presented by : nikhil agarwal - david r. cheriton school of …gweddell/cs848/presentations/... ·...
Post on 19-May-2018
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R. Kontchakov, Birkbeck College London, UK
C. Lutz, Universit¨at Bremen, Germany
D. Toman, University of Waterloo, Canada
F.Wolter, University of Liverpool, UK
M. Zakharyaschev, Birkbeck College London, UK
Presented By : Nikhil Agarwal
Problem and Motivation
φ(x) = ∃y, z (city(x) ∧ has_airport(x, y) ∧ located_in(x, US)∧ named_for(y, z) ∧ ww2_ hero(z))
“Can you give me all the US cities which has an airport named after a WW2 hero.”
Assumptions
• Database containing tables for φ(x)
• Doesn't contain concept ww2_hero
• Contains ww2_deco (WW2 Decoration)
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Problem and Motivation
• Atoms constructed for the query :
city(Chicago)
has_airport(Chicago,ORD)
located_in(Chicago, US)
named_for(ORD,Ohare)
recipient_of(O’Hare, ww2_medal_of_honor)
ww2_deco(ww2_medal_of_honor)
• But doesn’t contain any data for ww2_hero
• New Ontology for rewritten queries
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Problem and Motivation
∀x, y (recipient_of(x, y) ∧ ww2_deco(y) → ww2_hero(x))
• answers iff answers
• Reduction can be done by
• construct DB’ with ww2_hero
• ww2_hero has all names with ww2_decoration
• rewrite φ(x) to φ’(x) and ww2_hero(z) as
ww2_hero(z) ∨ ∃v (recipient_of(z, v) ∧ ww2_deco(v))
• For this reduction, conditions considered are
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Problem and Solution
• D’ computable in polynomial time in D and not dependent on
• doesn’t depend on D
• Query Rewriting doesn’t allow D’=D
• Alternative approach
• D’ is computable in polynomial time in and D
• is polynomial in and
• More transparent query rewritings
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DL-Lite Horn
• Concept C from concept name Ai
• Roles R from role name Pi
• Tbox has concept inclusions of form
• Interpretations are
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DL-Lite Horn
• As usual
• are all individual names in
• KB is PTIME-complete
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DL-Lite Horn
•
• ans(q, ) – set of all answers to q in
• cert(q, ) – set of all certain answers to q over
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Canonical Model • is not finite in this case
• Start with and apply CI (Concept inclusion) to
•
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Canonical Model
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Canonical Model • contains a homomorphic image of
• This helps in reduction using canonical model
• An example showing q’ depends only on q and
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Canonical Model
•
• is an answer iff
• R(a,y) is entailed by and
• R(a,y) is entailed by B(a) or T(z,a)
• so a is answer to q(x) iff a is answer to
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Finite FO Generating Model
• contains all answers of
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Finite FO Generating Model • Consider a fork shape query
• Models obtained will be
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Conjunctive Query Answering
• Consider a CQ
• rewrite q to q+ in such a way that
• q+ becomes
• φ1, φ2 and φ3 are Boolean connectives of equalities t1 = t2 (terms or constants)
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Conjunctive Query Answering
• φ1 is the first filter/eliminator/rewritten portion
• eliminates all cR since those are implicit
• labeled nulls and hidden from user
• φ2 implements the matching from tree witness
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Conjunctive Query Answering
• φ3 prevents cyclic triangle situation
• Can’t be mapped into a tree
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Experimental and Extension
• Query rewriting implemented in QuoOnto
• q rewritten into unions of Q and CQ
• In Worst case the size of is
• Experiments show 5-10 fold increase on data
• More concept hierarchy more data size
• Can be applied to for medical terminologies
• CQ for is PTIME so can’t be used for rewrite
• Applies to extended called
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Conclusion
• Query rewriting can be done on OBDA
• How DL-Lite Horn is used in combined approach
• Canonical model over given ontology
• Constructing Generating model from canonical model
• Relation of answers in both the models
• Conjunctive query answering using these models
• Refining CQ through Boolean combinations
• Some experimental facts
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