regions and may be split into sub-regions. But don't overlap.

[2] Of course there are many alternative ways of organizing information in flat-files, relational databases, hyper-texts, wikis, time-based (weblogs / calendars / RSS) etc. etc. But this table isn't about comparing them. It's meant to distinguish trees from partial orders, so the idea that there is still some ordering is important. Systems that do away with ordering altogether we'll consider elsewhere. (Probably everywhere else on this wiki :-)

-- PhilJones


More thoughts ...


Some tree-like things are also distinguishable by being EdgeLabelledVsNodeLabelled.


Ming wonders why not full lattices : http://ming.tv/flemming2.php?did=10&vid=10&amode=standard&aoffset=0&time=1085505564


Interesting application of thinking about powers in hierarchies : SemanticWeb/SoHeavy


See also :


CategoryTypology