## Characterizing and Computing Semantically Correct Answers from Databases with Annotated Logic and Answer Sets

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### BibTeX

@MISC{Barceló_characterizingand,

author = {Pablo Barceló and Leopoldo Bertossi and Loreto Bravo},

title = {Characterizing and Computing Semantically Correct Answers from Databases with Annotated Logic and Answer Sets},

year = {}

}

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### Abstract

A relational database may not satisfy certain integrity constraints (ICs) for several reasons. However most likely most of the information in it is still consistent with the ICs. The answers to queries that are consistent with the ICs can be considered sematically correct answers, and are characterized [2] as ordinary answers that can be obtained from every minimally repaired version of the database. In this paper we address the problem of specifying those repaired versions as the minimal models of a theory written in Annotated Predicate Logic [27]. It is also shown how to specify database repairs using disjunctive logic program with annotation arguments and a classical stable model semantics.

### Citations

1854 |
Foundations of Logic Programming
- Lloyd
- 1987
(Show Context)
Citation Context ...placing, for p ∈P, every positive literal p(¯s) byp(¯s, t ⋆⋆ ) and every negative literal ¬p(¯s) byp(¯s, f ⋆⋆ ). Now Q ⋆⋆ can be transformed into a query program Π(Q ⋆⋆ ) by a standard transformation =-=[30, 1]-=-. This query program will be run in combination with Π ⋆ (DB, IC ).sExample 11. For the query Q(y) :∃zBook(kafka, y, z), we generate Q ⋆⋆ (y) : ∃zBook(kafka,y,z,t ⋆⋆ ), that is transformed into the qu... |

1516 |
Foundations of Databases
- Abiteboul, Hull, et al.
- 1995
(Show Context)
Citation Context ... results presented here extend those presented in [3] in different ways. First, we show how to annotate other important classes of ICs found in database praxis, e.g. referential integrity constraints =-=[1]-=-, and the correspondence results are extended. Next, the problem of consistent query answering is characterized as a problem of non monotonic entailment. We also show how the the APC theory that speci... |

1492 | The stable model semantics for logic programming
- Gelfond, Lifschitz
- 1988
(Show Context)
Citation Context ...ground atoms M is a stable model of Π(DB, IC ) iff it is a minimal model of Π M , where Π M = {A1 ∨ ···∨An ← B1, ··· ,Bm | A1 ∨···∨An ← B1, ··· ,Bm, not C1, ··· , not Ck ∈ Π and Ci /∈ Mfor 1 ≤ i ≤ k} =-=[23, 24]-=-. Definition 5. A Herbrand model M is coherent if it does not contain a pair of literals of the form {p(ā, ta),p(ā, fa)}. ✷ Example 8. (example 7 continued) The coherent stable models of the program p... |

521 |
Knowledge Representation, reasoning, and declarative problem solving with Answer sets (Book draft
- Baral
- 2001
(Show Context)
Citation Context ...h programs have nonmonotonic consequences and a Π P 2 -complete complexity [18]. Answer set programming hassbeen successfully used in formalizing and implementing complex nommonotonic reasoning tasks =-=[7]-=-. Under those circumstances, the problem then is to come up with the best logic programming specifications and the best way to use them, so that the computational complexity involved does not go beyon... |

283 | Consistent query answers in inconsistent databases
- Arenas, Bertossi, et al.
- 1999
(Show Context)
Citation Context ...st likely most of the information in it is still consistent with the ICs. The answers to queries that are consistent with the ICs can be considered semantically correct answers, and are characterized =-=[2]-=- as ordinary answers that can be obtained from every minimally repaired version of the database. In this paper we address the problem of specifying those repaired versions as the minimal models of a t... |

279 | Complexity and expressive power of logic programming
- Dantsin, Eiter, et al.
- 2001
(Show Context)
Citation Context ...programs [10] introduced below. These programs have better computational complexity than general disjunctive programs in the sense that the complexity is reduced from Π P 2 -complete to coNP-complete =-=[18, 29]-=-. The dependency graph of a ground disjunctive program Π is defined as a directed graph where each literal is a node and there is an arch from L to L ′ iff there is a rule in which L appears positive ... |

