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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
Lifted firstorder probabilistic inference
 In Proceedings of IJCAI05, 19th International Joint Conference on Artificial Intelligence
, 2005
"... Most probabilistic inference algorithms are specified and processed on a propositional level. In the last decade, many proposals for algorithms accepting firstorder specifications have been presented, but in the inference stage they still operate on a mostly propositional representation level. [Poo ..."
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Cited by 122 (8 self)
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Most probabilistic inference algorithms are specified and processed on a propositional level. In the last decade, many proposals for algorithms accepting firstorder specifications have been presented, but in the inference stage they still operate on a mostly propositional representation level. [Poole, 2003] presented a method to perform inference directly on the firstorder level, but this method is limited to special cases. In this paper we present the first exact inference algorithm that operates directly on a firstorder level, and that can be applied to any firstorder model (specified in a language that generalizes undirected graphical models). Our experiments show superior performance in comparison with propositional exact inference. 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 68 (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.
On A Theory of Probabilistic Deductive Databases
 THEORY AND PRACTICE OF LOGIC PROGRAMMING
, 2001
"... We propose a framework for modeling uncertainty where both belief and doubt can be given independent, firstclass status. We adopt probability theory as the mathematical formalism for manipulating uncertainty. An agent can express the uncertainty in her knowledge about a piece of information in the ..."
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Cited by 28 (0 self)
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We propose a framework for modeling uncertainty where both belief and doubt can be given independent, firstclass status. We adopt probability theory as the mathematical formalism for manipulating uncertainty. An agent can express the uncertainty in her knowledge about a piece of information in the form of a confidence level, consisting of a pair of intervals of probability, one for each of her belief and doubt. The space of confidence levels naturally leads to the notion of a trilattice, similar in spirit to Fitting's bilattices. Intuitively, the points in such a trilattice can be ordered according to truth, information, or precision. We develop a framework for probabilistic deductive databases by associating confidence levels with the facts and rules of a classical deductive database. While the trilattice structure offers a variety of choices for defining the semantics of probabilistic deductive databases, our choice of semantics is based on the truthordering, which we find to be closest to the classical framework for deductive databases. In addition to proposing a declarative semantics based on valuations and an equivalent semantics based on fixpoint theory, we also propose a proof procedure and prove it sound and complete. We show that while classical Datalog query programs have a polynomial time data complexity, certain query programs in the probabilistic deductive database framework do not even terminate on some input databases. We identify a large natural class of query programs of practical interest in our framework, and show that programs in this class possess polynomial time data complexity, i.e. not only do they terminate on every input database, they are guaranteed to do so in a number of steps polynomial in the input database size.
A Survey of FirstOrder Probabilistic Models
, 2008
"... There has been a long standing division in Artificial Intelligence between logical and probabilistic reasoning approaches. While probabilistic models can deal well with inherent uncertainty in many realworld domains, they operate on a mostly propositional level. Logic systems, on the other hand, c ..."
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Cited by 10 (0 self)
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There has been a long standing division in Artificial Intelligence between logical and probabilistic reasoning approaches. While probabilistic models can deal well with inherent uncertainty in many realworld domains, they operate on a mostly propositional level. Logic systems, on the other hand, can deal with much richer representations, especially firstorder ones, but treat uncertainty only in limited ways. Therefore, an integration of these types of inference is highly desirable, and many approaches have been proposed, especially from the 1990s on. These solutions come from many different subfields and vary greatly in language, features and (when available at all) inference algorithms. Therefore their relation to each other is not always clear, as well as their semantics. In this survey, we present the main aspects of the solutions proposed and group them according to language, semantics and inference algorithm. In doing so, we draw relations between them and discuss particularly important choices and tradeoffs.
Beyond Fuzzy: Parameterized Approximations of Heyting Algebras for Uncertain Knowledge
"... Abstract. We propose a parameterized framework based on a Heyting algebra and Lukasiewicz negation for modeling uncertainty for belief. We adopt a probability theory as mathematical formalism for manipulating uncertainty. An agent can express the uncertainty in her knowledge about a piece of informa ..."
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Abstract. We propose a parameterized framework based on a Heyting algebra and Lukasiewicz negation for modeling uncertainty for belief. We adopt a probability theory as mathematical formalism for manipulating uncertainty. An agent can express the uncertainty in her knowledge about a piece of information in the form of belief types: as a single probability, as an interval (lower and upper boundary for a probability) or as a confidence level. The probabilistic logic programs can be parameterized by different kinds of conjunctive/disjunctive ”probabilistic strategies ” for their rules based on residuumimplication. The underlying algebra for belief computation is a parameterized approximation of strict (without negation) Heyting (or briefly ’parameterized Heyting’) algebra with a unique epistemic negation: it is a set of Lukasiewiczstyle residuated lattices and extension of fuzzy logic technique to wide family of probabilistic logic programming and deductive databases. Such framework offers a clear semantics for the satisfaction relation of different probabilistic formalisms used for handling uncertainty, and is open toward the extension of logic languages for formulae with residuumbased implications also in the body of rules. 1
Temporal Probabilistic Logic Programs: State and Revision
"... There are numerous applications where we have to deal with temporal uncertainty associated with events. The Temporal Probabilistic (TP) Logic Programs should provide support for validtime indeterminacy of events, by proposing the concept of an indeterminate instant, that is, an interval of timepoi ..."
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There are numerous applications where we have to deal with temporal uncertainty associated with events. The Temporal Probabilistic (TP) Logic Programs should provide support for validtime indeterminacy of events, by proposing the concept of an indeterminate instant, that is, an interval of timepoints (event’s timewindow) with an associated, lower and upper, probability distribution. In particular, we propose the new semantics, for the TP Logic Programs of Dekhtyar and Subrahmanian. Our semantics, based on the possible world semantics is a generalization of the possible world semantics for (non temporal) Probabilistic Logic Programming, and we define the new syntax for PTprograms, with time variable explicitly represented in all atoms, and show how the standard role of Herbrand interpretations used as possible worlds for probability distributions is coherently extended to Temporal Probabilistic Logic Programming. 1
Temporal Probabilistic Logic Programs: State and Revision
"... There are numerous applications where we have to deal with temporal uncertainty associated with events. The Temporal Probabilistic (TP) Logic Programs should provide support for validtime indeterminacy of events, by proposing the concept of an indeterminate instant, that is, an interval of time ..."
Abstract
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There are numerous applications where we have to deal with temporal uncertainty associated with events. The Temporal Probabilistic (TP) Logic Programs should provide support for validtime indeterminacy of events, by proposing the concept of an indeterminate instant, that is, an interval of timepoints (event’s timewindow) with an associated, lower and upper, probability distribution. In particular, we propose the new semantics, for the TP Logic Programs of Dekhtyar and Subrahmanian. Our semantics, based on the possible world semantics is a generalization of the possible world semantics for (non temporal) Probabilistic Logic Programming, and we define the new syntax for PTprograms, with time variable explicitly represented in all atoms, and show how the standard role of Herbrand interpretations used as possible worlds for probability distributions is coherently extended to Temporal Probabilistic Logic Programming. 1