Conservative Inference Rule for Uncertain Reasoning under Incompleteness
  In this paper we formulate the problem of inference under incomplete
information in very general terms. This includes modelling the process
responsible for the incompleteness, which we call the incompleteness process.
We allow the process behaviour to be partly unknown. Then we use Walleys theory
of coherent lower previsions, a generalisation of the Bayesian theory to
imprecision, to derive the rule to update beliefs under incompleteness that
logically follows from our assumptions, and that we call conservative inference
rule. This rule has some remarkable properties: it is an abstract rule to
update beliefs that can be applied in any situation or domain; it gives us the
opportunity to be neither too optimistic nor too pessimistic about the
incompleteness process, which is a necessary condition to draw reliable while
strong enough conclusions; and it is a coherent rule, in the sense that it
cannot lead to inconsistencies. We give examples to show how the new rule can
be applied in expert systems, in parametric statistical inference, and in
pattern classification, and discuss more generally the view of incompleteness
processes defended here as well as some of its consequences.