253 |
Reasoning about action using a possible models approach
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- 1988
(Show Context)
Citation Context ... are several similarities between our approach to consistency handling and those followed by the belief revision/update community. Database repairs coincide with revised models defined by Winslett in =-=[35]-=-. The treatment in [35] is mainly propositional, but a preliminary extension to first order knowledge bases can be found in [16]. Those papers concentrate on the computation of the models of the revis... |

216 |
Towards a logical reconstruction of relational database theory
- Reiter
- 1984
(Show Context)
Citation Context ...Equivalently, if we associate to DB a first order structure, also denoted with DB, in the natural way, i.e. by applying the domain closure and unique names assumptions and the closed world assumption =-=[33]-=- that makes false any ground atom not explicitly appearing in the set of atoms DB, it may happen that DB, as a structure, does not satisfy the IC . We denote with DB |=Σ IC the fact that the database ... |

211 | Xsb as an efficient deductive database engine
- Sagonas, Swift, et al.
- 1994
(Show Context)
Citation Context ...complexity of consistent query answering [15]. If the original program can be transformed into a normal program, then also other efficient implementations could be used for query evaluation, e.g. XSB =-=[34]-=-, that has been already successfully applied in the context of consistent query answering via query transformation, with nonexistentially quantified conjunctive queries [14]. Example 17. (example 12 c... |

170 | Theory of generalized annotated logic programming and its applications
- Kifer, Subrahmanian
- 1992
(Show Context)
Citation Context ...nt answer. Query Q3(x): ∃zBook(x, metamorph,z)hasx = kafka as a consistent answer. ✷ 2.2 Annotating DBs and ICs Annotated Predicate Calculus (APC ) was introduced in [27] and also studied in [12] and =-=[28]-=-. It constitutes a non classical logic, where classically inconsistent information does not trivializes logical inference, reasoning about causes of inconsistency becomes possible, making one of its g... |

145 | Propositional semantics for disjunctive logic programs
- Ben-Eliyahu, Dechter
- 1994
(Show Context)
Citation Context ...Section 9.s8.1 Head cycle free programs In some cases, the repair programs we have introduced may be transformed into equivalent non disjunctive programs. This is the case of head-cycle-free programs =-=[10]-=- introduced below. These programs have better computational complexity than general disjunctive programs in the sense that the complexity is reduced from Π P 2 -complete to coNP-complete [18, 29]. The... |

102 | A Deductive System for Nonmonotonic Reasoning
- Eiter, Leone, et al.
- 1997
(Show Context)
Citation Context ...urrent alternative relies on finding those ground query atoms that belong to all the stable models once they have been computed via a ground instantiation of the original program (see Example 11). In =-=[20]-=- intelligent grounding strategies for pruning in advance the instantiated program have been explored and incorporated into DLV. It would be interesting to explore to what extent the program can be fur... |

99 | Propositional circumscription and extended closed world reasoning are Π P 2 -complete
- Eiter, Gottlob
- 1993
(Show Context)
Citation Context ..., we have formulated the problem of CQA as a problem of nonmonotonic reasoning, more precisely of minimal entailment, whose complexity, even in the propositional case, can be at least Π P 2 -complete =-=[19]-=-. Having a problem of nonmonotonic reasoning with such complexity, it is not strange to try to use disjunctive logic programs with negation with a stable or answer set semantics to solve the problem o... |

95 | A logic for reasoning with inconsistency - Kifer, Lozinskii - 1992 |

68 |
Enhancing disjunctive datalog by constraints
- Buccafurri, Leone, et al.
(Show Context)
Citation Context ...Computing from the Program The database repairs could be computed using an implementation of the disjunctive stable models semantics like DLV [21], that also supports denial constraints as studied in =-=[13]-=-. In this way we are able to prune out the models that are not coherent, imposing for every predicate p the constraint ← p(¯x, ta),p(¯x, fa). Example 12. Consider the database instance {p(a)} that is ... |

65 | Updating logical databases
- Fagin, Kuper, et al.
- 1986
(Show Context)
Citation Context ...ies for representing and querying simultaneously and implicitly all the repairs of the database. Furthermore, we work in a fully first-order framework. The semantics of database updates is treated in =-=[22]-=-, a treatment that is close to belief revision. That paper represents databases as collections of theories, in such a way that under updates a new collection of theories is generated that minimally di... |

