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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

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Reviews

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This revision (revision ID 5883) 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

	Submission to event WOP2009:Main

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 }}
 {{Logical OP Description Template
-|Motivation=This is a logical pattern to define a partition. It is independant of a specific domain. Partitions are a common modeling structure.
+|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 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.
+|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=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)
+|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]):
-''EquivalentClasses(Partition, ObjectUnionOf(B1, ..., Bn))''
+''(define-concept P (or C0 C1 ... Cn) )''
+''(disjoint Ci Cj)'' ( 0 ≤ i,j ≤ n, i ≠ j ).
-''DisjointClasses(B1, ..., Bn)''
+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.
 }}
 {{Logical OP Example Template