UMBEL - Annex D 20120521

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UMBEL Annex D: Inferencing with UMBEL

UMBEL Annex Document - 21 May 2012

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http://techwiki.umbel.org/index.php/UMBEL_-_Annex_D
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Last update
$Date: 2012/5/21 16:28:36 $
Version
Version No.: 1.05
Volume
TR 12-5-21-D
Authors
Michael Bergman - Structured Dynamics
Frédérick Giasson - Structured Dynamics

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UMBEL: Upper Mapping and Binding Exchange Layer by Structured Dynamics LLC and Ontotext AD is provided under the Creative Commons Attribution 3.0 license. See the attribution section for how to cite the effort.

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Copyright © 2009-2012 by Structured Dynamics LLC and Ontotext AD.

Terminology Note

As of version 0.80, 'Reference Concept' (RefConcept) has replaced the notion of 'Subject Concept' (SubjectConcept). Historical documentation may still use the older term and some use is kept in current documentation for continuity reasons. Please treat the two terms as synonomous.

INFERENCING: 'Exploding the Domain'

The goal of the UMBEL reference concept structure is to define a structure of upper concepts for a myriad of domains, and to link them to external ontologies (external conceptual structures). This creates contexts for things and kinds of things. The inferencing capabilities of this UMBEL reference concept structure extends the context of each referenced concept.

By inferring facts and creating a context for any given reference concept, we explode their domain. This explosion of facts gives us a much richer understanding of these reference concept classes and individuals belonging to these classes. It is how and why UMBEL creates value.

Important: Exploding the Domain can only occur where linkages are drawn between classes in the reference and external ontologies. See further quadrants A and C in the Figure 1 of the UMBEL Specifications.

Reference Concepts Relations can be Inferred

UMBEL is a reference concepts structure. As described in the UMBEL specification document, the UMBEL References Structure has two views: a class view and an individual view. Hierarchical relations between concepts classes of this structure are described using the OWL ontology. The OWL ontology enables us to infer facts between different reference concept classes. We are using two different properties defined in the OWL ontology to describe two different hierarchical relationships between the UMBEL reference concepts:

  1. rdfs:subClassOf - used to say that a reference concept A is a more specific concept than reference concept B.
  2. owl:equivalentClass - used to say that a reference concept C is equivalent to a reference D.

By taking a look at the Figure 1 below, we can infer that the reference concept rc:Business is a more specific concept than the reference concept rc:CommercialOrganization and the reference concept rc:Organization.

Umbel techdoc fig4.png
Figure 1. Basic Inference Example

External Class Relationships Can be Inferred

One of the characteristics of the UMBEL reference concept structure is to be able to link external ontology classes to UMBEL reference concept classes. This characteristic enables us to perform inferencing between external ontology classes using the UMBEL reference concept structure. This inferencing is possible according to the consistency/inconsistency principles introduced by the OWL 2 schema language.

Just like when UMBEL reference concepts are hierarchically related, the hierarchical relationship between UMBEL reference concepts and external ontology classes is also done using the rdfs:subClassOf property. This property is used to assert that an external ontology class is a sub-class of, or a super-class of, a UMBEL reference concept.

Additionally we can define an equivalency relationship between an external ontology class with an UMBEL reference concept class by using the owl:equivalentClass property. This lets us assert that a class A, defined in an external ontology, is an equivalent class to an UMBEL reference concept class B.

In OWL, the owl:equivalentClass property is defined as:

"[...] owl:equivalentClass is a built-in property that links a class description to another class description. The meaning of such a class axiom is that the two class descriptions involved have the same class extension (i.e., both class extensions contain exactly the same set of individuals). [...] NOTE: The use of owl:equivalentClass does not imply class equality. Class equality means that the classes have the same intensional meaning (denote the same concept). [...] ."

As applied to UMBEL this means that if an external ontology class foo:Bar is owl:equivalentClass with the UMBEL reference concept class rc:Person, then all individuals belonging to the class foo:Bar also belong to the class rc:Person.

These three properties are used below to prove the consistency of the inference of two external ontology classes using the UMBEL reference concept structure.

Finally we introduce a link relationship property between an external ontology class and an UMBEL reference concept class: the umbel:isAbout and its inverse property umbel:isRelatedTo properties.

These properties are used to assert an associative link between a reference concept and a RDFS Class. This relationship can be described as a subset of individuals of the class A is equivalent to a subset of individuals of the class B. This asserts that there is a relation between an external ontology class and an UMBEL reference concept; but it doesn't say anything about the semantic nature of the relationship.

Re-use of External Ontology Properties

Once we are able to infer relationships between UMBEL reference concept classes and external ontology classes, we are then able to re-use, in a coherent way, the defined properties from these external ontologies to describe other instances of UMBEL reference concept classes. This inheritance of linked properties, so to speak, is where one of the main powers of the UMBEL reference concept structure resides.

By linking external ontologies classes to the UMBEL reference concepts structure, we make sure that we can coherently re-use properties defined in these ontologies to describe instance records of types that were not previously available to these ontologies.

