Moving towards the SWAN Collections Ontology [2]

The idea of reasoning with sequential structures in OWL-DL is appealing. However, as already mentioned, we cannot use the RDF vocabulary in OWL-DL.

Drummond et al. [1] proposed a way of representing sequential structures in OWL-DL. Analyzing the work of Hirsh & Kudenko [2] Drummond argued that "their representation requires extensive rewriting, the relation of the resulting structures to the original lists is not intuitive and, more importantly, the resulting structures grow as the square of the length of the list". Then, he describes a general list pattern, an intuitive approach related to that suggested by Hayes [3] and incorporated in the Semantic Web Best Practice Working Group’s note on n-ary relations.

The list pattern works as follow:
Each item is held in a “cell” (OWLList); each cell has 2 pointers, one to a head (hasContents - functional) and one to the tail cells (hasNext - functional); the end of the list is indicated by a terminator (EmptyList) which also serves to represent the empty list. A transitive property, isFollowedBy, as a super-property of hasNext as been defined as well. In other words the members of any list are the contents of the first element plus the contents of all of the following elements. A separate OWL vocabulary has been defined as the RDF vocabulary cannot be used in OWL-DL.

Through the transitive property followedBy it is possible to ask things like: give me all the items that are followedBy "AC" for instance and it doesn't matter what is in between the item and the sequence itself.

In Manchester Syntax:


OWLList can express:


For instance for the pattern (A*):

List_only_As --> List AND
hasContents ONLY A AND
isFollowedBy ONLY (List AND hasContents ONLY A)

Still, in OWL-DL there are a bunch of constraints that cannot be defined (and I would suggest to read the paper for the complete list).

The list ontology page.


[1] Nicholas Drummond, Alan Rector, Robert Stevens, Georgina Moulton, Matthew Horridge, Hai Wang and Julian Sedenberg (2006). Putting OWL in Order: Paterns for sequences in OWL. OWL Experiences and Directions (OWLED 2006), Athens, Georgia, USA.
[2] Hirsh, H. and D. Kudenko. Representing Sequences in Description Logics. in Fourteenth National Conference on Artificial Intelligence. 1997.
[3] Noy, N.F. and A. Rector, N-ary relations. 2004, Editors Draft, Semantic Web Best Practices Working Group, W3C.

Moving towards the SWAN Collections Ontology [1]

RDF Containers
RDF allows the usage of three kinds of containers:

• rdf:Bag - A Bag represents a group of resources or literals, possibly including duplicate members, where there is no significance in the order of the members. For example, a Bag might be used to describe a group of part numbers in which the order of entry or processing of the part numbers does not matter.
• rdf:Seq - A Sequence or Seq represents a group of resources or literals, possibly including duplicate members, where the order of the members is significant. For example, a Sequence might be used to describe a group that must be maintained in alphabetical order.
• rdf:Alt - An Alternative or Alt represents a group of resources or literals that are alternatives (typically for a single value of a property). For example, an Alt might be used to describe alternative language translations for the title of a book, or to describe a list of alternative Internet sites at which a resource might be found. An application using a property whose value is an Alt container should be aware that it can choose any one of the members of the group as appropriate.

For example, a statement about "The resolution was approved by the Rules Committee, having members Fred, Wilma, and Dino" will have the form in triples:

ex:resolution exterms:approvedBy ex:rulesCommittee .
ex:rulesCommittee rdf:type rdf:Bag .
ex:rulesCommittee rdf:_1 ex:Fred .
ex:rulesCommittee rdf:_2 ex:Wilma .
ex:rulesCommittee rdf:_3 ex:Dino .

and this is much better than:

ex:resolution exterms:approvedBy ex:Fred .
ex:resolution exterms:approvedBy ex:Wilma .
ex:resolution exterms:approvedBy ex:Dino .

since these statements say that each member individually approved the resolution.

For further examples RDF Primer.

But containers only say that certain identified resources are members; they do not say that other members do not exist. There is no way to exclude that there might be another graph somewhere that describes additional members.

RDF Collections
RDF provides support for describing groups containing only the specified members, in the form of RDF collections. An RDF collection is a group of things represented as a list structure in the RDF graph.

in RDF/XML a collection is something like this:

<rdf:Description rdf:about="http://e.org/family/349">      
<s:familyMembers rdf:parseType="Collection">
<rdf:Description rdf:about="http://e.org/person/Paolo"/>
<rdf:Description rdf:about="http://e.org/person/Emanuele"/>
<rdf:Description rdf:about="http://e.org/person/Maria"/>
<rdf:Description rdf:about="http://e.org/person/Franco"/>
</s:familyMembers>
</rdf:Description>

this can also be written in RDF/XML by writing out the same triples (without using rdf:parseType="Collection") using the collection vocabulary:

<rdf:Description rdf:about="http://e.org/family/349">
   <s:familyMembers rdf:nodeID="sch1"/>
</rdf:Description>

<rdf:Description rdf:nodeID="sch1">
   <rdf:first rdf:resource="http://e.org/person/Paolo"/>
   <rdf:rest rdf:nodeID="sch2"/>
</rdf:Description>

<rdf:Description rdf:nodeID="sch2">
   <rdf:first rdf:resource="http://e.org/person/Emanuele"/>
<rdf:rest rdf:nodeID="sch3"/>
</rdf:Description>

<rdf:Description rdf:nodeID="sch3">
   <rdf:first rdf:resource="http://e.org/person/Maria"/>
   <rdf:rest rdf:nodeID="sch4"/>
</rdf:Description>

<rdf:Description rdf:nodeID="sch4">
   <rdf:first rdf:resource="http://e.org/person/Franco"/>
   <rdf:rest rdf:resource=
"http://www.w3.org/1999/02/22-rdf-syntax-ns#nil"/>
</rdf:Description>

For more examples RDF Primer.

RDF imposes no "well-formedness" conditions on the use of the collection vocabulary (it is possible, for instance, to define multiple rdf:first elements), thus, RDF applications that require collections to be well-formed should be written to check that the collection vocabulary is being used appropriately, in order to be fully robust. Maybe OWL which can define additional constraints on the structure of RDF graphs, can rule out some of these cases?

OWL and Ordering
OWL have no support for ordering, but the natural constructs from the underlying RDF vocabulary (rdf:List and rdf:nil) are unavailable in OWL-DL because they are used in its RDF serialization. In principle, rdf:Seq is not illegal but it depends on lexical ordering and has no logical semantics accessible to a DL classifier. In other terms: (1) The elements in a container are defined using the relations rdf:_1, rdf:_2, and so on that have no formal definition in RDF. Using them for the purpose of reasoning will require us to define and enforce the properties of these relations. (2) It is not possible to define a container that has elements only of a specific type. (3) For updating a specific element in a container in a remote source, one is forced to transmit the whole container. (4) It is not possible to associate provenance information with the elements in a container [1].

But OWL has greater expressivity than RDF (with constructs such as transitive properties) and reasoning capabilities (for checking consistency and inferring subsumption). Thus, the idea of reasoning with sequential structures in OWL-DL looks appealing.

[1] Vinay K. Chaudhri, Bill Jarrold, John Pacheco. Exporting Knowledge Bases into OWL. OWL Experiences and Directions (OWLED 2006), Athens, Georgia, USA.