Combining Deduction by Certainty with the Power of Magic

Schmidt, Helmut; Steger, Nikolaus; Güntzer, Ulrich; Kießling, Werner; Azone, Rüdiger; Bayer, Rudolf

doi:10.1016/b978-0-444-88433-6.50014-9

Cited by 8 publications

(4 citation statements)

References 11 publications

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“…Kiessling and his group [Kiessling et al 1992;Thone et al 1995;Schmidt et al 1987] have developed a framework called DUCK for reasoning with uncertainty. They provide an elegant logical axiomatic theory for uncertain reasoning in the presence of rules.…”

Section: Related Workmentioning

confidence: 99%

ProbView

Lakshmanan¹,

Leone

Ross

et al. 1997

ACM Trans. Database Syst.

254

123

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Probability theory is mathematically the best understood paradigm for modeling and manipulating uncertain information. Probabilities of complex events can be computed from those of basic events on which they depend, using any of a number of strategies. Which strategy is appropriate depends very much on the known interdependencies among the events involved. Previous work on probabilistic databases has assumed a fixed and restrictive combination strategy (e.g., assuming all events are pairwise independent). 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 Lakshmanan'a prototype probabilistic database system called ProbView on top of Dbase V.0. We validate our complexity results with experiments and show that rewriting certain types of queries to other equivalent forms often yields substantial savings.

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Section: Related Workmentioning

confidence: 99%

ProbView

Lakshmanan¹,

Leone

Ross

et al. 1997

ACM Trans. Database Syst.

254

123

View full text Add to dashboard Cite

show abstract

“…(1) Fuzzy logic programming: this was essentially introduced by van Emden in his seminal paper on quantitative deduction (van Emden, 1986), and further developed by various researchers, including Steger et al (1989) and Schmidt et al (1989).…”

Section: Non-probabilistic Formalismsmentioning

confidence: 99%

On a theory of probabilistic deductive databases

Lakshmanan

Sadri²

2001

Theory and Practice of Logic Programming

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We propose a framework for modeling uncertainty where both belief and doubt can be given independent, first-class 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 truth-ordering, 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.

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“…Kiessling and his group [23,50,41] have developed a framework called DUCK for reasoning with uncertainty. They provide an elegant, logical, axiomatic theory for uncertain reasoning in the presence of rules.…”

Section: Relationship With Work In Probabilistic Databasesmentioning

confidence: 99%

Probabilistic temporal databases, I

Dekhtyar

Ross

Subrahmanian

2001

ACM Trans. Database Syst.

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Dyreson and Snodgrass have drawn attention to the fact that in many temporal database applications, there is often uncertainty present about the start time of events, the end time of events, the duration of events, etc. When the granularity of time is small (e.g. milliseconds), a statement such as "Packet p was shipped sometime during the first 5 days of January, 1998" leads to a massive amount of uncertainty (5 24 60 60 1000)possibilities. As noted in [53], past attempts to deal with uncertainty in databases have been restricted to relatively small amounts of uncertainty in attributes. Dyreson and Snodgrass have taken an important first step towards solving this problem. In this paper, we first introduce the syntax of Temporal-Probabilistic (TP) relations and then show how they can be converted to an explicit, significantly more space-consuming form called Annotated Relations. We then present a Theoretical Annotated Temporal Algebra (TATA). Being explicit, TATA is convenient for specifying how the algebraic operations should behave, but is impractical to use because annotated relations are overwhelmingly large. Next, we present a Temporal Probabilistic Algebra (TPA). We show that our definition of the TP-Algebra provides a correct implementation of TATA despite the fact that it operates on implicit, succinct TP-relations instead of the overwhelmingly large annotated relations. Finally, we report on timings for an implementation of the TP-Algebra built on top of ODBC.

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Combining Deduction by Certainty with the Power of Magic

Cited by 8 publications

References 11 publications

ProbView

ProbView

On a theory of probabilistic deductive databases

Probabilistic temporal databases, I

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