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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 ..."
Abstract

Cited by 62 (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.