Re-using Properties

One of the utilities of the UMBEL reference concept structure is that it defines the main concepts applicable to a myriad of domains. Since the current ontological space is weak, UMBEL can be used to describe things by using defined reference concepts when no specific ontologies exist for describing these things. The real power behind the inference capabilities of UMBEL between reference concept classes and external ontology classes is that it enables us to re-use external ontology properties to describe any instances of an applicable reference concept class, in a coherent way.

Figure 1 above shows how an instance of the class rc:Business can coherently re-use external properties defined in the FOAF Ontology to describe this instance.

However, this approach begs the question: why do we use the foaf:made property to describe an individual belonging to the rc:Business class?

The clue resides in the domains and ranges of properties.

The domain of this property is a foaf:Agent and there are no apparent relationships between a rc:Business and a foaf:Agent. First we have to know that the class foaf:Organization is a sub-class of the class foaf:Agent. This means that individuals belonging to the class foaf:Organization are all included in the class extension of the indicated class description by the domain of the property foaf:made. This means that we can use foaf:Organization in the domain of the property foaf:made.

From there, we have to check the UMBEL reference concept structure to understand what is happening. The foaf:Organization class is equivalent to the rc:Organization class. By definition, this means all individuals belonging to both classes are the same. This therefore means that we can use the rc:Organization class in the domain of the foaf:made property too since it is the same class extension.

By following the path in Figure 1 above, we notice that rc:Business is a sub-class of rc:Organization. Since we know that rc:Organization is an equivalent class with foaf:Organization, this means that rc:Business is a sub-class of foaf:Organization. This means that we can define an instance of the class rc:Business using properties where the foaf:Organization belongs to the class extension of the indicated class description of the domain, or range, of certain properties.

Formally, we can demonstrate that fact this way:

  1. rc:Organization = foaf:Organization
  2. rc:CommercialOrganizationrc:Organization
  3. rc:Businessrc:CommercialOrganization

So we can infer that:

  1. sc:Businessrc:CommercialOrganization
  2. sc:Businessrc:Organization
  3. sc:Businessfoaf:Organization

Given the inference step 3, we know that rc:Business is a subset of foaf:Organization. This means that all individuals belonging to rc:Business also belong to foaf:Organization.

The definition of rdfs:domain says:

An rdfs:domain axiom asserts that the subjects of such property statements must belong to the class extension of the indicated class description.

This means:

  1. foaf:OrganizationClass extension of Properties X
    1. Note: Properties X are properties such as foaf:made, foaf:name, etc.
  2. rc:BusinessClass extension of Properties X

In conclusion, we can use Properties X to describe instances of the class rc:Business.

These inference steps are consistent given the UMBEL reference concept structure and its defined linkage to external ontology classes.

Re-using Properties to Describe an Individual of a External Ontology Class

In the example above, we showed how we can use the inference capabilities of UMBEL to know which properties, defined in external ontologies, can coherently be used to describe instances of reference concept classes.

Now we will see how we can use the same inferencing power to relate two a priori unrelated external classes to re-use properties defined in one ontology to describe the other.

Figure 2 below shows that, according to the UMBEL reference concept structure, the class foaf:Project is a sub-class of the class event:Event. This means that we can re-use the properties event:product, event:factor and event:time to describe instances of the class foaf:Project. How is this possible?

Umbel techdoc fig5.png
Figure 2. Re-use of Properties on External Ontology Classes

Formally, we can demonstrate that fact this way:

  1. rc:Event = event:Event
  2. rc:Project = foaf:Project
  3. rc:Projectrc:Event

So we can infer that:

  1. foaf:Projectrc:Event (3, 6)
  2. foaf:Projectevent:Event (1, 8)

Given the step #2, we know that foaf:Project is a subset of event:Event.1 This means that all individuals belonging to foaf:Project also belong to event:Event.

Given the definition of the rdfs:domain property, we then have:

  1. event:EventClass extension of Properties X
  • Note: Properties X are properties such as event:product, event:factor, event:time, etc.
  1. foaf:ProjectClass extension of Properties X

In conclusion, we can use Properties X to describe instances of the class foaf:Project.

Again, these inference steps are consistent given the UMBEL reference concept structure and its defined linkage to external ontology classes.

Caveats for Class Relationship Assignments

Clearly, these powers may be easily misused and mis-applied if the actual class relationships do not meet the required instance membership requirements. Great care must be made in analyzing carefully these three types of class relationships.

Fortunately, once made, these relations occur between UMBEL and external ontologies and will pertain to all uses of those external ontologies. Also, only a very few assignments need to emerge in order to see the exploding the domain phenomenon.

For the dozen or so external ontologies related to UMBEL to date, there have been on average roughly two equivalentClass and two subClassOf assignments per ontology. This relatively small degree of linkage has a multiplier effect, however, that also increases as a function of the number of linked external ontologies.

ENDNOTES

Copyright © 2009-2012 by Structured Dynamics LLC and Ontotext AD.