Database Repairing and Consistent Query Answering

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1 () Keys Université de Mons (UMONS) October 20, 2009

2 Outline () Keys 1 2 () Keys

3 Disclaimer () Keys Not a comprehensive overview. Selected topics, biased by personal interests. See [BC03, Ber06, Cho06, Cho07] for overviews.

4 Outline () Keys 1 2 () Keys

5 Context: Inconsistent, Incomplete, Imprecise Data () Keys Traditional database approach Data integrity assume data is consistent, certain, precise. Completeness All relevant data is in the database (CWA). How about, for example, today s citation databases? ISI Web of Science is incomplete for computer science [MCSvL09]. CiteSeer seems no longer be actively maintained. Google Scholar is imprecise (e.g., misspelled names, citations from web pages that are no publications,...)...

6 Context: Inconsistent, Incomplete, Imprecise Data () Keys Traditional database approach Data integrity assume data is consistent, certain, precise. Completeness All relevant data is in the database (CWA). How about, for example, today s citation databases? ISI Web of Science is incomplete for computer science [MCSvL09]. CiteSeer seems no longer be actively maintained. Google Scholar is imprecise (e.g., misspelled names, citations from web pages that are no publications,...)...

7 Inconsistent Data () Keys Inconsistent data Data violating integrity constraints: Classical dependencies: key, fd, egd, tgd,... New dependencies [Fan08, FGJ08]: cfd, md,... Conditional functional dependency [CFG + 07] ZIP, CountryCode = 44 Street Matching dependency [S09] Phone : 1.0 Street : 0.9 If two tuples match on Phone, then the similarity between their Street-values must exceed 0.9 (e.g., Spen Ln Spem Ln).

8 Data Cleaning Data cleaning Fix errors by some minimal change. () Keys Data cleaning CC Phone Name Street City ZIP Mike New St York A Joe Spen Ln York A1 Kind of changes that can be considered: Delete the first or the second row. Modify New St in Spen Ln (or vice versa). Replace one occurrence of A1 with a new fresh value..

9 Repair () Keys Relative to a database db a set IC of integrity constraints. Definition Repair A repair rep is a database (over the same schema) such that: : rep = IC; Preferential: there is no database rep such that rep = IC rep is preferred to rep, relative to some (partial) preference order.

10 Example () Keys repairing WorksFor EName DName Ed Toys Dept DName Shoes Inclusion dependency WorksFor[2] Dept[1] Two consistent databases: WorksFor EName DName Ed Toys WorksFor EName DName Ed Toys Dept Dept DName Shoes Toys DName Toys We may prefer the first way of repairing.

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12 Preference Order on the Repair Space () Keys Several preference orders have been proposed: Based on symmetric difference Based on cardinality Loosely sound semantics Based on homomorphism Based on metric distance... Jan Chomicki coined the term semantic explosion in this context.

13 Symmetric Difference Repairs [ABC99] () Keys Definition rep 1 rep 2 if (db rep 1 ) (db rep 2 ) Minimize (w.r.t. ) the set of deleted inserted facts. Equivalent definition rep 1 (rep 2 db) rep 1 rep 2 if (rep 1 \ db) rep 2 rep 1 rep 2 Symmetric difference repair Let db = {P( a)} rep 1 = {P( a), Q( b)} rep 2 = {} Then, rep 1 rep 2 are not comparable by.

14 Example of Symmetric Difference Repair () Keys Infinitely many repairs WorksFor EName DName Ed Toys Dept DName Budget Shoes 3000K Inclusion dependency WorksFor[2] Dept[1] Symmetric difference repairs: WorksFor EName DName Dept DName Budget Shoes 3000K WorksFor EName DName Ed Toys Dept DName Budget Shoes 3000K Toys 9999K

15 Example of Symmetric Difference Repair () Keys Set inclusion vs. counting EMP Name Rank Sal Ed clerk 28 Tim clerk 30 An boss 20 An clerk 40 Functional dependency Name Rank, Sal (EMP(x 1, clerk, s 1 ) EMP(x 2, boss, s 2 ) s 1 s 2 ) The symmetric difference repairs are: Name Rank Sal Ed clerk 28 Tim clerk 30 An clerk 40 Name Rank Sal An boss 20