52 |
A logic programming approach to the integration, repairing and querying of inconsistent databases
- Greco, Greco, et al.
- 2001
(Show Context)
Citation Context ...restricted to be “binary”, i.e. universal with at most two database literals (plus built-in formulas). A similar, independent approach to database repair based on logic programs was also presented in =-=[26]-=-. The basic idea behind the logic programming based approach to consistent query answering is that since we need to deal with all the repairs of a database, we had better specify the class of the repa... |

49 |
A model-based belief revision system
- Chou, Winslette
- 1994
(Show Context)
Citation Context ...y. Database repairs coincide with revised models defined by Winslett in [35]. The treatment in [35] is mainly propositional, but a preliminary extension to first order knowledge bases can be found in =-=[16]-=-. Those papers concentrate on the computation of the models of the revised theory, i.e., the repairs in our case, but not on query answering. Comparing our framework with that of belief revision, we h... |

48 | Specifying and querying database repairs using logic programs with exceptions
- Arenas, Bertossi, et al.
- 2000
(Show Context)
Citation Context ...in terms of the ICs and queries that can handle. Although most of the ICs found in database praxis are covered by the positive cases in [2], the queries are restricted to conjunctions of literals. In =-=[4, 6]-=-, a more general methodology based on logic programs with a stable model semantics was introduced. There is a one to one correspondence between the stable models of the logic programs and the database... |

37 | Logic programs for querying inconsistent databases
- Barceló, Bertossi
- 2003
(Show Context)
Citation Context ...presented here works for arbitrary FO queries and universal ICs, what considerable extends the cases that could be handled in [2, 4, 3]. This paper improves, combines and extends results presented in =-=[8, 9]-=-. The main extensions have to do with the analysis and optimizations of the logic programs for consistent query answering introduced here. This paper is structured as follows. In Section 2 we give som... |

34 | Consistent Answers from Integrated Data Sources - Bertossi, Chomicki, et al. - 2002 |

29 |
Answer Sets for Consistent Query Answering
- Arenas, Bertossi, et al.
(Show Context)
Citation Context ...in terms of the ICs and queries that can handle. Although most of the ICs found in database praxis are covered by the positive cases in [2], the queries are restricted to conjunctions of literals. In =-=[4, 6]-=-, a more general methodology based on logic programs with a stable model semantics was introduced. There is a one to one correspondence between the stable models of the logic programs and the database... |

29 | Querying inconsistent databases: Algorithms and implementation
- Celle, Bertossi
- 2000
(Show Context)
Citation Context ...query evaluation, e.g. XSB [34], that has been already successfully applied in the context of consistent query answering via query transformation, with nonexistentially quantified conjunctive queries =-=[14]-=-. Example 17. (example 12 continued) The repair program is HCF because, as it can be seen from the (relevant part of the) dependency graph, there is no cycle involving both p(x, fa) andq(x, ta), the a... |

28 | XSB as an e#cient deductive database engine - Sagonas, Swift, et al. - 1994 |

25 | Programming with Non-determinism in Deductive Databases
- Giannotti, Greco, et al.
- 1997
(Show Context)
Citation Context ...(5) could be replaced by: p(¯x, fa) ∨ q(¯x ′ ,y,ta) ← p(¯x, t ⋆ ), not aux(¯x ′ ), not q(¯x ′ , null, td),choice(¯x ′ ,y). (8) where choice( ¯ X, ¯ Y ) is the static non-deterministic choice operator =-=[25]-=- that selects one value for attribute tuple ¯ Y for each value of the attribute tuple ¯ X.In equation (8), choice(¯x ′ ,y) would select one value for y from the domain for each combination of values ¯... |

