This wiki uses Semantic MediaWiki. Semantic MediaWiki is a MediaWiki extension that enables the easy and high-quality storage of semantic relationships within the wiki text. Searching using Semantic MediaWiki is not only extremely effective, it also helps understand and appreciate the different relationships between content.
Basics of semantic search
Properties and values
A given wiki page can have a relation with another page via a property-value combination. For instance, normality is not transitive is a fact about normal subgroup. Thus, the page on normality is not transitive lists it as having the property fact about with value normal subgroup.
Note that the term property is used in the wiki in another sense: as things that collections of objects either satisfy or do not satisfy.
The Special:SearchByProperty page
The Special:SearchByProperty page allows you to enter a property and a value, and lists all pages for which that property takes that value. For instance, if you go to this page, and enter the property as "Fact about" with value "Normal subgroup", you get all the pages that have been marked as facts about normal subgroup.
One drawback of SearchByProperty is that you need to enter the exact name of the page, and pages redirecting to that page are not accepted. The Special:Ask feature, which is more all-encompassing, overcomes this problem.
Here are some important SearchByProperty options:
- Property "defining ingredient" with value any term/definition: This lists all the pages whose definitions build upon the given definition.
- Property "fact about" with value any term/definition: This lists all the facts about or related to that term or definition.
- Property "conjunction involving" with value any property (in the property-theoretic sense): This lists all terms obtained by taking a conjunction of that property with another property.
- Property "uses" with value any fact: This lists all the facts whose proofs use that fact.
- Property "survey article about" with value any term/definition/fact: This lists all survey articles about that term/definition/fact.
- Property "stronger than" with value any term/property/notion: This lists all the notions/properties considered stronger than the given one.
- Property "weaker than" with value any term/property/notion: This lists all the notions/properties considered weaker than the given one.
In addition, there are some others involving searching over journal papers, textbook references and other reference materials.
The Special:Ask page
This is a more versatile page, allowing querying for multiple property-value combinations, as well as membership in categories. The left column, under the heading Query, requires a listing of all the queries. The right column, under the heading Additional Printouts, can be used to obtain additional information on these queries. Sorting conditions can also be added.
For each property-value combination, the syntax is:
For instance, entering the query:
[[Stronger than::Normal subgroup]][[Weaker than::Characteristic subgroup]]
returns all subgroup properties that have been marked as being stronger than normality and weaker than characteristicity.
You can also mix category containments with property-value queries:
[[Category:Transitive subgroup properties]][[Stronger than::Normal subgroup]]
lists all transitive subgroup properties that have been marked as stronger than normality.
For such queries, you can request additional printouts for values of other properties on these pages. For instance, for the above query, if you enter:
under Additional printouts, additional information on where each of these terms is defined is printed.
Semantic search thus also allows for category intersection. However, for more advanced category intersection, including category exclusion, you should use Special:MultiCategorySearch.
Semantic search and browsing from within pages
Most pages have clickable lists to automatically generated semantic lists.
At the top of the page, there is a box describing the type of term or fact (standard, semi-standard, basic, elementary, local to the wiki, non-standard). Within this box, there is a link to basic semantic searches. For definitions, there are links to "defining ingredient" (definitions built on it), "fact about" (facts about it), and "Survey article about" (survey articles about it). Clicking through these lists may give a quick overview.
These lists are intended to complement, rather than substitute, the material present on the page. It is always recommended that you read material within the article rather than simply browsing these lists.
If the article is about a subgroup property or group property, there may be a box to this effect that also links to related property-specific semantic lists, such as property implications and non-implications, property satisfactions and dissatisfactions, and metaproperty satisfactions and dissatisfactions. A link of this kind is displayed only if the number of facts in the corresponding list is positive.
Scroll down to the bottom of the page to see a factbox (a factbox is visible only if there are things to be displayed). The magnofying glass icons automatically list all other pages with the same property-value combination.
There is also a "Browse properties" link in the toolbox (left-hand sidebar) that helps initiate a semantic browsing mode. This link is displayed only for pages that support such a mode.