OlafNoppens (Talk | contribs) |
OlafNoppens (Talk | contribs) (The Partition Pattern describes how to model a partition. The pattern reflects the simplest case where a named concept is the partition of (arbitrary) concepts. Future work will be concerned with a m) |
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{{Logical OP Example Template | {{Logical OP Example Template | ||
| − | |SolutionExample=http://www.informatik.uni-ulm.de/ki/Noppens/ | + | |ProblemExample=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)'' | ||
| + | |||
| + | |SolutionExample=http://www.informatik.uni-ulm.de/ki/Noppens/generation.owl | ||
}} | }} | ||
{{Logical OP Reference Template}} | {{Logical OP Reference Template}} | ||
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Last modified date is: 2009-10-07 |
| Name | Partition |
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| SubmittedBy | OlafNoppens |
| 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 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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| 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) |
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| Pattern solution example | http://www.informatik.uni-ulm.de/ki/Noppens/generation.owl |
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This revision (revision ID 5884) 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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'Ontology Design Patterns'
