Conditional independence structures and graphical models

In this paper we study conditional independence structures arising from conditional probabilities and lower conditional probabilities. Such models are based on notions of stochastic independence apt to manage also those situations where zero evaluations on possible events are present: this is particularly crucial for lower probability. The "graphoid" properties of such models are investigated, and the representation problem of conditional independence structures is dealt with by generalizing the well-known classic separation criteria for undirected and directed acyclic graphs. Our graphical models describe the independence statements and the possible logical dependencies among the random variables.