Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Consistent conditional in noncooperative game theory
International Journal of Game Theory
Nonmonotonic reasoning, preferential models and cumulative logics
Artificial Intelligence
Probability and conditionals
Conditional Independence in A Coherent Finite Setting
Annals of Mathematics and Artificial Intelligence
Stochastic Independence in a Coherent Setting
Annals of Mathematics and Artificial Intelligence
Probabilistic Reasoning as a General Unifying Tool
ECSQARU '01 Proceedings of the 6th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Conditional independence structure and its closure: Inferential rules and algorithms
International Journal of Approximate Reasoning
Correction of incoherent conditional probability assessments
International Journal of Approximate Reasoning
An order of magnitude calculus
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Generalizing inference rules in a coherence-based probabilistic default reasoning
International Journal of Approximate Reasoning
Incoherence correction strategies in statistical matching
International Journal of Approximate Reasoning
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This paper examines concepts of independence for full conditional probabilities; that is, for set-functions that encode conditional probabilities as primary objects, and that allow conditioning on events of probability zero. Full conditional probabilities have been used in economics, in philosophy, in statistics, in artificial intelligence. This paper characterizes the structure of full conditional probabilities under various concepts of independence; limitations of existing concepts are examined with respect to the theory of Bayesian networks. The concept of layer independence (factorization across layers) is introduced; this seems to be the first concept of independence for full conditional probabilities that satisfies the graphoid properties of Symmetry, Redundancy, Decomposition, Weak Union, and Contraction. A theory of Bayesian networks is proposed where full conditional probabilities are encoded using infinitesimals, with a brief discussion of hyperreal full conditional probabilities.