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32
Complexity of Answering Queries Using Materialized Views
 In PODS
, 1998
"... We study the complexity of the problem of answering queries using materialized views. This problem has attracted a lot of attention recently because of its relevance in data integration. Previous work considered only conjunctive view definitions. We examine the consequences of allowing more expressi ..."
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Cited by 284 (5 self)
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We study the complexity of the problem of answering queries using materialized views. This problem has attracted a lot of attention recently because of its relevance in data integration. Previous work considered only conjunctive view definitions. We examine the consequences of allowing more expressive view definition languages. The languageswe consider for view definitions and user queries are: conjunctive queries with inequality, positive queries, datalog, and firstorder logic. We show that the complexity of the problem depends on whether views are assumed to store all the tuples that satisfy the view definition, or only a subset of it. Finally, we apply the results to the view consistency and view selfmaintainability problems which arise in data warehousing. 1 Introduction The notion of materialized view is essential in databases [34] and is attracting more and more attention with the popularity of data warehouses [28]. The problem of answering queries using materialized views [24...
ULDBs: Databases with uncertainty and lineage
 IN VLDB
, 2006
"... This paper introduces ULDBs, an extension of relational databases with simple yet expressive constructs for representing and manipulating both lineage and uncertainty. Uncertain data and data lineage are two important areas of data management that have been considered extensively in isolation, howev ..."
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Cited by 238 (25 self)
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This paper introduces ULDBs, an extension of relational databases with simple yet expressive constructs for representing and manipulating both lineage and uncertainty. Uncertain data and data lineage are two important areas of data management that have been considered extensively in isolation, however many applications require the features in tandem. Fundamentally, lineage enables simple and consistent representation of uncertain data, it correlates uncertainty in query results with uncertainty in the input data, and query processing with lineage and uncertainty together presents computational benefits over treating them separately. We show that the ULDB representation is complete, and that it permits straightforward implementation of many relational operations. We define two notions of ULDB minimality—dataminimal and lineageminimal—and study minimization of ULDB representations under both notions. With lineage, derived relations are no longer selfcontained: their uncertainty depends on uncertainty in the base data. We provide an algorithm for the new operation of extracting a database subset in the presence of interconnected uncertainty. Finally, we show how ULDBs enable a new approach to query processing in probabilistic databases. ULDBs form the basis of the Trio system under development at Stanford.
ProbView: A Flexible Probabilistic Database System
 ACM TRANSACTIONS ON DATABASE SYSTEMS
, 1997
"... ... In this article, we characterize, using postulates, whole classes of strategies for conjunction, disjunction, and negation, meaningful from the viewpoint of probability theory. (1) We propose a probabilistic relational data model and a generic probabilistic relational algebra that neatly capture ..."
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Cited by 169 (14 self)
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... In this article, we characterize, using postulates, whole classes of strategies for conjunction, disjunction, and negation, meaningful from the viewpoint of probability theory. (1) We propose a probabilistic relational data model and a generic probabilistic relational algebra that neatly captures various strategies satisfying the postulates, within a single unified framework. (2) We show that as long as the chosen strategies can be computed in polynomial time, queries in the positive fragment of the probabilistic relational algebra have essentially the same data complexity as classical relational algebra. (3) We establish various containments and equivalences between algebraic expressions, similar in spirit to those in classical algebra. (4) We develop algorithms for maintaining materialized probabilistic views. (5) Based on these ideas, we have developed
Model Checking vs. Theorem Proving: A Manifesto
, 1991
"... We argue that rather than representing an agent's knowledge as a collection of formulas, and then doing theorem proving to see if a given formula follows from an agent's knowledge base, it may be more useful to represent this knowledge by a semantic model, and then do model checking to see if the g ..."
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Cited by 117 (5 self)
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We argue that rather than representing an agent's knowledge as a collection of formulas, and then doing theorem proving to see if a given formula follows from an agent's knowledge base, it may be more useful to represent this knowledge by a semantic model, and then do model checking to see if the given formula is true in that model. We discuss how to construct a model that represents an agent's knowledge in a number of different contexts, and then consider how to approach the modelchecking problem.
On the Representation and Querying of Sets of Possible Worlds
, 1989
"... We represent a set of possible worlds using an incomplete information database. The representation techniques that we study range from the very simple Coddtable (a relation over constants and uniquely occurring variables called nulls) to much more complex mechanisms involving views of conditione ..."
