OWL Class Expressions in Anger

Restrictions = anonymous classes

An OWL restriction is an anonymous class whose members satisfy a condition on a property. Three flavours dominate real models:

• owl:someValuesFrom — ∃ R.C. Has at least one R-value of type C.
• owl:allValuesFrom — ∀ R.C. Every R-value (if any) is of type C. Note the trap: vacuously true when there are no R-values.
• owl:hasValue — ∃ R.{a}. Has the specific individual a as an R-value.

Plus the cardinality restrictions: min, max, exactly.

Necessary vs sufficient

rdfs:subClassOf says "every member of A is a member of B" — a necessary condition. owl:equivalentClass says "A is exactly the things that satisfy this condition" — both necessary and sufficient. The latter is what lets a reasoner classify an individual into a derived class.

OWL class expressions are job descriptions and the HR system that auto-tags matching employees.

At an employer, two kinds of statements coexist:

• 'A senior engineer is a kind of engineer.' — a one-way fact (every senior engineer is an engineer, but not every engineer is senior). This is rdfs:subClassOf — a necessary condition.
• 'An adult is exactly a person who has an age greater than 18.' — a two-way definition: anyone matching the description is automatically an adult; anyone who is an adult must match. This is owl:equivalentClass — necessary AND sufficient.

The HR system can only auto-tag people based on definitions of the second kind. Tell it 'a Senior is anyone with title=Engineer and years_at_company >= 5' and it'll silently retag every qualifying employee tonight. Tell it only 'every Senior is an Engineer' (necessary condition) and it'll never tag anyone — because the definition runs only one way. That gap between subClassOf and equivalentClass is the whole reason OWL reasoning becomes genuinely useful.

Tools & resources

• OWL 2 Manchester Syntax — the readable surface syntax for class expressions: https://www.w3.org/TR/owl2-manchester-syntax/
• OWL 2 Quick Reference — every constructor on one page: https://www.w3.org/TR/owl2-quick-reference/
• Protégé class-expression editor walkthrough: https://protegewiki.stanford.edu/wiki/Protege4UserDocs
• OWL Pizzas tutorial — step-by-step restrictions on a worked example: https://protege.stanford.edu/practical/