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Data exchange and incomplete information
 In Proc. PODS’06
, 2006
"... Data exchange is the problem of finding an instance of a target schema, given an instance of a source schema and a specification of the relationship between the source and the target, and answering queries over target instances in a way that is semantically consistent with the information in the sou ..."
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Data exchange is the problem of finding an instance of a target schema, given an instance of a source schema and a specification of the relationship between the source and the target, and answering queries over target instances in a way that is semantically consistent with the information in the source. Theoretical foundations of data exchange have been actively explored recently. It was also noticed that the standard certain answers semantics may behave in very odd ways. In this paper I explain that this behavior is due to the fact that the presence of incomplete information in target instances has been ignored; in particular, proper query evaluation techniques for databases with nulls have not been used, and the distinction between closed and open world semantics has not been made. I present a concept of target solutions based on the closed world assumption, and show that the space of all solutions has two extreme points: the canonical universal solution and the core, well studied in data exchange. I show how to define semantics of query answering taking into account incomplete information, and show that the wellknown anomalies go away with the new semantics. The paper also contains results on the complexity of query answering, upper approximations to queries (maybeanswers), and various extensions. 1.
An extension of the relational data model to incorporate ordered domains
 ACM Transactions on Database Systems
, 2001
"... We extend the relational data model to incorporate partial orderings into data domains, which we call the ordered relational model. Within the extended model, we define the Partially Ordered Relational Algebra (the PORA) by allowing the ordering predicate ⊑ to be used in formulae of the selection op ..."
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Cited by 15 (2 self)
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We extend the relational data model to incorporate partial orderings into data domains, which we call the ordered relational model. Within the extended model, we define the Partially Ordered Relational Algebra (the PORA) by allowing the ordering predicate ⊑ to be used in formulae of the selection operator (σ). The PORA expresses exactly the set of all possible relations which are invariant under orderpreserving automorphism of databases. This result characterises the expressiveness of the PORA and justifies the development of Ordered SQL (OSQL) as a query language for ordered databases. OSQL provides users with the capability of capturing the semantics of ordered data in many advanced applications, such as those having temporal or incomplete information. Ordered Functional Dependencies (OFDs) on ordered databases are studied, based on two possible extensions of domain orderings: (1) pointwiseordering and (2) lexicographical ordering. We present a sound and complete axiom system for OFDs in the first case and establish a set of sound and complete chase rules for OFDs in the second. Our results suggest that the implication problems for both cases of OFDs are decidable and that the enforcement of OFDs in ordered relations are practically feasible. In a wider perspective, the proposed model explores an important area of objectrelational databases, since ordered domains can be viewed as a general kind of data type. Categories and Subject Descriptors: H.2.1 [Database Management]: Logical Design—data
Ordered functional dependencies in relational databases
 Information Systems
, 1999
"... Abstract  We extend the relational data model to incorporate linear orderings into data domains, which we call the ordered relational model. The conventional Functional Dependencies (FDs) are examined in the context of ordered relational databases by using the notion of System Ordering Independence ..."
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Abstract  We extend the relational data model to incorporate linear orderings into data domains, which we call the ordered relational model. The conventional Functional Dependencies (FDs) are examined in the context of ordered relational databases by using the notion of System Ordering Independence (SOI), which refers to the desirable scenario that the ordering of tuples in a relation is independent of the implementation of the underlying DBMS. We also extend Armstrong's axiom system for FDs to object relations, which are a subclass of ordered relations that allow us to view tuples as objects. We formally de ne Ordered Functional Dependencies (OFDs) for the extended model by means of two possible extensions of domains, pointwiseorderings and lexicographical orderings. We rst present a sound and complete axiom system for OFDs in the case of pointwiseorderings and then establish a sound and complete set of chase rules for OFDs in the case of lexicographical orderings. Our main result shows that the implication problems for both cases of OFDs are decidable, and that
L.: The Semantics of Consistency and Trust in Peer Data Exchange Systems (extended version). http://www.scs.carleton.ca/ ∼ bertossi/papers/lparExt.pdf
"... Abstract. We propose and investigate a semantics for peer data exchange systems (or peer data management systems) where different peers are pairwise related to each other by means of data exchange constraints and trust relationships. These two elements plus the data at the peers’ sites and the local ..."
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Abstract. We propose and investigate a semantics for peer data exchange systems (or peer data management systems) where different peers are pairwise related to each other by means of data exchange constraints and trust relationships. These two elements plus the data at the peers’ sites and the local integrity constraints for a peer are made compatible via the proposed semantics by determining a set of solution instances, which are the intended virtual instances for the peer. The semantically correct answers from a peer to a query, called its peer consistent answers, are defined as those answers that are invariant under all its different solution instances. We show that solution instances can be specified as the models of logic programs with a stable model semantics. 1
Design by example for SQL table definitions with functional dependencies
 THE VLDB JOURNAL
, 2011
"... ..."
The implication problem of data dependencies over SQL table definitions: axiomatic, algorithmic and logical characterizations
"... We investigate the implication problem for classes of data dependencies over SQL table definitions. Under Zaniolo’s “no information ” interpretation of null markers we establish an axiomatization and algorithms to decide the implication problem for the combined class of functional and multivalued de ..."
