Difference between revisions of "Submissions:Partition"

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|Motivation=This is a logical pattern to define a partition. It is independant of a specific domain. Partitions are a common modeling structure.
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|Motivation=The Partition Pattern is a logical pattern that introduces axioms which model a partition of concepts. A partition is a general structure which is divided into several disjoint parts. With respect to ontologies the structure is a concept which is divided into several pair-wise disjoint concepts. This pattern reflects the simplest case where a named concept is defined as a partition of concepts.
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|Aim=The ontology engineer may say that a class is a partition over other classes (including class expressions). A partition is a structure dividing its content into several parts.
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|Aim=The Partition Pattern describes how to model a partition, i.e., a named concept which is divided into several disjoint concepts. Applying this pattern to an ontology will introduce the necessary axioms.
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|Solution=We introduce two axioms where Partition is the Partition class and B1,...,Bn are arbitrary class expressions (n >= 2) (expressed in OWL 2 Abstract Syntax)
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|Solution=Let ''P'' be a named concept that is the partition which is divided into several concepts ''C_i''. Then the partition is defined by introducing the following axioms (expressed in KRSS [1]):
  
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''EquivalentClasses(Partition, ObjectUnionOf(B1, ..., Bn))''
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''(define-concept P (or C0 C1 ... Cn) )''
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''(disjoint Ci Cj)'' ( 0 ≤ i,j ≤ n, i ≠ j ).
  
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''DisjointClasses(B1, ..., Bn)''
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Here ''(disjoint C_i C_j)''a placeholder for the pair-wise disjointness of all ''C_i''. Note that ''C_i'' can also be arbitrary concept expressions (even if this is not allowed in the original KRSS syntax).
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In OWL 2 [2] the axioms can be expressed as follows (using OWL 2 Abstract Syntax):
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''EquivalentClasses(P, ObjectUnionOf(C1, ..., Cn))''
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''DisjointClasses(C1, ..., Cn)''
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[1] Patel-Schneider, P. F., Swartout, B.: Description-Logic Knowledge Representation System Specification, 1993
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[2] Motik, B., Patel-Schneider, P. F., Parsia, B.: OWL 2 Structural Specification and Functional-Style Syntax. W3C Candidate Recommendation 11 June 2009.
 
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|SolutionExample=http://www.informatik.uni-ulm.de/ki/Noppens/owl/patterns/partition.owl
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|ProblemExample=In an ontology about family relationship we defined concepts such as ''Person'',
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''Aunt'' and ''ParentOfSon'' which are characterized by a relationships such as ''hasChild''(resp. the inverse relationship ''hasParent''), ''hasSibling'', '
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''married-with'' as well as by the gender of people (''Male'' respectively ''Female''). There are a lot of similar ontologies about family relationships.
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''EquivalentClasses(Parent-Of-Son ''ObjectSomeValuesFrom (has-Child Male) )''
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''EquivalentClasses(Parent-Of-Daughter ''ObjectSomeValuesFrom(has-Child Female) )''
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''EquivalentClasses(Aunt ObjectIntersectionOf(Uncle-Or-Aunt Female))''
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''EquivalentClasses(Uncle-Or-Aunt ObjectIntersectionOf(Person ObjectSomeValuesFrom(has-Sibling Parent)))''
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The concept ''Gender'' is partitioned in ''Male'' and ''Female''. Applying this pattern results in the following axioms:
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''EquivalentClasses(Gender, ObjectUnionOf(Male Female)) ''
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''DisjointClasses(Male Female)''
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|SolutionExample=http://www.informatik.uni-ulm.de/ki/Noppens/generation.owl
 
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|TakesInAccountReview=http://ontologydesignpatterns.org/wiki/Reviews:HenrikEriksson_about_Partition
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|TakesInAccountReview=http://ontologydesignpatterns.org/wiki/Reviews:LuigiIannone_about_Partition_2
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Latest revision as of 08:29, 31 May 2010

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Graphical representation

Diagram

Partition-diagram.png

General information

Name Partition
Also known as
Author(s)
SubmittedBy OlafNoppens



Description

Motivation The Partition Pattern is a logical pattern that introduces axioms which model a partition of concepts. A partition is a general structure which is divided into several disjoint parts. With respect to ontologies the structure is a concept which is divided into several pair-wise disjoint concepts. This pattern reflects the simplest case where a named concept is defined as a partition of concepts.
Aim The Partition Pattern describes how to model a partition, i.e., a named concept which is divided into several disjoint concepts. Applying this pattern to an ontology will introduce the necessary axioms.
Solution description Let P be a named concept that is the partition which is divided into several concepts C_i. Then the partition is defined by introducing the following axioms (expressed in KRSS [1]):

(define-concept P (or C0 C1 ... Cn) ) (disjoint Ci Cj) ( 0 ≤ i,j ≤ n, i ≠ j ).

Here (disjoint C_i C_j)a placeholder for the pair-wise disjointness of all C_i. Note that C_i can also be arbitrary concept expressions (even if this is not allowed in the original KRSS syntax).

In OWL 2 [2] the axioms can be expressed as follows (using OWL 2 Abstract Syntax):

EquivalentClasses(P, ObjectUnionOf(C1, ..., Cn))

DisjointClasses(C1, ..., Cn)

[1] Patel-Schneider, P. F., Swartout, B.: Description-Logic Knowledge Representation System Specification, 1993

[2] Motik, B., Patel-Schneider, P. F., Parsia, B.: OWL 2 Structural Specification and Functional-Style Syntax. W3C Candidate Recommendation 11 June 2009.

Elements
Implementation
Reusable component
Component type


Example

Problem example In an ontology about family relationship we defined concepts such as Person,

Aunt and ParentOfSon which are characterized by a relationships such as hasChild(resp. the inverse relationship hasParent), hasSibling, ' married-with as well as by the gender of people (Male respectively Female). There are a lot of similar ontologies about family relationships.

EquivalentClasses(Parent-Of-Son ObjectSomeValuesFrom (has-Child Male) ) EquivalentClasses(Parent-Of-Daughter ObjectSomeValuesFrom(has-Child Female) ) EquivalentClasses(Aunt ObjectIntersectionOf(Uncle-Or-Aunt Female)) EquivalentClasses(Uncle-Or-Aunt ObjectIntersectionOf(Person ObjectSomeValuesFrom(has-Sibling Parent)))

The concept Gender is partitioned in Male and Female. Applying this pattern results in the following axioms:

EquivalentClasses(Gender, ObjectUnionOf(Male Female)) DisjointClasses(Male Female)

Pattern solution example http://www.informatik.uni-ulm.de/ki/Noppens/generation.owl
Consequences


Pattern reference

Origin
Known use
Reference
Related ODP
Used in combination with
Test



Additional information

Scenarios

Scenarios about Partition

No scenario is added to this Content OP.

Reviews

Reviews about Partition
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This revision (revision ID 9707) takes in account the reviews: Partition (Http://ontologydesignpatterns.org/wiki/Reviews:MartaSabou about Partition, Http://ontologydesignpatterns.org/wiki/Reviews:HenrikEriksson about Partition, Http://ontologydesignpatterns.org/wiki/Reviews:LuigiIannone about Partition 2)

Other info at evaluation tab


Modeling issues

Modeling issues about Partition
There is no Modeling issue related to this proposal.
Some subquery has no valid condition.


References

Add a reference


Timer.png Submission to event

WOP:2009

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