16 Example of Symmetric Difference Repair () Keys Set inclusion vs. counting EMP Name Rank Sal Ed clerk 28 Tim clerk 30 An boss 20 An clerk 40 Functional dependency Name Rank, Sal (EMP(x 1, clerk, s 1 ) EMP(x 2, boss, s 2 ) s 1 s 2 ) The symmetric difference repairs are: Name Rank Sal Ed clerk 28 Tim clerk 30 An clerk 40 Name Rank Sal An boss 20

17 Cardinality Repairs () Keys Definition card rep 1 card rep 2 if db rep 1 < db rep 2 Cardinality repair Name Rank Sal Ed clerk 28 Tim clerk 30 An clerk 40 EMP Name Rank Sal Ed clerk 28 Tim clerk 30 An boss 20 An clerk 40 card Name Rank Sal An boss 20

18 Component-cardinality Repairs [AK09] () Keys Component-cardinality repairs WorksFor EName DName Ed Shoes An Shoes Dept DName Inclusion dependency WorksFor[2] Dept[1] Two consistent databases: rep 1 Ed Shoes WorksFor EName DName An Shoes Dept DName Shoes rep 2 WorksFor EName DName Dept DName rep 1 card rep 2, but rep 2 is preferred if we only consider Dept.

19 Loosely Sound Semantics [CLR03] () Keys Definition ls rep 1 ls rep 2 if rep 1 (rep 2 db) Maximize the set of preserved database facts. Open World Assumption: Add as much as you like. Loosely sound semantics Let db = {P( a)} rep 1 = {P( a), Q( b)} rep 2 = {} Then, rep 1 ls rep 2. Cardinality variant ls card rep 1 ls card rep 2 if rep 1 db > rep 2 db

20 Entire Tuples vs. Components of Tuples () Keys EMP Name Rank Sal Ed clerk 28 Tim clerk 30 An boss 20 An clerk 40 Name Rank, Sal (EMP(x 1, clerk,s 1 ) EMP(x 2, boss,s 2 ) s 1 s 2 ) Fixing components of tuples: Name Rank Sal Ed clerk 28 Tim clerk 30 An clerk 20 Name Rank Sal Ed clerk 28 Tim clerk 30 An boss 40

21 Entire Tuples vs. Components of Tuples () Keys EMP Name Rank Sal Ed clerk 28 Tim clerk 30 An boss 20 An clerk 40 Name Rank, Sal (EMP(x 1, clerk,s 1 ) EMP(x 2, boss,s 2 ) s 1 s 2 ) Fixing components of tuples: Name Rank Sal Ed clerk 28 Tim clerk 30 An clerk 20 Name Rank Sal Ed clerk 28 Tim clerk 30 An boss 40

22 Homomorphism Based Repairs [Wij05] Idea rep 1 ls rep 2 (rep 1 db) (rep 2 db) () Keys Replace A B with A homomorphic to B ; A B with glb(a, B). Definition Greatest Lower Bound glb(a, B) Lower bound: glb(a, B) is homomorphic to A to B; Greatest: every database that is homomorphic to A to B, is also homomorphic to glb(a, B). Definition hom rep 1 hom rep 2 if glb(rep 2,db) homomorphic to glb(rep 1,db), but not vice versa.

23 Recall Homomorphism () Keys Definition Homomorphism A database db 1, possibly with variables, is homomorphic to a database db 2 if there exists a substitution θ for the variables in db 1 such that θ(db 1 ) db 2. Homomorphism {R( a, a, a )} {R( b, b, a )} {R(x, x, a )} {R(u, w, a ), R(w, u, a )}

24 Example Homomorphism Repairs () Keys Homomorphism repair db Name Rank Sal Ed clerk 28 Tim clerk 30 An boss 20 An clerk 40 rep 2 Name Rank Sal Ed clerk 28 Tim clerk 30 An boss 40 glb(rep 2,db) Name Rank Sal Ed clerk 28 Tim clerk 30 An boss y An x 40 rep 2 db Name Rank Sal Ed clerk 28 Tim clerk 30

25 Numerical Attributes () Keys Assumptions Primary keys are satisfied immutable. Inconsistencies in numerical data. Inconsistent numerical data x y z(emp(x, y, z) (y < 5) (z 6000)) Two Approaches Update Based [FFP05] EMP Emp Status Sal Ed Tim Least Square Fixes [BBFL08]

26 Update Based [FFP05] () Keys Principle Update Based rep 1 is preferred to rep 2 if it requires updating a smaller set of values (in terms of set inclusion or cardinality). The actual new values after update do not matter. Update based x y z(emp(x, y, z) (y < 5) (z 6000)) EMP Emp Status Sal t 1 Ed t 2 Tim Emp Status Sal Ed Tim The atomic updates are (t 1, Status, 8 ) (t 2, Sal, 1000 ). The set of updated values is {(t 1, Status), (t 2, Sal)}.