24 | Scalar aggregation in fdinconsistent databases
- Arenas, Bertossi, et al.
- 2001
(Show Context)
Citation Context ...sThe program Π ⋆ (DB, IC ) we presented in previous sections is, therefore, extended with the following formulas: p(¯x, fa) ∨ q(¯x ′ , null, ta) ← p(¯x, t ⋆ ), not aux(¯x ′ ), not q(¯x ′ , null, td). =-=(5)-=- aux(¯x ′ ) ← q(¯x ′ ,y,td), not q(¯x ′ ,y,fa). (6) aux(¯x ′ ) ← q(¯x ′ ,y,ta). (7) Intuitively, clauses (6) and (7) detect if the formula ∃y(q(ā ′ ,y):t ∨ q(ā ′ ,y):ta)) is satisfied by the model. If... |

20 |
Disjunctive Stable Models
- Leone, Rullo, et al.
- 1997
(Show Context)
Citation Context ...programs [10] introduced below. These programs have better computational complexity than general disjunctive programs in the sense that the complexity is reduced from Π P 2 -complete to coNP-complete =-=[18, 29]-=-. The dependency graph of a ground disjunctive program Π is defined as a directed graph where each literal is a node and there is an arch from L to L ′ iff there is a rule in which L appears positive ... |

19 | Applications of annotated predicate calculus to querying inconsistent databases
- Arenas, Bertossi, et al.
- 2000
(Show Context)
Citation Context ... the fact that the atoms (and only the atoms) are annotated with values drawn from a truth-values lattice. The lattice Latt we will use throughout this paper is shown in Figure 1, first introduced in =-=[3]-=-. ⊤ fa f t ta fc td fd tc ⊥ Fig. 1. Latt with constraints values, database values and advisory values The lattice contain the usual truth values t, f, ⊤, ⊥, for true, false, inconsistent and unknown, ... |

19 |
A survey on paraconsistent semantics for extended logic programs
- DAMÁSIO, PEREIRA
- 1998
(Show Context)
Citation Context ...nding rules in program and omitting rules that could lead to other forms of repairs. In [12, 28] paraconsistent and annotated logic programs, with non classical semantics, are introduced. However, in =-=[17]-=- some transformation methodologies for paraconsistent logic programs [12] are shown that allow assigning to them extensions of classical semantics. Our programs have a fully standard stable model sema... |

19 | Declarative problem-solving in dlv - Eiter, Faber, et al. - 2001 |

13 | Repairing databases with annotated predicate logic
- Barceló, 2002
(Show Context)
Citation Context ...presented here works for arbitrary FO queries and universal ICs, what considerable extends the cases that could be handled in [2, 4, 3]. This paper improves, combines and extends results presented in =-=[8, 9]-=-. The main extensions have to do with the analysis and optimizations of the logic programs for consistent query answering introduced here. This paper is structured as follows. In Section 2 we give som... |

12 | On the Computational Complexity of Consistent Query Answers
- Chomicki, Marcinkowski
- 2000
(Show Context)
Citation Context ...¯xi) ← �m � j=1 qj(¯yj)∧ k�=i not pk(¯xk), i=1, ..., n. Such transformations can be justified or discarded on the basis of a careful analysis of the intrinsic complexity of consistent query answering =-=[15]-=-. If the original program can be transformed into a normal program, then also other efficient implementations could be used for query evaluation, e.g. XSB [34], that has been already successfully appl... |

6 | Complexity and Expressive - Dantsin, Eiter, et al. - 2001 |

2 |
Reasoning with Conflicting Information in Artificial Intelligence and Database Theory
- Pradhan
- 2001
(Show Context)
Citation Context ...se some semantics on the combined information. More generally speaking, we could think ICs on a database as constraints on the answers to queries rather than on the information stored in the databases=-=[32]-=-. In this case, retrieving answers to queries that are consistent wrt the ICs becomes a central issue in the development of DBMSs. In consequence, in any of the scenarios above and others, we are in t... |

2 | Reasoning with con information in arti intelligence and database theory - Pradhan - 2001 |

1 | Answer Sets for Consistent Query Answers. Under review for journal publication. CoRR paper cs.DB/0207094 - Arenas, Bertossi, et al. |

1 | ConsistentAnswers from Integrated Data Sources. In 'Flexible Query Answering Systems - Bertossi, Chomicki, et al. - 2002 |

1 | A DeductiveSystem for Non-Monotonic Reasoning - Eiter, Leone, et al. - 1997 |