Submissions:Partition

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{{Logical OP Description Template
{{Logical OP Description Template
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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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{{Logical OP Example Template
{{Logical OP Example Template

Revision as of 10:18, 7 October 2009


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Current revision ID: 5883


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


Pattern reference

Origin
Known use
Reference
Related ODP
Used in combination with
Test


Scenarios

Scenarios about Partition

No scenario is added to this Content OP.

Reviews

Reviews about Partition
Review article Posted on About revision (current is 5883)
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 5883) 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


Submission to event

WOP2009:Main

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