TransitiveGroups.Ontology

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Transitive Groups Ontology

An informal description of the Ontology of the Transitive Groups Knowledge Base developed so far.

Metadata and Semantics

All Transitive Group instances belong to the owl:Class sd:TransitiveGroup with predicates

The Transformation Process

Naming scheme

  • The names in the tables are in the form of "8T42". We convert this to a name in the form of "Gr8T42" (<http://symbolicdata.org/Data/TransitiveGroups/Gr8T43>), because there are some RDF problems with names starting with numbers.

Products

  • Groups can be represented as different kind of products. We have the following:
    • sd:isDirectProductOf
    • sd:isWreathProductOf
    • sd:isQuotientOfWreathProductOf

Each of them is a wreath product of two groups. We represent that in RDF as, e.g.,

<URI> sd:left sdtg:Gr3T1 ; sd:right sdtg:Gr3T1 .

In a first version we used blank nodes to store that information, but due to scoping issues blank nodes are not well supported by different RDF tools.

  • (2016-02-21) Hans-Gert Gräbe translated the data to a notion with named nodes as, e.g.,
sdtg:Gr3T1_Gr3T1 sd:left sdtg:Gr3T1 ; sd:right sdtg:Gr3T1 .

The Transitive Group Fingerprint

A list of all predicates with number of occurences can be generated with a SPARQL-Query:

PREFIX sd: <http://symbolicdata.org/Data/Model#>
select distinct ?p count(?s)
where { ?s a sd:TransitiveGroup . ?s ?p ?o .}
order by ?p

We list all properties with some comments:

  • sd:hasGenerator String - multiple permutations, e.g., "(1,3,9,7)(2,4,8,6)", "(1,6,9,4)(2,3,8,7)(5,10)", "(2,4,6,8,10)" that generate the group
  • sd:hasName String - e.g., "[52:42]22"
    • What's the rule for such a naming?
  • sd:hasOrder Integer - order of the group
  • sd:hasOrderFactorization String - e.g., "2^3 * 5^2"
  • sd:hasProperty URI - multiple of sd:abelian, sd:cyclic, sd:even, sd:irreducible, sd:nilpotent, sd:notSolvable, sd:primitive, sd:semiabelian, sd:simple, sd:solvable
    • At the moment merely an URI. To be extended to skos:Concept.
  • sd:isDirectProductOf sd:WreathProduct
  • sd:isQuotientOfWreathProductOf sd:WreathProduct
  • sd:isWreathProductOf sd:WreathProduct
  • sd:numberOfFieldsInDatabase Integer
  • sd:OrderOfCenter Integer - order of the center of the group