  We view the syntax-based approaches to default reasoning as a model-based
diagnosis problem, where each source giving a piece of information is
considered as a component. It is formalized in the ATMS framework (each source
corresponds to an assumption). We assume then that all sources are independent
and "fail" with a very small probability. This leads to a probability
assignment on the set of candidates, or equivalently on the set of consistent
environments. This probability assignment induces a Dempster-Shafer belief
function which measures the probability that a proposition can be deduced from
the evidence. This belief function can be used in several different ways to
define a non-monotonic consequence relation. We study and compare these
consequence relations. The -case of prioritized knowledge bases is briefly
considered.