27 Least Square Fixes [BBFL08] () Keys Principle least square fixes rep 1 is preferred to rep 2 if the distance between rep 1 db is smaller than the distance between rep 2 db. Least square fixes x y z(emp(x,y,z) (y < 5) (z 6000)) EMP Emp Status Sal Ed Tim Emp Status Sal Ed Tim Distance for Ed-tuple: w Status (2 2) 2 + w Sal ( ) 2 Distance for Tim-tuple: w Status (4 5) 2 + w Sal ( ) 2 Global distance: Σ

28 Comparison Numercial Attributes () Keys Repairs are different in both approaches. Comparison x y z(ects(x,y,z) (y + z 120)) ECTS SID Year1 Year2 Ed Tim SID Year1 Year2 Ed Tim This would not be a prefered repair in the update based approach.

29 Repair Checking () Keys Relative to a set IC of integrity constraints a type of repair. Definition Repair checking Repair checking is the complexity of (checking membership of) the set: RC(IC) = {(db, rep) rep is a repair of db} For results, see [CM05, AK09].

30 Topics to Work on () Keys Tailoring the repair process: Repair-to-source source-to-repair dependencies After double-checking the list of bosses: EMP db (x, boss, z) z EMP rep (x, boss, z ) Take into account provenance. Probability distribution over repairs. semi-structured data....

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32 Semantics () Keys Relative to a database db a set IC of integrity constraints. Definition answer The consistent (or certain) answer to a query q( x) is defined by: { a q( a) is true in every repair of db} For a Boolean query q, we say that q is consistently true if q is true in every repair.

33 Example () Keys rep 1 Name City Sal Blake Paris 10 EMP Name City Sal Blake Paris 10 Blake Rome 10 rep 2 Name City Sal Blake Rome 10 q 1 (y) = {y z(emp( Blake, y, z))} {} q 2 (z) = {z y(emp( Blake, y, z))} { 10 } y(emp( Blake, y, 10 )) is consistently true.

34 Complexity for Boolean () Keys Relative to: a set IC of integrity constraints; a type of repair (e.g. loosely sound semantics); a Boolean query q. Complexity query answering is the complexity (of deciding membership) of the set: (q,ic) = {db q is true in every repair of db}

35 Objectives () Keys Tractability Characterize queries q integrity constraints IC for which (q,ic) is in P. FO Definability Characterize queries q integrity constraints IC for which (q,ic) is first-order definable ( hence in P). First-order definable (q,ic) is first-order definable if there exists a first-order sentence ψ such that for every database db, db (q,ic) if only if db = ψ.

36 History () Keys Marcelo Arenas, Leopoldo E. Bertossi, Jan Chomicki: Answers in Inconsistent s. PODS 1999 [ABC99] Numerous publications since Implemented in prototypes systems. Hippo [CMS04b] ConQuer [FFM05]...

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38 Denial Constraints () Keys Definition Denial constraint A denial constraint has the form: x 1... x k (R 1 ( x 1 ) R k ( x k ) ϕ( x 1,..., x k )) where ϕ is a conjunction of atomic formulas using built-in predicates (=, <). Denial constraints For the schema EMP[Name, Rank, Sal]: u, x, y, z(emp(u, boss, y) EMP(x, clerk, z) y < z) x, y 1, z 1, y 2, z 2 (EMP(x, y 1, z 1 ) EMP(x, y 2, z 2 ) y 1 y 2 ) x, y 1, z 1, y 2, z 2 (EMP(x, y 1, z 1 ) EMP(x, y 2, z 2 ) z 1 z 2 )

39 Repairs () Keys We assume here that repairs are maximally consistent subsets of db. This corresponds to symmetric difference repairs or loosely sound semantics (adding new atoms is useless in the case of denials).

40 Exponential Number of Repairs () Keys Exponential number of repairs x(r(x, a ) R(x, b )) A B 1 a 1 b 2 a 2 b. n a n b There are 2 n different repairs.

