1. OWL Lists Nick Drummond Or Making reasoners work hard

2. Overview Use Cases Lists Theory RDF Lists OWL Lists Advantages/Disadvantages

3. Lists: Use Cases Examples include –Time related events (eg Metabolic processes) –Physically linked structures (eg Proteins) –Conceptually linked structures (eg Documents)

4. Lists Theory OWL & RDF Lists use the same idea ABC nil

5. RDF Lists Constructs are: –rdf:first – the top element in the list –rdf:rest – an rdf:list containing the other elements –rdf:nil – an rdf:list containing no other elements (terminator)

6. RDF Lists: Example The closed list ABC: rdf:list (rdf:first A rdf:rest rdf:list (rdf:first B rdf:rest rdf:list (rdf:first C rdf:rest rdf:nil))) Without the nil, this would be an open list ie one that starts with ABC

7. OWL Ordering Support There is no inbuilt ordering in OWL Ordering of statements in an OWL document has no semantics in OWL It is possible to model order at a very low level using RDF statements But, modelling at a lower level than OWL means we cannot reason with the information we have modelled

8. OWL Lists More expressive than rdf:list More constructs Reasonable Classes, not Individuals (at this point) Tool support currently basic

9. OWL Lists: Constructs class List hasNext only List class EmptyList hasContents max 0, hasNext max 0 object property hasContents functional object property hasRest transitive object property hasNext functional

10. OWL Lists: Example The closed list ABC: List and hasContents some A and hasNext some ( List and hasContent some B and hasNext some ( List and hasContents some C and hasNext some EmptyList)) Note that we dont have to specify the hasRest properties, as they can be inferred Eg this list hasRest some (List and hasContents some C)

11. OWL Lists: Advantages Specifying restrictions on the lists allows usage to be checked with the reasoner Tighter definition of constructs eg transitivity of hasRest allows statements to be made about (indirectly) following elements Logical statements can be made to represent many different patterns

12. OWL Lists: Advantages What can we express? –starts with, ends with –contains, does not contain –exactly matches –regular expressions (!) –restrictions/generalisations of the element type –list length (using cardinality)

13. OWL Lists: Disadvantages Computationally expensive Difficult to maintain without specialist tools Memory intensive (expressions are very large)

14. OWL Lists: Example (100 elements) meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:A) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:V) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:F) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:D) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:A) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:T) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:N) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:S) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:T) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:R) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:K) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:R) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:R) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:K) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:Q) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:P) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:M) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:F) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:L) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:E) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:S) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:W) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:S) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:N) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:D) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:H) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:E) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:L) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:I) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:P) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:D) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:Y) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:E) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:N) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:S) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:E) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:P) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:H) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:V) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:A) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:E) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:A) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:D) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:F) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:I) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:R) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:T) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:Y) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:L) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:E) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:S) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:R) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:I) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:V) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:F) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:Y) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:V) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:M) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:N) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:I) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:R) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:P) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:K) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:P) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:K) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:Y) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:I) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:W) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:L) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:S) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:R) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:H) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:G) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:E) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:S) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:I) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:Y) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:N) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:V) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:E) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:K) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:K) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:I) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:G) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:G) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:D) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:S) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:S) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:L) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:A) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:G) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:V) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:C) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:D) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:G) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:M) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:T) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:Y) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:E) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:E) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:I) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:E) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:K) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:E) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:Y) and (meta:hasNext some (SequenceOfAminoAcids and (meta:hasContents some amino:P) and (meta:hasNext some meta:EmptyList))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

15. OWL Structures (!) Possible, in theory, to create other structures by reifying the elements –Trees –Matrices How useful these could be is debatable