Ontology Languages

Origin. KIF (1992), OWL (2004). Formal vocabulary for domains. Description logic basis. Semantic Web standards. Foundation for knowledge representation.

Models. Classes, properties, individuals. TBox: terminology. ABox: assertions. Reasoning: subsumption, consistency. Open world assumption.

Formalism.

OWL constructs: Class(C) ObjectProperty(R) Individual(a) SubClassOf(C, D) EquivalentClasses(C, D)

Class constructors: C ⊓ D (intersection) C ⊔ D (union) ¬C (complement) ∃R.C (some values) ∀R.C (all values) ≥n R.C (min cardinality) ≤n R.C (max cardinality) {a, b, c} (enumeration)

Property axioms: SubPropertyOf(R, S) InverseOf(R, S) TransitiveProperty(R) FunctionalProperty(R) Domain(R, C), Range(R, D)

Individual axioms: ClassAssertion(C, a) PropertyAssertion(R, a, b) SameIndividual(a, b) DifferentIndividuals(a, b)

OWL profiles: OWL 2 EL: polynomial reasoning. OWL 2 QL: query-optimized. OWL 2 RL: rule-based. OWL 2 Full: undecidable.

Open world: Unknown ≠ false. CWA for databases vs OWA for ontologies.

Symbols.

Symbol	Unicode	Name	Meaning
⊓	U+2293	Intersection	Class and
⊔	U+2294	Union	Class or
∃R.C	—	Some	Existential
∀R.C	—	All	Universal
≡	U+2261	Equivalent	Same class

Metatheory. Based on SROIQ. Decidable for profiles. Complexity varies by profile. Tableau algorithms.

Applies to. Semantic Web. Biomedical ontologies. Enterprise knowledge. Data integration. AI reasoning.

Limitations. Profile restrictions. Reasoning scalability. OWA counterintuitive. Modeling complexity.