Pay-as-you-go OWL Query Answering Using a Triple Store
Yujiao Zhou, Yavor Nenov, Bernardo Cuenca Grau and Ian Horrocks
Pay-as-you-go Approach
Intuition‣ to delegate the bulk of the
computational workload to a highly scalable datalog reasoner
!‣ to minimise the use of a fully-
fledged reasoner
Evaluation‣ Evaluated on LUBM(100,1000), UOBM(1, 60, 500), FLY, DBPedia+travel
and NPD FactPages.
Average time without OWL 2 reasoning
Average timeAcknowledgements This work was supported by the Royal Society, the EPSRC projects Score!, ExODA, and MaSI3, and the FP7 project OPTIQUE.
Data
Lower
ELHO Lower
Data
Upper
Ontology
DU
Query
Summary
Datalog
Eng
ine
Datalog Engine
Datalog Engine
Summarisation
Full Reasoner Q
Dependency Analysis
Fragment
F
Full Reasoner QF
Output
Tracking by datalog encoding
triple store OWL 2 reasoner
L=LRL ∪ LEL ∪ … U
L = U
σ(cert(q, F)) ⊆ cert(q, σ(F))
Incomplete endomorphisms
Arrange calls to the reasoner according to the dependencies heuristically
Rule out non-answers
Done
Diagram Over-approx to datalog
!!!!
‣ upper bound U answer of q w.r.t the resulting set of rules U(Σ) and D.
Lower bounds ‣ basic lower bound LRL
answer of q w.r.t. the datalog fragment of Σ and D; ‣ EL lower bound LEL
answer of q w.r.t. the ELHO fragment of Σ and D.
Tracking encoding in datalog Intuition: to compute all the rules and facts that participate in a proof of q(a) in Σ∪D. This goal can be archived using datalog encoding. ‣ Example:
‣ If B1(x1),…,Bm(xm) → H(x) is a rule in U(Σ), Ht(x), B1 (x1), . . . , Bm (xm) → S(cr)∧B1
t (x1 )∧ . . . ∧Bm
t(xm ) is added to the tracking rule.
‣ Involved rules: {r | S(cr) is derived} Involved facts: {P(a) ∈ D | Pt(a) is derived}
Summarisation & dependency between answers ‣ Let σ be the summary function, σ(cert(q, F)) ⊆ cert(q, σ(F)) ‣ If there is an endomorphism from a to b in F, then
a ∈ cert(q, F) implies b ∈ cert(q, F)
‣ Existential knowledge
{. . . , A uB, . . .}
{C} {C}
{A, . . .}x1
{A, . . .}x2
R
R
{A, . . .}
{C}c
x1{A, . . .}
x2
R
R
{. . . , A tB, . . .}
‣ Disjunctive knowledge
DL Ontology Dataset QueriesLUBM(n) SHI 93 ~100,000n 14 (std)+10
!UOBM(n) SHIN 314 ~200,000n 15FLY SRI 144,407 6,308
88 5
DBPedia SHOIN 1,757 12,119,662 441 (atomic)NPD SHIF 819 3,817,079 329 (atomic)
LUBM(1000) UOBM(100) FLY DBPedia NPDQueries 22/24 12/15 5/5 439/441 294/329 Time(s) 18.4 0.7 0.2 0.3 0.1
LUBM(100) UOBM(1) FLY DBPedia NPD
Time(s) 29.6 1.8 0.2 3 3
Problem Setting‣Ontology Σ — a set of rules of the form φ(x) → Vi ∃yi ψ(x, yi) ‣ Data D — a set of ground atoms of the form P(a) ‣ Conjunctive queries — FO formula of the form q(x) ← ∃y ψ(x, y)
where ψ and φ are conjunctions of atoms.