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Cited by 7 (4 self)
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We investigate the implication problem for classes of data dependencies over SQL table definitions. Under Zaniolo’s “no information ” interpretation of null markers we establish an axiomatization and algorithms to decide the implication problem for the combined class of functional and multivalued dependencies in the presence of NOT NULL constraints. The resulting theory subsumes three previously orthogonal frameworks. We further show that the implication problem of this class is equivalent to that in a propositional fragment of Cadoli and Schaerf ’s family of paraconsistent S3 logics. In particular, S is the set of variables that correspond to attributes declared NOT NULL. We also show how our equivalences for multivalued dependencies can be extended to Delobel’s class of full firstorder hierarchical decompositions, and the equivalences for functional dependencies can be extended to arbitrary Boolean dependencies. These dualities allow us to transfer several findings from the propositional fragments to the corresponding classes of data dependencies, and vice versa. We show that our results also apply to Codd’s null interpretation “value unknown at present”, but not to Imielinski’s orrelations utilizing Levene and Loizou’s weak possible world semantics. Our findings establish NOT NULL constraints as an effective mechanism to balance not only the certainty in database relations but also the expressiveness with the efficiency of entailment relations. They also control the degree by which the implication of data dependencies over total relations is soundly approximated
Handling Inconsistency in Databases and Data Integration Systems
, 2007
"... c ○ Copyright by Loreto Bravo, 2007 For several reasons a database may not satisfy certain integrity constraints (ICs), for example, when it is the result of integrating several independent data sources. However, most likely, information in it is still consistent with the ICs; and could be retrieved ..."
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Cited by 5 (1 self)
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c ○ Copyright by Loreto Bravo, 2007 For several reasons a database may not satisfy certain integrity constraints (ICs), for example, when it is the result of integrating several independent data sources. However, most likely, information in it is still consistent with the ICs; and could be retrieved when queries are answered. Consistent answers with respect to a set of ICs have been characterized as answers that can be obtained from every possible minimal repair of the database. The goal of this research is to develop methods to retrieve consistent answers for a wide and practical class of constraints and queries from relational databases and from data integration systems. We will put special interest on databases with null values. We will give a semantics of satisfaction of constraints in the presence of null that generalizes the one used in commercial DBMS. Since there are interesting connections between the area of consistently querying virtual data integration systems and other areas, like querying incomplete databases, merging inconsistent theories, semantic reconciliation of data, schema mapping, data exchange, and query answering in peer data management systems, the results of this research could also be applied to them. In our research, we explore in more depth the connection with virtual data integration systems and peer data management systems. ii To my husband
Exploiting Functional Dependence in Query Optimization
, 2000
"... I authorize the University of Waterloo to lend this thesis to other institutions or individuals for the purpose of scholarly research. I further authorize the University of Waterloo to reproduce this thesis by photocopying or by other means, in total or in part, at the request of other institutions ..."
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Cited by 3 (1 self)
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I authorize the University of Waterloo to lend this thesis to other institutions or individuals for the purpose of scholarly research. I further authorize the University of Waterloo to reproduce this thesis by photocopying or by other means, in total or in part, at the request of other institutions or individuals for the purpose of scholarly research. iii The University of Waterloo requires the signatures of all persons using or photocopying this thesis. Please sign below, and give address and date. Functional dependency analysis can be applied to various problems in query optimization: selectivity estimation, estimation of (intermediate) result sizes, order optimization (in particular sort avoidance), cost estimation, and various problems in the area of semantic query optimization. Dependency analysis in an ansi sql relational model, however, is made complex due to the existence of null values, threevalued logic, outer joins, and duplicate rows. In this thesis we define the notions of strict and lax functional dependencies, strict and lax equivalence constraints, and null constraints, which capture both a
A TopDown Proof Procedure for Generalized Data Dependencies
"... . Data dependencies are well known in the context of relational database. They aim to specify constraints that the data must satisfy to model correctly the part of the world under consideration. The implication problem for dependencies is to decide whether a given dependency is logically implied by ..."
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Cited by 1 (1 self)
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. Data dependencies are well known in the context of relational database. They aim to specify constraints that the data must satisfy to model correctly the part of the world under consideration. The implication problem for dependencies is to decide whether a given dependency is logically implied by a given set of dependencies. A proof procedure for the implication problem, called \chase", has already been studied in the generalized case of tuplegenerating and equalitygenerating dependencies. The chase is a bottomup procedure: from hypotheses to conclusion, and thus is not goaldirected. It also requires the dynamic creation of new symbols, which can turn out to be a costly operation. This paper introduces a new proof procedure which is topdown: from conclusion to hypothesis, that is goaldirected. The originality of this procedure is that it does not act as classical theorem proving procedures, which require a special form of expressions, such as clausal form, obtained after skolemi...
Achieving Data Privacy . . .
, 2011
"... There may be sensitive information in a relational database that we want to keep hidden from a user of group thereof. The sensitive data is characterized as the contents of a view. Whenever the user poses queries about these secrecy views, the set of answers either becomes empty or contains tuples ..."
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There may be sensitive information in a relational database that we want to keep hidden from a user of group thereof. The sensitive data is characterized as the contents of a view. Whenever the user poses queries about these secrecy views, the set of answers either becomes empty or contains tuples with only null values. This is achieved through updates of the given instance. Since the database is not expected to be physically changed to produce this result, it is only virtually and minimally updated, and those changes are reflected in the view contents. Virtual updates are based on the use of null values as used in the SQL standard. The different ways to update the underlying database are specified as the models of logic programs with