Graphing with OWL Reasoning

Another version of OntoGraph (V1.0.2) was released today. The main goal was to add OWL reasoning to determine individuals' types. Why might this be important? Well, an individual might be referenced in an ontology, but not defined with a rdfs:type. Or, the individual might be defined with a type, and then also used as the subject or object in a triple. If the predicate of the triple (the relating property) is defined with domains and/or ranges, then a reasoner can infer the type(s) of the individual. This is also useful to find errors in the ontology, its logic and its semantics (more on that later).

Here is a simple example:

@prefix ninepts: <http://purl.org/ninepts/test#> .
@prefix owl: <http://www.w3.org/2002/07/owl#> .
@prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .

<http://purl.org/ninepts/test> rdf:type owl:Ontology .

<http://purl.org/ninepts/test#class1> rdf:type owl:Class .

<http://purl.org/ninepts/test#class2> rdf:type owl:Class .

<http://purl.org/ninepts/test#class3> rdf:type owl:Class .

<http://purl.org/ninepts/test#class4> rdf:type owl:Class .

<http://purl.org/ninepts/test#objProp1> rdf:type owl:ObjectProperty ;
   rdfs:domain ninepts:class3, ninepts:class4.

<http://purl.org/ninepts/test#objProp2> rdf:type owl:ObjectProperty ;
   rdfs:range ninepts:class1, ninepts:class2 .

<http://purl.org/ninepts/test#individual1> ninepts:objProp1 ninepts:individual2.

<http://purl.org/ninepts/test#individual3> ninepts:objProp2 ninepts:individual4.

This example is written in using the Turtle syntax, and basically defines 4 classes (class1 - class4), 2 properties (objProp1 and objProp2), and 4 individuals (individual1 - individual4). The property, objProp1, is defined with 2 classes as its domain (and no range), while objProp2 is defined with 2 classes as its range (and no domain). (No domain or no range for an object property means that there is no intended semantic - that anything, any "owl:Thing", is the domain or range.) The individuals are defined in 2 triples indicating that individual1 is related to individual2 (via objProp1), and individual3 is related to individual4 (via objProp2).

Without OWL reasoning, the individuals have no types. In fact, OntoGraph does not even find any individuals since it "locates" individuals by querying for any entity that has an explicit type of owl:NamedIndividual, or that has a type that begins with a prefix other than OWL or RDF/RDFS. (The query allows us to avoid returning classes (type owl:Class) and properties (type owl:ObjectProperty or owl:DatatypeProperty) when searching for individuals and their types.)

But, if we run OntoGraph with reasoning turned on, then we find that there are indeed 4 individuals, and that individual1 has the types defined for the domain of objProp1, and individual2 has the types defined for the range of objProp2. This is shown in the figure below, which was generated by OntoGraph.

If this seems odd, think about how the reasoner works ... The ontology defined individual1 as the subject of a triple with the predicate, objProp1. We know that any subject (the domain of the property) of objProp1 is defined to be of types, class3 and class4. So, individual1 is "reasoned" to be of those 2 types. Similarly, individual4 is the object of a triple with the predicate, objProp2. And, we know from the ontology that any object (the range of the property) of objProp2 is defined to be of types, class1 and class2. There you have it ...

The reasoner can't determine anything about individual2 or individual3, except that they are themselves individuals. The reasoner figures this out since they are an object and subject (respectively) in triples whose predicates are object properties. By the way, the reasoner also determined that they are of type, owl:Thing, which doesn't tell you much (everything is of type, owl:Thing, unless there is a logical inconsistency in the ontology). OntoGraph does not bother to show that detail since it adds no information to the graph (but does clutter it up).

Now, why did I talk earlier, about illustrating errors in the ontology? If you look at the ontology definition above, you see that the domain of objProp1 is "ninepts:class3, ninepts:class4". Many people writing ontologies mistakenly think that the definition means that the domain is EITHER class3 OR class4. But, that is incorrect. The definition actually means that the domain is BOTH class3 AND class4. Therefore, an individual must be of BOTH types (multiple inheritance), or stated another way, is defined as the intersection of both types. There are some ways to get around this, as discussed in these two posts from StackOverflow (using one property with multiple domains and how to define multiple domains and ranges). I am not going to repeat the answers (which are both very good), but will talk more about reasoning and errors in my next post.

As always, let me know if you have any questions.

Andrea