41 Conflict Hypergraph () Keys Relative to a database db a set of denial constraints. Definition Conflict hypergraph A conflict hypergraph is a hypergraph whose hyperedges are subsets of db. For every denial constraint x 1... x k (R 1 ( x 1 ) R k ( x k ) ϕ( x 1,..., x k )), if θ is a valuation such that θ( x i ) = a i for 1 i k db = R 1 ( a 1 ) R k ( a k ) ϕ( a 1,..., a k ), then {R 1 ( a 1 ),...,R k ( a k )} is an hyperedge.

42 Example Conflict Hypergraph [CM05] () Keys Conflict hypergraph EMP Name Rank Sal t 1 Ed clerk 28 t 2 Tim clerk 30 t 3 An boss 20 t 4 An clerk 40 Properties t t 3 2 t 4 t 1 Every repair is a maximal (w.r.t. ) subset of db that contains no hyperedge of the conflict hypergraph. The number of hyperedges is polynomial in the size of db.

43 Boolean () Keys Definition Boolean query A quantifier-free Boolean query is a Boolean combination of ground atoms. It can be assumed to be in CNF: φ 1 φ 2 φ l, where each φ i is of the form A 1 A m B 1 B n, with A 1,...,A m, B 1,...,B n distinct ground atoms. Boolean query EMP( An, clerk, 40 ) EMP( Ed, clerk, 28 )

44 Denial Constraints () Keys Question The problem is to verify for 1 i l whether φ i = A 1 A m B 1 B n is true in every repair. We ask instead whether φ i is false in some repair, i.e. whether some repair rep satisfies φ i = A 1 A m B 1 B n.

45 Denial Constraints () Keys Crux HProver algorithm [CM05, CMS04a] Any repair rep satisfying A 1 A m B 1 B n must verify the following conditions: 1 A 1,...,A m rep. 2 For each edge E in the conflict hypergraph, E rep. 3 Maximality: for 1 j n, if B j db, then there is an edge E j in the conflict hypergraph such that B j E j E j \ {B j } rep. Why is HProver polynomial in the size of db? The Maximality condition chooses n hyperedges among a polynomial number of hyperedges.

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47 Imprecise Data () Keys Primary key violations are a natural way to model imprecise data. Imprecise data Speakers Name Jan Jan Jef Jef Jean-Luc Affiliation UA UHasselt UMH UMons FUNDP Tuples with the same Name but different Affiliation are mutually exclusive. Tuples with different Name are independent.

48 Probabilistic Data [AFM06, HAKO09, DRS09] () Keys Probabilistic data Speakers Name Affiliation P Jan UA 0.6 Jan UHasselt 0.4 Jef UMH 0.8 Jef UMons 0.2 Jean-Luc FUNDP 1.0

49 () Keys Definition Boolean conjunctive query A Boolean conjunctive query has the form (R 1 ( x 1, x 1 ) R k ( x 1, x k )) This query contains a self-join if R i = R j for some i j. Since primary keys are underlined, IC can be read from q. We write (q) instead of (q,ic) if IC is clear from q.

50 Reduction From Graph 3-Colorability Theorem (q) is conp-complete for () Keys 1 2 q = x y z(c(x, z) C(y, z) E(x, y)) Graph is 3-colorable q is false in some repair 3 4 C Vertex Color 1 red 1 blue 1 yellow. 4 red 4 blue 4 yellow E From To

51 Reduction From Graph 3-Colorability Theorem (q) is conp-complete for () Keys 1 2 q = x y z(c(x, z) C(y, z) E(x, y)) Graph is 3-colorable q is false in some repair 3 4 C Vertex Color 1 blue 2 red 3 yellow 4 blue E From To

52 First-order Definability Example () Keys (q 0 ) is first-order definable rep 1 Name City Sal Blake Paris 10 EMP Name City Sal Blake Paris 10 Blake Rome 10 rep 2 Name City Sal Blake Rome 10 q 0 = y(emp( Blake, y, 10 )) is consistently true if only if the (possibly inconsistent) database satisfies y (EMP( Blake, y, 10 ) y z (EMP( Blake, y, z) z = 10 ))

53 First-order Definability Example () Keys (q 1 ) is first-order definable E EName DName Ed Shoes Ed Toys D DName Budget Boss Shoes 3000K An Shoes 3100K An Toys 3200K An q 1 = y z(e( Ed, y) D(y, z, An )) is consistently true if only if the (possibly inconsistent) database satisfies y (E( Ed, y) y (E( Ed, y ) z (D(y, z, An ) z w (D(y, z, w) w = An ))))

