Questions about domain and range (chapter 13)

[LaraAcuna]

Hello Xiaoqi, thank you so much for your work in writing about ontology engineering! I am learning this subject and your content has been very valuable to me. I am looking for some guidance regarding domain and range.

In chapter 13.5.2 you talk about multi-domain and multi-range with the example of the property realizedBy and the multi-range classes Business_Process and Application. I get that saying this will cause an intersection between both classes. You also say that ontology engineers may reuse a single semantic relationship rather than, for example, creating two separate properties realizedByBusinessProcess and realizedByApplication. Now here are my questions.

Since a multi-range property will infer an instance having all those classes, but in this case won't make sense an individual of both Business_Process class and Application class, is it acceptable to create both properties realizedByBusinessProcess and realizedByApplication? or is there another, preferred, way?

Following this idea, I don't know if you can use "OR" while adding the Range axiom. Something like "Range: Business_Process or Application". Will that work? is it advisable?

I know that you can add SubClass Of axioms too.
Suppose I add these axioms in the Business_Capability class:
"SubClass Of realizedBy some BusinessProcess" and "SubClass Of realizedBy some Application".
And I leave no range axiom in realizedBy property.
Is that any useful?

I am a bit lost on how to deal with these kinds of properties, I hope you can give me some advice.
Thanks in advance for your time! Sorry if this is not the right place, I'll kindly email you if that's preferred.

[yasenstar]

Hello Lara,
Thanks for your question, it touches the point that really easily confuse when making conceptual modeling.
Let me examine that and back to you soon.
Xiaoqi

[yasenstar]

Hi Lara,

Thanks again for your thoughtful question and kind words. This is exactly the right place to ask -- and your questions touch on a subtle but important point that many ontology engineers encounter.

As I've completed recently the first 4 volumes ebook structure packaging, and now in the half way of writing SKDL, let me try to address your questions here in order and in different comment so that it would be easier to exchange ideas:

1. Are multiple ranges interpreted as AND or OR?

In OWL, when you define multiple ranges for a property (e.g. rdfs:rang Business_Process and rdfs:range Application), they are interprested as AND (intersection), not OR.

You asked: "Can yo use OR while adding the Range axiom? Something like Range: Business_Process or Application?"

The answer is Yes.

In Protégé, the Class Expression Eidtor support the syntax with entering Business_Process or Application, this will be treated as a class expression and then set it as the range.

In RDF source, you may see them in sequence as below:

    <owl:ObjectProperty rdf:about="http://www.semanticweb.org/v0cn037/ontologies/2026/7/untitled-ontology-25#realized_By">
        <rdfs:domain rdf:resource="http://www.semanticweb.org/v0cn037/ontologies/2026/7/untitled-ontology-25#Business_Capability"/>
        <rdfs:range rdf:resource="http://www.semanticweb.org/v0cn037/ontologies/2026/7/untitled-ontology-25#Application"/>
        <rdfs:range rdf:resource="http://www.semanticweb.org/v0cn037/ontologies/2026/7/untitled-ontology-25#Business_Process"/>
    </owl:ObjectProperty>

This means an individual in the range of that property would be inferred to be both a Business_Process AND an Application simultaneously -- which, as you correctly noted, it usually not what you want.

The same applices to multiple domains as well: they are also interpreted as conjunction (intersection).

[yasenstar]

2. The owl:unionOf Approach (Recommended)

If you want a property whose range can be either Business_Process or Application (but not necessarily both), you can define a union class as the range:

:RealizableByClass a owl:Class ;
    owl:unionOf ( :Business_Process :Application ) .
:realized_By_Union rdfs:range :RealizableByClass .

This is the most semantically correct approach in OWL. It tells the reasoners: the target of realized_By_Union must belong to a class that is either Business_Process or Application.

Important note:
If you use owl:unionOf without ensuring the classes are disjount, an individual could still be inferred to be both (if it is asserted as both).
If you want exclusive OR (either but not both), you would need to declare the classes disjoint.

In Protégé, your rdf model - after creating the domain/range - should ahve following source:

    <owl:ObjectProperty rdf:about="http://www.semanticweb.org/v0cn037/ontologies/2026/7/untitled-ontology-25#realized_By_Union">
        <rdfs:domain rdf:resource="http://www.semanticweb.org/v0cn037/ontologies/2026/7/untitled-ontology-25#Business_Capability"/>
        <rdfs:range>
            <owl:Class>
                <owl:unionOf rdf:parseType="Collection">
                    <rdf:Description rdf:about="http://www.semanticweb.org/v0cn037/ontologies/2026/7/untitled-ontology-25#Application"/>
                    <rdf:Description rdf:about="http://www.semanticweb.org/v0cn037/ontologies/2026/7/untitled-ontology-25#Business_Process"/>
                </owl:unionOf>
            </owl:Class>
        </rdfs:range>
    </owl:ObjectProperty>

The rdf specially for this question is here: https://github.com/yasenstar/protege_pizza/blob/main/ebook/rdf/pizza-ebook_13.5.2.rdf, including two properties for this and previous point 1, for reference.

[yasenstar]

3. Creating Separate Properties (Your First Suggestion)

You asked: "Is it acceptable to create both properties realizedByBusinessProcess and realizedByApplication?"

