Database Repairing and Consistent Query Answering by Leopoldo Bertossi, M. Tamer Ozsu

By Leopoldo Bertossi, M. Tamer Ozsu

Integrity constraints are semantic stipulations database may still fulfill in an effort to be a suitable version of exterior truth. In perform, and for plenty of purposes, a database would possibly not fulfill these integrity constraints, and therefore it's stated to be inconsistent. in spite of the fact that, and probably, a wide section of the database continues to be semantically right, in a feeling that should be made certain. After having supplied a proper characterization of constant information in an inconsistent database, the traditional challenge emerges of extracting that semantically right information, as question solutions. The constant facts in an inconsistent database is generally characterised because the facts that persists throughout the entire database cases which are constant and minimally range from the inconsistent example. these are the so-called maintenance of the database. particularly, the constant solutions to a question posed to the inconsistent database are these solutions that may be at the same time acquired from the entire database maintenance. As anticipated, the proposal of fix calls for an sufficient thought of distance that enables for the comparability of databases with recognize to how a lot they vary from the inconsistent example. in this foundation, the minimality situation on upkeep might be effectively formulated. during this monograph we current and talk about those primary strategies, varied fix semantics, algorithms for computing constant solutions to queries, and in addition complexity-theoretic effects relating to the computation of upkeep and doing constant question answering. desk of Contents: creation / The Notions of fix and constant solution / Tractable CQA and question Rewriting / Logically Specifying maintenance / determination difficulties in CQA: Complexity and Algorithms / upkeep and knowledge cleansing

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3 CHARACTERIZING CONSISTENT DATA In order to define the admissible instances we mentioned above, we must first have a way to compare database instances, in terms of their distances to the instance D at hand. 4 Let D be a fixed instance for a relational schema S . (a) For two instances D1 , D2 for S , we say that D1 is at least as close to D as D2 , denoted D1 D D2 , iff (D, D1 ) ⊆ (D, D2 ). Here, (S1 , S2 ) := (S1 S2 ) ∪ (S2 S1 ) is the symmetric set difference between two sets. (b) D1 ≺D D2 holds iff D1 D D2 , but not D2 D D1 .

Of sentences in L(S ). 5 (a) A repair of D is an instance D for S that: 1. , D |= IC. 2. Is the class of instances for S that satisfy IC. D -minimal in (b) Rep(D, IC) denotes the class of repairs of instance D wrt IC. From this definition, we can see that a repair of D differs from D by a minimal set of insertions or deletions of tuples wrt set inclusion. Notice that the built-in predicates are not subject to changes, they have fixed extensions. Consider D = {P (a), P (b), Q(a), R(a), R(c)}, and IC = {∀x(P (x) → Q(x)), ∀x(Q(x) → R(x))}.

Nk } ∩ M = ∅, then {A1 , . . , An } ∩ M = ∅. M is a minimal model of if it is a model of , and has no model that is properly contained in M. MM ( ) denotes the class of minimal models of . , without not), as follows: Delete every rule A1 ∨ . . ∨ An ← P1 , . . , Pm , not N1 , . . , not Nk for which {N1 , . . , Nk } ∩ S = ∅. Next, transform each remaining rule A1 ∨ . . ∨ An ← P1 , . . , Pm , if S ∈ not N1 , . . , not Nk into A1 ∨ . . ∨ An ← P1 , . . , Pm . Now, S is a stable model of MM (gr( ) ↓).

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