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71
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 193 (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
Provenance semirings
 PODS'07
, 2007
"... We show that relational algebra calculations for incomplete databases, probabilistic databases, bag semantics and whyprovenance are particular cases of the same general algorithms involving semirings. This further suggests a comprehensive provenance representation that uses semirings of polynomials. ..."
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Cited by 179 (27 self)
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We show that relational algebra calculations for incomplete databases, probabilistic databases, bag semantics and whyprovenance are particular cases of the same general algorithms involving semirings. This further suggests a comprehensive provenance representation that uses semirings of polynomials. We extend these considerations to datalog and semirings of formal power series. We give algorithms for datalog provenance calculation as well as datalog evaluation for incomplete and probabilistic databases. Finally, we show that for some semirings containment of conjunctive queries is the same as for standard set semantics.
Parameter learning of logic programs for symbolicstatistical modeling
 Journal of Artificial Intelligence Research
, 2001
"... We propose a logical/mathematical framework for statistical parameter learning of parameterized logic programs, i.e. de nite clause programs containing probabilistic facts with a parameterized distribution. It extends the traditional least Herbrand model semantics in logic programming to distributio ..."
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Cited by 111 (20 self)
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We propose a logical/mathematical framework for statistical parameter learning of parameterized logic programs, i.e. de nite clause programs containing probabilistic facts with a parameterized distribution. It extends the traditional least Herbrand model semantics in logic programming to distribution semantics, possible world semantics with a probability distribution which is unconditionally applicable to arbitrary logic programs including ones for HMMs, PCFGs and Bayesian networks. We also propose a new EM algorithm, the graphical EM algorithm, thatrunsfora class of parameterized logic programs representing sequential decision processes where each decision is exclusive and independent. It runs on a new data structure called support graphs describing the logical relationship between observations and their explanations, and learns parameters by computing inside and outside probability generalized for logic programs. The complexity analysis shows that when combined with OLDT search for all explanations for observations, the graphical EM algorithm, despite its generality, has the same time complexity as existing EM algorithms, i.e. the BaumWelch algorithm for HMMs, the InsideOutside algorithm for PCFGs, and the one for singly connected Bayesian networks that have beendeveloped independently in each research eld. Learning experiments with PCFGs using two corpora of moderate size indicate that the graphical EM algorithm can signi cantly outperform the InsideOutside algorithm. 1.
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 76 (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
Logic programs with annotated disjunctions
 In Proc. Int’l Conf. on Logic Programming
, 2004
"... Abstract. Current literature offers a number of different approaches to what could generally be called "probabilistic logic programming". These are usually based on Horn clauses. Here, we introduce a new formalism, Logic Programs with Annotated Disjunctions, based on disjunctive lo ..."
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Cited by 74 (6 self)
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Abstract. Current literature offers a number of different approaches to what could generally be called &quot;probabilistic logic programming&quot;. These are usually based on Horn clauses. Here, we introduce a new formalism, Logic Programs with Annotated Disjunctions, based on disjunctive logic programs. In this formalism, each of the disjuncts in the head of a clause is annotated with a probability. Viewing such a set of probabilistic disjunctive clauses as a probabilistic disjunction of normal logic programs allows us to derive a possible world semantics, more precisely, a probability distribution on the set of all Herbrand interpretations. We demonstrate the strength of this formalism by some examples and compare it to related work.
Probabilistic Datalog: Implementing Logical Information Retrieval for Advanced Applications
 Journal of the American Society for Information Science
, 1999
"... In the logical approach to information retrieval (IR), retrieval is considered as uncertain inference. ..."
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Cited by 61 (8 self)
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In the logical approach to information retrieval (IR), retrieval is considered as uncertain inference.
Probabilistic Logic Programming
 In Proc. of the 13th European Conf. on Artificial Intelligence (ECAI98
, 1998
"... . We present a new approach to probabilistic logic programs with a possible worlds semantics. Classical program clauses are extended by a subinterval of [0; 1] that describes the range for the conditional probability of the head of a clause given its body. We show that deduction in the defined proba ..."
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Cited by 59 (11 self)
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. We present a new approach to probabilistic logic programs with a possible worlds semantics. Classical program clauses are extended by a subinterval of [0; 1] that describes the range for the conditional probability of the head of a clause given its body. We show that deduction in the defined probabilistic logic programs is computationally more complex than deduction in classical logic programs. More precisely, restricted deduction problems that are Pcomplete for classical logic programs are already NPhard for probabilistic logic programs. We then elaborate a linear programming approach to probabilistic deduction that is efficient in interesting special cases. In the best case, the generated linear programs have a number of variables that is linear in the number of ground instances of purely probabilistic clauses in a probabilistic logic program. 1 INTRODUCTION There is already a quite extensive literature on probabilistic propositional logics and their various dialects. The most fa...
The Complexity of Query Reliability
 IN PODS
, 1998
"... The reliability of database queries on databases with uncertain information is studied, on the basis of a probabilistic model for unreliable databases. While it was already known that the reliability of quantifierfree queries is computable in polynomial time, we show here that already for conjunctiv ..."
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Cited by 49 (2 self)
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The reliability of database queries on databases with uncertain information is studied, on the basis of a probabilistic model for unreliable databases. While it was already known that the reliability of quantifierfree queries is computable in polynomial time, we show here that already for conjunctive queries, the reliability may become highly intractable. We exhibit a conjunctive query whose reliability problem is complete for FP #P . We further show, that FP #P is the typical complexity level for the reliability problems of a very large class of queries, including all secondorder queries. We study approximation algorithms and prove that the reliabilities of all polynomialtime evaluable queries can be efficiently approximated by randomized algorithms. Finally we discuss the extension of our approach to the more general metafinite database model where finite relational structures are endowed with functions into an infinite interpreted domain; in addition queries may use aggregate ...
A Parametric Approach to Deductive Databases with Uncertainty
, 1997
"... Numerous frameworks have been proposed in recent years for deductive databases with uncertainty. These frameworks differ in (i) their underlying notion of uncertainty, (ii) the way in which uncertainties are manipulated, and (iii) the way in which uncertainty is associated with the facts and rules o ..."
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Cited by 48 (6 self)
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Numerous frameworks have been proposed in recent years for deductive databases with uncertainty. These frameworks differ in (i) their underlying notion of uncertainty, (ii) the way in which uncertainties are manipulated, and (iii) the way in which uncertainty is associated with the facts and rules of a program. On the basis of (iii), these frameworks can be classified into implication based (IB) and annotation based (AB) frameworks. In this paper, we develop a generic framework called the parametric framework as a unifying umbrella for IB frameworks. We develop the declarative, fixpoint, and prooftheoretic semantics of programs in the parametric framework and show their equivalence. Using this framework as a basis, we study the query optimization problem of containment of conjunctive queries in this framework, and establish necessary and sufficient conditions for containment for several classes of parametric conjunctive queries. Our results yield tools for use in the query optimization for large classes of query programs in IB deductive databases with uncertainty.
Query evaluation in probabilistic relational databases
 Theoretical Computer Science
, 1997
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