Epistemic Description Logic

Origin. Donini et al. (1992). Combine DL with epistemic operators. Knowledge about ABox: K. Introspection: what is known. Foundation for ontology-based epistemic reasoning.

Models. DL knowledge bases with epistemic operator. K φ: φ is known (true in all models). Nonmonotonic via epistemic closed world. Multi-agent variants.

Formalism.

Epistemic operator: K C: concept C is known K-concepts: add K to DL concept language

Extended concepts: C ::= A | ¬C | C ⊓ D | ∃R.C | K C Epistemic on top of ALC (typically).

Semantics: Epistemic interpretation: set of DL models. E ⊨ K C(a) iff for all I ∈ E: I ⊨ C(a) "Known in all compatible models."

Epistemic closed world: K-minimal model: assume K φ for minimal φ. Nonmonotonic: closed-world on K.

Example: TBox: Employee ⊑ Person ABox: Employee(john) K Person(john): known (derivable) ¬K HasBonus(john): not known (open world)

Query: K ∃HasProject.Important(john)? "Is it known John has an important project?"

Complexity: Epistemic ALC: EXPTIME (same as ALC). With closed-world: higher complexity. Undecidable for some combinations.

Symbols.

Symbol	Unicode	Name	Meaning
K	—	Knows	Epistemic operator
⊓	U+2293	Intersection	Concept and
⊑	U+2291	Subsumption	Subclass
⊨	U+22A8	Entails	Epistemic satisfaction

Metatheory. EXPTIME for epistemic ALC. Closed-world increases complexity. Relationship to autoepistemic logic.

Applies to. Ontology queries. Incomplete knowledge. Data integration. Closed-world reasoning. Multi-agent ontologies.

Limitations. Complexity concerns. CWA interactions. Multi-agent harder. Tool support limited.