###
3rd International Symposium
on

Imprecise
Probabilities and Their Applications

ISIPTA '03

#####
University of Lugano

Lugano, Switzerland

14-17 July 2003

####
ELECTRONIC PROCEEDINGS

# Graphical representation of asymmetric graphoid structures

### Abstract

Independence models induced by some uncertainty measures (e.g. conditional
probability, possibility) do not
obey the usual graphoid properties, since they do not satisfy the symmetry property.
They are efficiently representable through directed acyclic l-graphs by using L-separation
criterion.
In this paper, we show that in general there is not a l-graph which describes completely all the independence statements of a given
model;
hence we introduce in this context the notion of minimal I-map and we
show how to build it, given an ordering on the variables.

** Keywords. ** Conditional independence models, directed acyclic graph, L-separation criterion, I-map

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** Authors addresses: **

Dipartimento Metodi e Modelli Matematici

Universita' La Sapienza

via Scarpa n. 16 Roma,

00161, Italy

** E-mail addresses: **

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