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Reasoning & Inference

This page is a guided tour of the reasoning features ontoink can visualise — from basic RDFS up to OWL 2 — each with a small, self-contained example.

How to use each diagram: click Reasoning, then read the inferred triples in the panel. Tick "Show on graph" to overlay them as purple edges. Every diagram below defaults its reasoner dropdown to Server: OWL-RL, which materialises the full RDFS + OWL-RL closure and surfaces every inference listed. Switch to HermiT (owlready2) or Konclude to compare an OWL-DL reasoner.

Reasoner backends

  • OWL-RL (default here) — pure-Python; the most complete materialiser of RDFS/OWL inferences, including class subsumptions like Novel ⊑ Book ⟹ ∃reads.Novel ⊑ ∃reads.Book.
  • HermiT / Konclude — OWL-DL tableau reasoners; strongest on classification & consistency.
  • Browser: Konclude WASM — runs in your browser (no server), but only classifies the T-box (class subsumptions), so it shows fewer instance-level facts.
  • Server backends need the API (ONTOINK_MODE=all/api); the browser one works on static hosts.

1. RDFS — taxonomy & property hierarchies

rdfs:subClassOf, rdfs:subPropertyOf, rdfs:domain, rdfs:range.

Axiom Stated Inferred
Dog ⊑ Animal rex a Dog rex a Animal
hasMother ⊑ hasParent alice hasMother berta alice hasParent berta
hasPet rdfs:domain Person alice hasPet rex alice a Person
hasPet rdfs:range Animal alice hasPet rex rex a Animal

2. OWL — property characteristics

owl:inverseOf, owl:SymmetricProperty, owl:TransitiveProperty.

Characteristic Stated Inferred
childOf owl:inverseOf hasChild alice hasChild bob bob childOf alice
marriedTo a owl:SymmetricProperty alice marriedTo carol carol marriedTo alice
ancestorOf a owl:TransitiveProperty alice→bob→dan alice ancestorOf dan

3. OWL — identity & keys

owl:FunctionalProperty, owl:InverseFunctionalProperty, owl:sameAs.

Axiom Stated Inferred
hasBirthMother a owl:FunctionalProperty tom hasBirthMother mary, maria mary owl:sameAs maria
hasEmail a owl:InverseFunctionalProperty p1, p2 hasEmail e1 p1 owl:sameAs p2
alice owl:sameAs alicia alice knows bob alicia knows bob

4. OWL — class & property equivalence

owl:equivalentClass, owl:equivalentProperty.

Axiom Stated Inferred
Person ≡ Human alice a Human alice a Person
enjoys ≡ likes alice likes coffee alice enjoys coffee

5. OWL 2 — property restrictions

5a. Existential — owl:someValuesFrom (∃)

Reader ≡ ∃reads.Book, NovelReader ≡ ∃reads.Novel. Because every Novel is a Book, the reasoner derives a class subsumption and classifies the reader.

Inferred: NovelReader ⊑ Reader, mobyDick a Book, alice a Reader, alice a NovelReader.

5b. Universal — owl:allValuesFrom (∀)

VegetarianDish ≡ ∀ingredient.VegetarianFood, VeganDish ≡ ∀ingredient.VeganFood.

Inferred: VeganDish ⊑ VegetarianDish, buddhaBowl a VegetarianDish, tofu a VegetarianFood.

5c. Value — owl:hasValue

Italian ≡ (bornIn = Italy).

Inferred: mario a Italian.

6. OWL 2 — boolean class constructors

6a. Intersection — owl:intersectionOf (⊓)

Mother ≡ Woman ⊓ Parent (a defined class).

Inferred: mary a Mother, Mother ⊑ Woman, Mother ⊑ Parent.

6b. Union — owl:unionOf (⊔)

Parent ≡ Mother ⊔ Father.

Inferred: Mother ⊑ Parent, Father ⊑ Parent, mary a Parent.

7. OWL 2 — property chains

owl:propertyChainAxiom: hasParent ∘ hasParent ⟹ hasGrandparent.

Inferred: anna hasGrandparent carl.

8. Necessary vs. definition — rdfs:subClassOf vs owl:equivalentClass

The same restriction body, ∃reads.Book, attached two ways. ontoink draws them differently — ⊑ (solid triangle) for the necessary condition, ≡ (hollow diamond) for the definition — and the reasoner treats them differently.

  • Subscriber rdfs:subClassOf ∃reads.Book — necessary: every Subscriber reads a Book, but a book-reader is not inferred to be a Subscriber.
  • BookLover owl:equivalentClass ∃reads.Book — definition: a BookLover is exactly a book-reader, so alice is classified as a BookLover.

Inferred: alice a BookLover and Subscriber ⊑ BookLover — but not alice a Subscriber.

9. Reasoning + SHACL together

A small ontology with an inverse property, a symmetric property and a subclass. After reasoning, click "Validate with Inferences" to run the SHACL shape over the reasoned graph (the Person shape requires an rdfs:label).

Inferred: rex isPetOf alice (inverse), bob knows alice (symmetric), rex a Animal (subclass).

Coverage at a glance

Standard Feature Example
RDFS subClassOf, subPropertyOf, domain, range §1
OWL inverseOf, SymmetricProperty, TransitiveProperty §2
OWL FunctionalProperty, InverseFunctionalProperty, sameAs §3
OWL equivalentClass, equivalentProperty §4
OWL 2 someValuesFrom, allValuesFrom, hasValue §5
OWL 2 intersectionOf, unionOf §6
OWL 2 propertyChainAxiom §7
Modelling subClassOf vs equivalentClass (necessary vs definition) §8
SHACL validation over inferred triples §9

Try your own

Open the Playground and paste any of these snippets (or your own ontology), then click Reasoning and switch backends to see how RDFS, OWL-RL and OWL-DL reasoners differ.