54 Rewrite Rules that Emerge [Wij09b] () Keys Rewrite rule for conjunctive queries without self-join 1 First, express all constraints on variables constants in a conjunction ϕ of equalities. For example, x y(r(x, y) S(y, a )) is expressed as R(x, y 1 ) S(y 2, w a ) y 1 = y 2 w a = a }{{} ϕ 2 Next, apply the following rewrite rules: Rew[R( x, y) q ϕ] = x y(r( x, y) y(r( x, y) Rew[q ϕ])) Induction basis: Rew[ϕ] = ϕ 3 Manual simplification may be applied for readability.

55 db = Rew[q]? q is true in every repair () Keys For q a conjunctive query without self-join, db satisfies Rew[q] q true in every in every repair. is not generally true Let q = x y z(r(x, z) S(y, z)). Rew[q] = x z (R(x, z) z (R(x, z ) y w (S(y, w) w (S(y, w ) z = w )))) R A C 1 a 2 b S B C 3 a 3 b By symmetry, same problem for x y z(s(y, z) R(x, z)).

56 Kind of Results [Wij09b] () Keys Theorem Let q be conjunctive without self-join. (q) is first-order definable if q has a rooted join tree such that whenever R( x, y) is the parent of S( u, w), then at least one of the following conditions is satisfied: every variable that occurs in x, occurs in u; or if variable v occurs in both R( x, y) S( u, w), then v occurs in u. satisfying theorem s conditions R 4 (z, w) R 0 (x, y) {x, y} {y} R 2 (y, z) {z} R 1 (x, y) {y} R 3 (y, a )

57 Join Tree () Keys Definition Join tree A join tree for a conjunctive query q is an undirected tree whose vertices are the atoms of q such that: Connectedness Condition: whenever the same variable v occurs in two atoms A B, then v occurs in each atom on the unique path linking A B. It is common to label each edge with the set of variables that occur in both end points.

58 Kind of Results [Wij09a] () Keys Theorem Let q = (R( x, y) S( u, w)). Let L be the set of atoms that occur in both atoms. Let X be the set of variables that occur in x. Let U be the set of variables that occur in u. (q) is first-order definable if only if X U or U X or L X or L U.

59 Open Questions () Keys Are the following statements equivalent for every Boolean conjunctive query q without self-join? 1 For some ordering of the atoms in q, for every database db, db = Rew[q] iff db (q). 2 (q) is first-order definable. 3 (q) is not conp-complete. Clearly, 1 = 2, 2 = 3. Is there a Boolean conjunctive query q without self-join such that (q) is first-order definable but our rewrite rule does not apply? Is there a Boolean conjunctive query q without self-join such that (q) is in P but not first-order definable?

60 Open Questions () Keys Are the following statements equivalent for every Boolean conjunctive query q without self-join? 1 For some ordering of the atoms in q, for every database db, db = Rew[q] iff db (q). 2 (q) is first-order definable. 3 (q) is not conp-complete. Clearly, 1 = 2, 2 = 3. Is there a Boolean conjunctive query q without self-join such that (q) is first-order definable but our rewrite rule does not apply? Is there a Boolean conjunctive query q without self-join such that (q) is in P but not first-order definable?

61 Topics to Work on () Keys Almost-certain answers. Semi-structured Web data. Argumentation....

62 References I () Keys Marcelo Arenas, Leopoldo E. Bertossi, Jan Chomicki. query answers in inconsistent databases. In PODS, pages ACM Press, Periklis Andritsos, Ariel Fuxman, Renée J. Miller. Clean answers over dirty databases: A probabilistic approach. In Ling Liu, Andreas Reuter, Kyu-Young Whang, Jianjun Zhang, editors, ICDE, page 30. IEEE Computer Society, Foto N. Afrati Phokion G. Kolaitis. Repair checking in inconsistent databases: algorithms complexity. In Fagin [Fag09], pages Leopoldo E. Bertossi, Loreto Bravo, Enrico Franconi, Andrei Lopatenko. The complexity approximation of fixing numerical attributes in databases under integrity constraints. Inf. Syst., 33(4-5): , Leopoldo E. Bertossi Jan Chomicki. answering in inconsistent databases. In Jan Chomicki, Ron van der Meyden, Gunter Saake, editors, Logics for Emerging Applications of s, pages Springer, Leopoldo E. Bertossi. query answering in databases. SIGMOD Record, 35(2):68 76, 2006.

