DP Collection

Sets, classes, collections and aggregates aim to associate arbitrary entities together with different minimal criteria.

Types

'set'

A set is an arbitrary collection of items (of any type), for which there may be zero members (aka empty set).

'class'

A class is a set that is extensionally defined through one or more properties that all its members share.

'collection'

A collection is a set for which i) there exists at least one member at any given time and ii) each item is of the same type.

'aggregate'

An aggregate is a collection for which there exists at least two members at the same time.

relations 'has member'

items in a set/collection/aggregate are specified with the 'has member' relation.

examples If a collection contains only one kind of member, then we can write a class axiom like 'Collection of x-type valued items' equivalentClass 'collection' and 'has member' some ('x' and 'has value' some Literal) and 'has member' only ('x' and 'has value' only Literal)

If a collection consists of values that must be paired together, we can write:

 'Collection of xy-valued-pairs' 
 equivalentClass 
  'collection' 
  and 'has member' some ('xy-pair' and 'has component part' some ('x' and 'has value' some Literal) 
  and 'has component part' some ('y' and 'has value' some Literal) )

example instantiation (in pretty turtle syntax]:

  :cxy a 'Collection of xy-valued-pairs' ; 
  'has member' [ 
    a 'xy-pair'; 
    'has component part' [ a 'x'; 'has value' 1^^xsd:int] ;
    'has component part' [ a 'y'; 'has value' 2^^xsd:int] ; 
  ] .