Separoids: A mathematical framework for conditional independence and irrelevance
We introduce an axiomatic definition of a mathematical structure that we term a separoid. We develop some general mathematical properties of separoids and related axiom systems, as well as connections with other mathematical structures, such as distributive lattices, Hilbert spaces, and graphs, And we show, by means of a detailed account of a number of models of the separoid axioms, how the concept of separoid unifies a variety of notions of 'irrelevance' arising out of different formalisms for representing uncertainty in Probability, Statistics, Artificial Intelligence, and other fields.
separoid irrelevance distributive lattice basic separoid belief function belief independence covariance independence directed markov gaphoid hyper independence join-orthogonal linear independence markov meta independence modular natural independence orthogonal independence orthogonoid possibility function probabilistic independence qualitative independence semi-graphoid semilattice statistical independence strong orthogonoid strong separoid submodular undirected markov variation independence