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Cited by 115 (3 self)
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We represent a set of possible worlds using an incomplete information database. The representation techniques that we study range from the very simple Coddtable (a relation over constants and uniquely occurring variables called nulls) to much more complex mechanisms involving views of conditionedtables (programs applied to Coddtables augmented by equality and inequality conditions). (1) We provide matching upper and lower bounds on the datacomplexity of testing containment, membership, and uniqueness for sets of possible worlds. We fully classify these problems with respect to our representations. (2) We investigate the datacomplexity of querying incomplete information databases for both possible and certain facts. For each fixed positive existential query on conditionedtables we present a polynomial time algorithm solving the possible fact problem. We match this upper bound by two NPcompleteness lower bounds, when the fixed query contains either negation or recursion ...
Tractable Reasoning via Approximation
 Artificial Intelligence
, 1995
"... Problems in logic are wellknown to be hard to solve in the worst case. Two different strategies for dealing with this aspect are known from the literature: language restriction and theory approximation. In this paper we are concerned with the second strategy. Our main goal is to define a semantical ..."
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Cited by 92 (0 self)
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Problems in logic are wellknown to be hard to solve in the worst case. Two different strategies for dealing with this aspect are known from the literature: language restriction and theory approximation. In this paper we are concerned with the second strategy. Our main goal is to define a semantically wellfounded logic for approximate reasoning, which is justifiable from the intuitive point of view, and to provide fast algorithms for dealing with it even when using expressive languages. We also want our logic to be useful to perform approximate reasoning in different contexts. We define a method for the approximation of decision reasoning problems based on multivalued logics. Our work expands and generalizes in several directions ideas presented by other researchers. The major features of our technique are: 1) approximate answers give semantically clear information about the problem at hand; 2) approximate answers are easier to compute than answers to the original problem; 3) approxim...
Models for Incomplete and Probabilistic Information
 IEEE Data Engineering Bulletin
, 2006
"... Abstract. We discuss, compare and relate some old and some new models for incomplete and probabilistic databases. We characterize the expressive power of ctables over infinite domains and we introduce a new kind of result, algebraic completion, for studying less expressive models. By viewing probab ..."
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Cited by 63 (9 self)
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Abstract. We discuss, compare and relate some old and some new models for incomplete and probabilistic databases. We characterize the expressive power of ctables over infinite domains and we introduce a new kind of result, algebraic completion, for studying less expressive models. By viewing probabilistic models as incompleteness models with additional probability information, we define completeness and closure under query languages of general probabilistic database models and we introduce a new such model, probabilistic ctables, that is shown to be complete and closed under the relational algebra. 1
Probabilistic Deductive Databases
, 1994
"... Knowledgebase (KB) systems must typically deal with imperfection in knowledge, e.g. in the form of imcompleteness, inconsistency, uncertainty, to name a few. Currently KB system development is mainly based on the expert system technology. Expert systems, through their support for rulebased program ..."
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Cited by 57 (2 self)
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Knowledgebase (KB) systems must typically deal with imperfection in knowledge, e.g. in the form of imcompleteness, inconsistency, uncertainty, to name a few. Currently KB system development is mainly based on the expert system technology. Expert systems, through their support for rulebased programming, uncertainty, etc., offer a convenient framework for KB system development. But they require the user to be well versed with the low level details of system implementation. The manner in which uncertainty is handled has little mathematical basis. There is no decent notion of query optimization, forcing the user to take the responsibility for an efficient implementation of the KB system. We contend KB system development can and should take advantage of the deductive database technology, which overcomes most of the above limitations. An important problem here is to extend deductive databases into providing a systematic basis for rulebased programming with imperfect knowledge. In this paper, we are interested in an exension handling probabilistic knowledge.
The Complexity of Querying Indefinite Data about Linearly Ordered Domains
 In The Proceedings of the Eleventh ACM SIGACTSIGMODSIGART Symposium on Principles of Database Systems
, 1992
"... In applications dealing with ordered domains, the available data is frequently indefinite. While the domain is actually linearly ordered, only some of the order relations holding between points in the data are known. Thus, the data provides only a partial order, and query answering involves determin ..."
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Cited by 40 (2 self)
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In applications dealing with ordered domains, the available data is frequently indefinite. While the domain is actually linearly ordered, only some of the order relations holding between points in the data are known. Thus, the data provides only a partial order, and query answering involves determining what holds under all the compatible linear orders. In this paper we study the complexity of evaluating queries in logical databases containing such indefinite information. We show that in this context queries are intractable even under the data complexity measure, but identify a number of PTIME subproblems. Data complexity in the case of monadic predicates is one of these PTIME cases, but for disjunctive queries the proof is nonconstructive, using wellquasiorder techniques. We also show that the query problem we study is equivalent to the problem of containment of conjunctive relational database queries containing inequalities. One of our results implies that the latter is \Pi p 2 ...
An Introduction to ULDBs and the Trio System
 IEEE Data Engineering Bulletin, Special Issue on Probabilistic Databases
, 2006
"... ..."