Generating Graphoids from Generalised Conditional Probability
  We take a general approach to uncertainty on product spaces, and give
sufficient conditions for the independence structures of uncertainty measures
to satisfy graphoid properties. Since these conditions are arguably more
intuitive than some of the graphoid properties, they can be viewed as
explanations why probability and certain other formalisms generate graphoids.
The conditions include a sufficient condition for the Intersection property
which can still apply even if there is a strong logical relations hip between
the variables. We indicate how these results can be used to produce theories of
qualitative conditional probability which are semi-graphoids and graphoids.
