ISO 15926 inheritance rules (draft)
This is the first incomplete analysis. Feel free to comment and suggest ideas for 3. OWL Inheritance part)
Transfer between formal languages requires careful consideration of semantics in each particular language. It seems there is some disagreement concerning inheritance rules for different language representations of ISO 15926.
1. Part 2 representation
In Part 2 semantic meanings of the standard are expressed in EXPRESS language and in plain English (two languages are used, contrary to the appearance). Analysis of inheritance is required for two kinds of data: EXPRESS attributes and relationships.
1.1. For EXPRESS attributes the answer is rather straightforward - attribute names are defined for types and inherited from supertype for subtype, attribute values are “attached” to particular things and are never inherited.
1.2. Relationships require more careful consideration. Any relationship is defined as an ordered pair. If one place in this pair is taken by the class A, then it is just a single pair. It doesn’t follow from the existence of this pair that any member of this class A is paired in relationship with the same thing paired with A.
Class_of_relationship is a set of the relationship pairs united according to some principle. Class_of_relationship A is defined together with two classes_of_class B and C, members of which may play roles in pairs constituting A. As Part 2 explicitly states, class_of_relationship is “defining constraints in terms of the types of things that can participate in the member relationships”. Again, there is nothing to suggest that individual members of B and C inherit something other then possibility to be united in a relationship from A.
1.3. Special attention must be paid to identification relationships, as Part 2 provides only one unique identifier as id attribute and further requires that “other identifiers, external to the system, used for a particular thing are recorded using the class_of_identification entity data type.”
According to the Part 2 definitions:
“A class_of_identification is a class_of_representation_of_thing that indicates that the pattern is used to refer to the represented thing.”
“A class_of_representation_of_thing is a class_of_relationship that indicates that all members of the pattern class_of_information_representation represent the thing.”
Notice that both definitions above suggest that pairs in the class_of_identification are presumed to have one member in common - identified thing. Therefore, if the class B is identified by the pattern “xxxx”, we have class_of_identification as a set of pairs {(B, x) | xϵ “xxxx”}, not {(b, x) | bϵ B, xϵ “xxxx”}
In this sense the class_of_identification is similar to the class_of_relationship_with_related_end_1.
The same idea can be represented by an axiom (candidate for Part 7 Annex B):
ClassOfRepresentationOfThing(x) ^ RepresentationOfThing(y) ^ RepresentationOfThing(z) ^
Classification(w) ^ hasClassified(w,y) ^ hasClassifier(w,x) ^
Classification(v) ^ hasClassified(v,z) ^ hasClassifier(v,x) ^
hasRepresented(y,m) ^ hasRepresented(z,n) → m=n
2. Part 7 representation - FOL
Analysis for the first order logic predicates used to represent ISO 15926 in Part 7 is even simpler.
If we have class A, some logic formula L(A) and classification relationship
Classification(x) ^ hasClassified(x,b) ^ hasClassifier(x,A),
it is impossible to deduce L(b) from these data.
Whatever aspect is modelled as L(A), it is not in any way inherited by members of A. In the semantics induced by FOL no metadata attribute or relationship is inherited from the class by members of that class.
3. Part 8 representation - OWL
(to be continued)
Transfer between formal languages requires careful consideration of semantics in each particular language. It seems there is some disagreement concerning inheritance rules for different language representations of ISO 15926.
1. Part 2 representation
In Part 2 semantic meanings of the standard are expressed in EXPRESS language and in plain English (two languages are used, contrary to the appearance). Analysis of inheritance is required for two kinds of data: EXPRESS attributes and relationships.
1.1. For EXPRESS attributes the answer is rather straightforward - attribute names are defined for types and inherited from supertype for subtype, attribute values are “attached” to particular things and are never inherited.
1.2. Relationships require more careful consideration. Any relationship is defined as an ordered pair. If one place in this pair is taken by the class A, then it is just a single pair. It doesn’t follow from the existence of this pair that any member of this class A is paired in relationship with the same thing paired with A.
Class_of_relationship is a set of the relationship pairs united according to some principle. Class_of_relationship A is defined together with two classes_of_class B and C, members of which may play roles in pairs constituting A. As Part 2 explicitly states, class_of_relationship is “defining constraints in terms of the types of things that can participate in the member relationships”. Again, there is nothing to suggest that individual members of B and C inherit something other then possibility to be united in a relationship from A.
1.3. Special attention must be paid to identification relationships, as Part 2 provides only one unique identifier as id attribute and further requires that “other identifiers, external to the system, used for a particular thing are recorded using the class_of_identification entity data type.”
According to the Part 2 definitions:
“A class_of_identification is a class_of_representation_of_thing that indicates that the pattern is used to refer to the represented thing.”
“A class_of_representation_of_thing is a class_of_relationship that indicates that all members of the pattern class_of_information_representation represent the thing.”
Notice that both definitions above suggest that pairs in the class_of_identification are presumed to have one member in common - identified thing. Therefore, if the class B is identified by the pattern “xxxx”, we have class_of_identification as a set of pairs {(B, x) | xϵ “xxxx”}, not {(b, x) | bϵ B, xϵ “xxxx”}
In this sense the class_of_identification is similar to the class_of_relationship_with_related_end_1.
The same idea can be represented by an axiom (candidate for Part 7 Annex B):
ClassOfRepresentationOfThing(x) ^ RepresentationOfThing(y) ^ RepresentationOfThing(z) ^
Classification(w) ^ hasClassified(w,y) ^ hasClassifier(w,x) ^
Classification(v) ^ hasClassified(v,z) ^ hasClassifier(v,x) ^
hasRepresented(y,m) ^ hasRepresented(z,n) → m=n
2. Part 7 representation - FOL
Analysis for the first order logic predicates used to represent ISO 15926 in Part 7 is even simpler.
If we have class A, some logic formula L(A) and classification relationship
Classification(x) ^ hasClassified(x,b) ^ hasClassifier(x,A),
it is impossible to deduce L(b) from these data.
Whatever aspect is modelled as L(A), it is not in any way inherited by members of A. In the semantics induced by FOL no metadata attribute or relationship is inherited from the class by members of that class.
3. Part 8 representation - OWL
(to be continued)