63 References II () Keys Gao Cong, Wenfei Fan, Floris Geerts, Xibei Jia, Shuai Ma. Improving data quality: Consistency accuracy. In Christoph Koch, Johannes Gehrke, Minos N. Garofalakis, Divesh Srivastava, Karl Aberer, An Deshpe, Daniela Florescu, Chee Yong Chan, Venkatesh Ganti, Carl-Christian Kanne, Wolfgang Klas, Erich J. Neuhold, editors, VLDB, pages ACM, Jan Chomicki. query answering: Opportunities limitations. In DEXA Workshops, pages IEEE Computer Society, Jan Chomicki. query answering: Five easy pieces. In Thomas Schwentick Dan Suciu, editors, ICDT, volume 4353 of Lecture Notes in Computer Science, pages Springer, Andrea Calì, Domenico Lembo, Riccardo Rosati. On the decidability complexity of query answering over inconsistent incomplete databases. In PODS, pages ACM, Jan Chomicki Jerzy Marcinkowski. Minimal-change integrity maintenance using tuple deletions. Inf. Comput., 197(1-2):90 121, Jan Chomicki, Jerzy Marcinkowski, Slawomir Staworko. Computing consistent query answers using conflict hypergraphs. In David A. Grossman, Luis Gravano, ChengXiang Zhai, Otthein Herzog, David A. Evans, editors, CIKM, pages ACM, 2004.

64 References III () Keys Jan Chomicki, Jerzy Marcinkowski, Slawomir Staworko. Hippo: A system for computing consistent answers to a class of sql queries. In Elisa Bertino, Stavros Christodoulakis, Dimitris Plexousakis, Vassilis Christophides, Manolis Koubarakis, Klemens Böhm, Elena Ferrari, editors, EDBT, volume 2992 of Lecture Notes in Computer Science, pages Springer, Nilesh N. Dalvi, Christopher Ré, Dan Suciu. Probabilistic databases: diamonds in the dirt. Commun. ACM, 52(7):86 94, Ronald Fagin, editor. Theory - ICDT 2009, 12th International Conference, St. Petersburg, Russia, March 23-25, 2009, Proceedings, volume 361 of ACM International Conference Proceeding Series. ACM, Wenfei Fan. Dependencies revisited for improving data quality. In Maurizio Lenzerini Domenico Lembo, editors, PODS, pages ACM, Ariel Fuxman, Elham Fazli, Renée J. Miller. Conquer: Efficient management of inconsistent databases. In Fatma Özcan, editor, SIGMOD Conference, pages ACM, Sergio Flesca, Filippo Furfaro, Francesco Parisi. query answers on numerical databases under aggregate constraints. In Gavin M. Bierman Christoph Koch, editors, DBPL, volume 3774 of Lecture Notes in Computer Science, pages Springer, 2005.

65 References IV () Keys Wenfei Fan, Floris Geerts, Xibei Jia. A revival of integrity constraints for data cleaning. PVLDB, 1(2): , Jiewen Huang, Lyublena Antova, Christoph Koch, Dan Olteanu. Maybms: a probabilistic database management system. In Ugur Çetintemel, Stanley B. Zdonik, Donald Kossmann, Nesime Tatbul, editors, SIGMOD Conference, pages ACM, Bertr Meyer, Christine Choppy, Jørgen Staunstrup, Jan van Leeuwen. Viewpoint - research evaluation for computer science. Commun. ACM, 52(4):31 34, Shaoxu Song Lei Chen Discovering matching dependencies. CoRR, abs/ , repairing using updates. ACM Trans. Syst., 30(3): , query answering under primary keys: a characterization of tractable queries. In Fagin [Fag09], pages

66 References V () Keys. On the consistent rewriting of conjunctive queries under primary key constraints. Inf. Syst., 34(7): , 2009.

Consistent Query Answering

Consistent Query Answering Sławek Staworko 1 University of Lille INRIA Mostrare Project DEIS 2010 November 9, 2010 1 Some slides are due to [Cho07] Sławek Staworko (Mostrare) CQA DEIS 2010 1 / 33 Overview