Table 4: Ontology intersection of Confious.owl &
Confof.owl.
Paper ⊏ Article; Paper ⊏ Contribution; Accepted_Paper
⊏ Paper; abstract_of_paper ⊏ Article; Rejected_Paper ⊏
Paper; Undecided_Paper ⊏ Paper; Paper⊓Poster∅;
Paper⊓short_
paper
∅; Author ⊏ Person ;
Contact_Person ⊏Human;
∀x,y: (x,y) (writes)
op
implies x Author and y
Contribution;
∀x,y: (x,y) (writenby)
op
implies x Contribution
and y Author;
writes≡writtenby
━
;
∀x,y: (x,y) (has_author)
op
implies x Article and y
Human;
∀x,y: (x,y) (is_author_of)
op
implies x Human and
y Article;
has_author
≡
is_author_of
━
;
∀x,y: (x,y) (is_concerned)
op
implies y Paper;
When context condition data, i.e., domain is
"conference" and entities are "paper" and "author",
are entered into the rule engine, the context rule in
Table 2 fires. The contextual information in the rule
is then inserted into the OWL reasoner to help
further integrating the ontology intersection. This
process is actually an integration of the ontology
intersection with the contextual information. The
process of non-contradiction is applied also for this
integration.
With OWL 2, inverse object properties can be
defined, such as “has_author” and “is_author_of”
are inverse properties. That is to say, if two
individuals x and y are related by “has_author”, then
y and x are related by “is_author_of”. One
integration rule about the inverse relation is:
ObjectProperty-Inverse-rule:
If O: r1 (A, B) and O: r2 (B, A) and
inverseProperties (O: r1, O: r2) and O: r3 (B, A)
and O: r4 (A, B) and inverseProperties (O: r3, r4)
AND
Q: r1 (A, B) and Q: r3 (B, A) and
inverseProperties (Q:r1, Q: r3)
Then r2(B, A) and r4 (A, B) and
inverseProperties (r2, r4)
The rule is shown in functional-style syntax, rather
than using DL syntax as in the tables. O and Q
symbolize two general ontologies. For example, O:
r1 (A, B) states that the class A is the domain of the
property r1 in ontology O, and the class B is the
range of the property r1 in O. InverseProperties (O:
r1, O: r2) means that r1 and r2 are inverse
properties. This integration rule shows the transfer
of inverse role relations in two ontologies. A and B
are two string identical classes in ontology O.
Properties r1, r2, r3 and r4 are four object properties.
If there are two definitions of inverse properties in
one ontology as inverseProperties(O:r1. O:r2) and
inserseProperties(O:r3, O:r4); and if in the other
ontology, the inverse property is between the inverse
properties from the previous ontology, i.e.,
inversProperties(Q:r1, Q:r3); and all definitions are
about the string-identical two classes A and B. The
inverse property will transfer to the other unrelated
properties, i.e., invserProperties(r2, r4). In the rule
condition, namespaces O and Q are used. In the
result part, the namespace is escaped since the result
is the new independent ontology, the ontology
intersection.
Back to the example, there two pairs of inverse
properties are identified in Table 4:
InverseProperties (writes, writtenby) and
InverseProperties (is_author_of, has_author). From
the contextual information in Table 2,
InverseProperties (writePaper, hasAuthor) is
identified. "hasAuthor" is string-identical to
"has_author". However, the rule conditions are not
completely fulfilled. The property "writes" and
"writePaper" are not equivalent. The integration
module asks the knowledge expert in such a
situation:
EquivalentProperties(writes,writePaper)?.
When the knowledge expert confirms the axiom, it is
added into the ontology intersection.
Another axiom, which needs to be confirmed, is
EquivalentClasses(Contact_Person, Author)?. The class
"Contact_Person" is defined in confious.owl, where
a contact_person is a human and is_author of an
article. And it is not defined in other ontologies;
therefore, it is not a problem to add this axiom.
When this axiom is confirmed, the integration rule is
fired.
Accordingly, the new knowledge in the result is:
"is_author_of" is the inverse property "writtenby",
shown below:
∀
x,y: (x,y)
(writterBy)
op
implies x
Paper and y
Author;
∀
x,y: (x,y)
(is_author_of)
op
implies x
Contact_Person and y
Paper;
is_author_of
≡
writtenBy
━
;
Author
⊏
Human; writes
≡
writePaper;
Contact_Person
≡
Author
The final result is a non-contradictory ontology
intersection under the open world assumption,
shown below:
Article≡Contribution; abstract_of_paper
⊏
Article; Rejected_Paper
⊏
Paper;
OntologyIntegrationwithContextualInformation
489