In the third paragraph of the cited page, it is stated that "MediaWiki's categories have many different interpretations. For example, the category City might comprise all articles about particular cities, i.e. a member of this category is a city. Or it might describe the topic area of articles, such as articles on city squares, urbanism, etc. Or both. MediaWiki encourages this practical usage of categories: a category forms a collection of articles that are considered useful or interesting for users, and categories are organized so users can browse narrower or broader groupings and find related concepts."
It might be useful to be able to assign types to categories, so that one could specify the reason one is putting a given article in a given category. A fairly straightforward way to do this (in terms of syntax) would be to add a "Category" type to Semantic MediaWiki, which tells it to treat the Property as if it were a Category. You could then do things like:
[[Property:Class]] includes '[[has Type:Category]]' [[Property:Topic]] includes '[[has Type:Category]]' [[Los Angeles]] includes '[[Class::City]]' instead of '[[Category:City]]' [[Urbanism]] includes '[[Topic::City]]' instead of '[[Category:City]]'
Both Los Angeles and Urbanism would be listed under Property:City; but a semantic search for cities would be able to exclude Urbanism and the like by focusing on [[Class::City]].
A more elaborate implementation of this would also change the way that Category pages are displayed so that articles are grouped according to type: for example, [[:Category:City]] would list all cities (i.e. [[Class::City]]) first, followed by the city-related articles (i.e. [[Topic::City]]), and finally other articles (i.e. [[Category:City]]).
This is low-priority because you can already achieve most of these results by defining Class and Topic Properties that aren't '[[has Type:Category]]', and then using '[[Class:City]]' or '[[Topic:City]]' on the relevant pages in addition to '[[Category:City]]' rather than instead of it. The only capability that this skips is the grouping of similar pages in the Category index.