DL-Lite

Origin. Calvanese et al. (2007). Lightweight description logic. Polynomial query answering. Foundation for OWL 2 QL. Designed for databases with ontologies.

Models. Restricted expressiveness for tractability. Conjunctive query answering in AC⁰. First-order rewritable. Ontology-based data access.

Formalism.

DL-Lite_core: Concepts: A, ∃R, ∃R⁻ Left side of inclusion: B ::= A | ∃R | ∃R⁻ Right side: C ::= B | ¬B Inclusions: B ⊑ C

DL-Lite_R (with roles): Role inclusions: R ⊑ S Disjointness: Disj(R, S) Role inverses.

DL-Lite_F (functional roles): (funct R): R is functional At most one R-successor.

Restrictions: No full existentials ∃R.C No conjunction on left of ⊑ No universal ∀R.C

Query answering: Input: TBox T, ABox A, query q Output: certain answers cert(q, T, A) Answers true in all models.

First-order rewritability: Query q over T rewrites to FOL query q'. cert(q, T, A) = eval(q', A) Use SQL on database.

Complexity: TBox reasoning: PTIME Query answering: AC⁰ in data complexity Combined: PTIME

Symbols.

Symbol	Unicode	Name	Meaning
∃R	—	Unqualified ∃	Has R-successor
⊑	U+2291	Inclusion	Subsumption
Disj	—	Disjoint	No overlap
funct	—	Functional	At most one

Metatheory. FO-rewritable. AC⁰ data complexity. PTIME combined. Complete for ontology-based data access.

Applies to. OWL 2 QL. Database integration. SPARQL over relational. Large-scale ontologies. Enterprise data.

Limitations. Very limited expressiveness. No qualified restrictions. No conjunction in subsumption. Tradeoff for tractability.