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= Adding membership relationships to ISO 15926-2 in OWL =
Status of this document: Sketch

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Author:

 * [mailto:martin.georg.skjaeveland@dnv.com Martin G. Skjæveland], DNV

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= Table of Contents =
[[PageOutline(2-3,,inline)]]

== Abstract ==
This article suggests a formalization of the membership relationships expressed more or less informally in the text definition of the entity types of ISO 15926-2:2003 and how they may be expressed in OWL.

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== Introduction ==
ISO 15926-2 defines a quite substantial hierarchy of membership relationships. An example of one such sub hierarchy is the following:

  A class_of_class_of_individual is a class_of_class whose members are instances of class_of_individual. (ISO 15926-2:2003, p. 166)

  A class_of_individual is a class whose members are instances of possible_individual. (ISO 15926-2:2003, p. 117)

{{{
#!graphviz.dot
digraph G { overlap=false; ranksep=.6; nodesep=.7; label="Figure 1";
node [fontname=Arial, fontsize=8];
edge  [fontname=Arial, fontsize=6];

class_of_class_of_individual [shape="box", width=2];
class_of_individual [shape="box", width=2];
possible_individual [shape="box", width=2];

"ROTATING MECHANICAL EQUIPMENT CLASS" [shape="none", label="ROTATING MECHANICAL\nEQUIPMENT CLASS"];
PUMP [shape="none"];
"#TheOldPumpInMyGarage" [shape="none"];

class_of_class_of_individual -> "ROTATING MECHANICAL EQUIPMENT CLASS" [label="instance"];
class_of_individual -> PUMP [label="instance"];
possible_individual -> "#TheOldPumpInMyGarage" [label="instance"];

"ROTATING MECHANICAL EQUIPMENT CLASS" -> PUMP [label="member"];
PUMP -> "#TheOldPumpInMyGarage" [label="member"];
}
}}}
''Figure 1: An example of a membership hierarchy. `#TheOldPumpInMyGarage` is a member of `PUMP`, `PUMP` is a member of `ROTATING MECHANICAL EQUIPMENT CLASS`. `ROTATING MECHANICAL EQUIPMENT CLASS` is an instance of class_of_class_of_individual, `PUMP` is an instance of class_of_individual and `#TheOldPumpInMyGarage` is an instance of possible_individual.''

However, this hierarchy is not included in the EXPRESS listing of ISO 15926-2 due to what seems to be lack of expressiveness in the EXPRESS language: "It should be noted that the EXPRESS subtypes of class defined in this part of ISO 15926 are instances of class_of_class, though the EXPRESS language specification does not allow this to be stated" (ISO 15926-2:2003, p. 37). This information is naturally therefore not included in the OWL representation of the EXPRESS file. (Read more: [wiki:ISO15926inOWLtranslateEXPRESStoOWL].) The membership relation/(Classification) is together with the specialization relation the most fundamental way to describe the universe of interest. Capturing this information is thus important to ensure that the ISO 15926-2 data model is used as intended.

== OWL representation ==
The membership relation is represented in ISO 15926-2 using the entity type CLASSIFICATION: classification is a relationship that indicates membership of a class (ISO 15926-2:2003, p. 33). The OWL definition of CLASSIFICATION in the OWL file http://rds.posccaesar.org/2008/02/OWL/ISO-15926-2_2003 is the following

{{{
Class: Classification
    SubClassOf: 
        Relationship,
        hasClassifier exactly 1 Class,
        hasClassified exactly 1 Class
}}}
The EXPRESS definition is found here: [http://www.tc184-sc4.org/wg3ndocs/wg3n1328/lifecycle_integration_schema/lexical/classification.html classification].

[diagram]

The owl:ObjectProperties hasClassified and hasClassifier is defined in ISO 15926-2 OWL as

{{{
ObjectProperty: hasClassifier
  Domain: 
    Classification

ObjectProperty: hasClassified
  Domain: 
    Classification
}}}
We want to put local restrictions on the use of Classification on specific entity types, e.g., such as (informally) "a !ClassOfIndividual may only have !PossibleIndividual-s as members". To be able to do so we need to define the inverse !ObjectProperies of hasClassifier and hasClassified, respectively isClassifierIn and isClassifiedIn:

{{{
ObjectProperty: isClassifierIn
  Inverses: 
    hasClassifier

ObjectProperty: isClassifiedIn
  Inverses: 
    hasClassified
}}}
This allows us to state that "a !ClassOfIndividual may only be a classifier in a Classification which has a !PossibleIndividual as classified" and "a !PossibleIndividual may only be classified in a Classification which has a !ClassOfIndividual as classifier", in OWL:

{{{
Class: part2:ClassOfIndividual
  SubClassOf: 
    isClassifierIn only (part2:hasClassified only part2:PossibleIndividual)
    
Class: part2:PossibleIndividual
  SubClassOf: 
    isClassifiedIn only (part2:hasClassifier only part2:ClassOfIndividual)
}}}

== Identified membership relationships in ISO 15926-2 ==

== Candidate membership relationships in ISO 15926-2 ==
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