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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.
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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

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Additional information

Scenarios

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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)

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Modeling issues

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