Statistical treatment of the information content of a database
Information Systems
IEEE Transactions on Software Engineering
IEEE Transactions on Software Engineering
Probabilistic reasoning in intelligent systems: networks of plausible inference
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Uncertainty and vagueness in knowledge based systems
Uncertainty and vagueness in knowledge based systems
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ACM Transactions on Database Systems (TODS)
Multivalued dependencies and a new normal form for relational databases
ACM Transactions on Database Systems (TODS)
On the Equivalence of Database Models
Journal of the ACM (JACM)
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A complete axiomatization for functional and multivalued dependencies in database relations
SIGMOD '77 Proceedings of the 1977 ACM SIGMOD international conference on Management of data
Introduction to Bayesian Networks
Introduction to Bayesian Networks
Uncertain Information Processing in Expert Systems
Uncertain Information Processing in Expert Systems
The Management of Probabilistic Data
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Representation of Bayesian Networks as Relational Databases
IPMU'94 Selected papers from the 5th International Conference on Processing and Management of Uncertainty in Knowledge-Based Systems, Advances in Intelligent Computing
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Proceedings of the Seventh International Working Conference on Scientific and Statistical Database Management
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Theory of Relational Databases
Theory of Relational Databases
A method for implementing a probabilistic model as a relational database
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
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IEEE Transactions on Knowledge and Data Engineering
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Proceedings of the 2007 ACM SIGMOD international conference on Management of data
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This paper demonstrates the relational structure of belief networks by establishing an extended relational data model which can be applied to both belief networks and relational applications. It is demonstrated that a Markov network can be represented as a generalized acyclic join dependency (GAJD) which is equivalent to a set of conflict-free generalized multivalued dependencies (GMVDs). A Markov network can also be characterized by an entropy function, which greatly facilitates the manipulation of GMVDs. These results are extensions of results established in relational theory. It is shown that there exists a complete set of inference rules for the GMVDs. This result is important from a probabilistic perspective. All the above results explicitly demonstrate that there is a unified model for relational database and probabilistic reasoning systems. This is not only important from a theoretical point of view in that one model has been developed for a number of domains, but also from a practical point of view in that one system can be implemented for both domains. This implemented system can take advantage of the performance enhancing techniques developed in both fields. Thereby, this paper serves as a theoretical foundation for harmonizing these two important information domains.