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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{{Takes in account review
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|TakesInAccountReview=http://ontologydesignpatterns.org/wiki/Reviews:MartaSabou_about_Partition
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{{Takes in account review
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|TakesInAccountReview=http://ontologydesignpatterns.org/wiki/Reviews:HenrikEriksson_about_Partition
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{{Takes in account review
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|TakesInAccountReview=http://ontologydesignpatterns.org/wiki/Reviews:LuigiIannone_about_Partition_2
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|Event=WOP2009:Main
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|Event=WOP:2009
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Current revision


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Current revision ID: 9707

Graphical representation

Diagram

Image: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
Review article Posted on About revision (current is 9707)
LuigiIannone about Partition 24550827 September 2009 56165,616
MartaSabou about Partition 24550838 September 2009 56795,679
HenrikEriksson about Partition 24550849 September 2009 57485,748
LuigiIannone about Partition 2 245508510 September 2009 57505,750
RinkeHoekstra about Partition 245513025 October 2009 59015,901

This revision (revision ID 9707) takes in account the reviews: 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
Modeling issue Competency question Domains
Multiple Alternative Classification Criteria Allow me to retrieve all "elements" (classes/individuals) of a "domain concept" viewed by a combination of "values" (or "terms") from various "classification criteria" (or "facets").
View Inheritance For example
in the case of the representation of the "wine" domain concept:
  • Allow me to select a bottle of wine by color
    region
    flavour and(or) ocassion.

In the case of the representation of the "pizza" domain concept:

  • Allow me to select a pizza based on the type of base
    the toppings and(or) the name.


References

Add a reference


Submission to event

WOP:2009

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