In my view, Yes, this is acceptable and is a common modeling pattern in practice, however, keep in mind the pros and cons:

Advantages:

• Clearer semantics -- each property expresses exactly one type of relationship
• Easier for humans to understand and maintain
• No risk of unintended inference

Disadvantages:

• More properties to maintain
• Duplicates the core semantic pattern

This is the trade-off!

In many real-world ontologies, separate properties are preferred for clarity and governance, especially when the relationship has different characteristics depending on the target type.

After creating these two properties separately, below you can see the source in RDF model:

    <!-- http://www.semanticweb.org/v0cn037/ontologies/2026/7/untitled-ontology-25#realizedByApplication -->

    <owl:ObjectProperty rdf:about="http://www.semanticweb.org/v0cn037/ontologies/2026/7/untitled-ontology-25#realizedByApplication">
        <rdfs:domain rdf:resource="http://www.semanticweb.org/v0cn037/ontologies/2026/7/untitled-ontology-25#Business_Capability"/>
        <rdfs:range rdf:resource="http://www.semanticweb.org/v0cn037/ontologies/2026/7/untitled-ontology-25#Application"/>
    </owl:ObjectProperty>

    <!-- http://www.semanticweb.org/v0cn037/ontologies/2026/7/untitled-ontology-25#realizedByBusinessProcess -->

    <owl:ObjectProperty rdf:about="http://www.semanticweb.org/v0cn037/ontologies/2026/7/untitled-ontology-25#realizedByBusinessProcess">
        <rdfs:domain rdf:resource="http://www.semanticweb.org/v0cn037/ontologies/2026/7/untitled-ontology-25#Business_Capability"/>
        <rdfs:range rdf:resource="http://www.semanticweb.org/v0cn037/ontologies/2026/7/untitled-ontology-25#Business_Process"/>
    </owl:ObjectProperty>

[yasenstar]

4. Using SubClassOf Axioms Without Range (Your Third Suggestion)

You asked: "Suppose I add in Business_Capability: 'SubClassOf realizedBy some Business_Process' and 'SubClassOf realizedBy some Application', and leave no range axiom. Is that useful?

Although I don't utilize this way often, but Yes, this is useful and is actually a very common pattern!

I add another clean test RDF here: https://github.com/yasenstar/protege_pizza/blob/main/ebook/rdf/pizza-ebook_13.5.2_2.rdf

After creating these two restrictions, you may find the source are adding line-items under Class paragraphs, not Properties anymore:

    <!-- http://www.semanticweb.org/v0cn037/ontologies/2026/7/untitled-ontology-26#Business_Capability -->

    <owl:Class rdf:about="http://www.semanticweb.org/v0cn037/ontologies/2026/7/untitled-ontology-26#Business_Capability">
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.semanticweb.org/v0cn037/ontologies/2026/7/untitled-ontology-26#realizedBy"/>
                <owl:someValuesFrom rdf:resource="http://www.semanticweb.org/v0cn037/ontologies/2026/7/untitled-ontology-26#Application"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.semanticweb.org/v0cn037/ontologies/2026/7/untitled-ontology-26#realizedBy"/>
                <owl:someValuesFrom rdf:resource="http://www.semanticweb.org/v0cn037/ontologies/2026/7/untitled-ontology-26#Business_Process"/>
            </owl:Restriction>
        </rdfs:subClassOf>
    </owl:Class>

What this does in my observation:

• It restricts the usage of realizedBy locally to the class Business_Capability
• The reasoner can still infer that if a Business_Capability has a realizedBy relationship, the target is an instance of Business_Process or Application (depending on which restriction applies).

Comparison with Range Axiom:

Approach	Scope	Inferernce Behavior
rdfs:range	Global -- applies to every use of the property anywhere	Inferred for all subjects
SubClassOf some restriction	Local -- applies only to instance of the class where it's defined	Inferred only for those instances

From my point of view, this is actually a recommended practice in some ontology engineering circles because it avoids the global side effects of rdsf:range while still providing useful inference. It also allows you to define different target types for different subclasses.

[yasenstar]

My summary view with above points, @LaraAcuna, feel free to review and comment, I'll leave this discussion open before your confirmation.

Approach	When to Use
Separate properties (realizedByBusinessProcess, realizedByApplication	When the relationship has different characteristics or governance requirements for each target type
owl:unionOf range	When the property is semantically the same, but can point to different types; good for reuse and consistency
Local restrictions (SubClassOf some)	When you want to avoid global side effects; excellent for modular ontologies to consider
Multiple rdfs:range axioms	Avoid if possible -- because of the un-intended AND/intersection semantics

Hope those have addressed your questions and concerns in some level, good luck! 🛩️

[yasenstar]

Update eBook chapter 13 contents and publish Volume 2 with v0.48.0, thanks greatly @LaraAcuna , here I'm closing this discussion thread and feel free to comments if any new points pop up.

[LaraAcuna]

Hello Xiaoqi!
Thank you for your explanations! When to use each case is what is just what helps me see the better practices, I understand very clearly now and know better how to proceed with my project.
Cheers and good luck with your ebook, I've been reading it and it's a great read so far 🙌

[yasenstar]

Thanks Lara for your kind confirmation. Enjoy your reading and practicing on ontology.