Introduction to mathematical logic (3rd ed.)
Introduction to mathematical logic (3rd ed.)
Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Axioms and algorithms for inferences involving probabilistic independence
Information and Computation
Information Sciences: an International Journal
Stochastic independence, algebraic independence and abstract connectedness
Theoretical Computer Science
Independence concepts in possibility theory: part I
Fuzzy Sets and Systems
Representation of irrelevance relations by annotated graphs
Fundamenta Informaticae
Conditional independence relations in possibility theory
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems - special issue on models for imprecise probabilities and partial knowledge
Probabilistic Networks and Expert Systems
Probabilistic Networks and Expert Systems
Semigraphoids and structures of probabilistic conditional independence
Annals of Mathematics and Artificial Intelligence
Separoids: A Mathematical Framework for Conditional Independence and Irrelevance
Annals of Mathematics and Artificial Intelligence
A hypergraph-theoretic analysis of collapsibility and decomposability for extended log-linear models
Statistics and Computing
Formal Properties of Conditional Independence in Different Calculi of AI
ECSQARU '93 Proceedings of the European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty
Chain graphs: semantics and expressiveness
ECSQARU '95 Proceedings of the European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty
Causal networks: semantics and expressiveness
UAI '88 Proceedings of the Fourth Annual Conference on Uncertainty in Artificial Intelligence
UAI '88 Proceedings of the Fourth Annual Conference on Uncertainty in Artificial Intelligence
Conditional Independences among Four Random Variables III: Final Conclusion
Combinatorics, Probability and Computing
Directed cyclic graphical representations of feedback models
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Critical remarks on single link search in learning belief networks
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
Exploiting independencies to compute semigraphoid and graphoid structures
International Journal of Approximate Reasoning
Conditional independences in gaussian vectors and rings of polynomials
WCII'02 Proceedings of the 2002 international conference on Conditionals, Information, and Inference
Local computations in Dempster--Shafer theory of evidence
International Journal of Approximate Reasoning
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The topic of this survey are structures of stochastic conditional independence. Two basic questions are dealt with: the problem of characterization of conditional independence models and the problem of their mathematical description and computer representation. Basic formal properties of conditional independence are recapitulated and the problem of axiomatic characterization of stochastic conditional independence models is mentioned. Classic graphical methods of description of these structures are recalled, in particular, the method which uses chain graphs. Limitation of graphical approaches motivated an attempt at a non-graphical approach. A certain method of description of stochastic conditional independence models which uses non-graphical tools called ‘structural imsets’ is outlined.