Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Information Sciences: an International Journal
Multivalued dependencies and a new normal form for relational databases
ACM Transactions on Database Systems (TODS)
An Almost Linear-Time Algorithm for Computing a Dependency Basis in a Relational Database
Journal of the ACM (JACM)
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
Reasoning about Uncertainty
Logical and algorithmic properties of stable conditional independence
International Journal of Approximate Reasoning
ACM Transactions on Database Systems (TODS)
Appropriate inferences of data dependencies in relational databases
Annals of Mathematics and Artificial Intelligence
On the implication problem for probabilistic conditional independency
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
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Conditional independence provides an essential framework to deal with knowledge and uncertainty in Artificial Intelligence, and is fundamental in probability and multivariate statistics. Its associated implication problem is paramount for building Bayesian networks. Saturated conditional independencies form an important subclass of conditional independencies. Under schema certainty, the implication problem of this subclass is finitely axiomatizable and decidable in almost linear time. We study the implication problem of saturated conditional independencies under both schema certainty and uncertainty. Under schema certainty, we establish a finite axiomatization with the following property: every independency whose implication is dependent on the underlying schema can be inferred by a single application of the so-called symmetry rule to some independency whose implication is independent from the underlying schema. Removing the symmetry rule from the axiomatization under schema certainty results in an axiomatization for a notion of implication that leaves the underlying schema undetermined. Hence, the symmetry rule is just a means to infer saturated conditional independencies whose implication is truly dependent on the schema.