DAG representation of asymmetric independence models arising in coherent conditional possibility theory

In this paper we study the representation by means of an acyclic directed graph (DAG) of the independence model induced by a coherent T-conditional possibility (where T stands for the minimum or a strict t-norm). Such models are in general not closed under symmetric property, so we must rely on a proper asymmetric notion of vertex separation which produces structures closed under all graphoid properties and their reverses except for symmetry (namely, asymmetric graphoids). Focusing on this kind of models we present an efficient procedure to generate and represent them symbolically. We then introduce asymmetric Markov properties and prove their equivalence, providing in this way a method to extract the model encoded in a DAG. Finally, an algorithm to build a minimal I-map, given an ordering of the random variables, is drawn.