| Abstract: |
We concern ourselves with the situation in which we use the
Dempster-Shafer belief structure to provide a representation of a random
variables in which our knowledge of the probability distribution is
imprecise. We discuss the role of compatibility relations as a means of
enabling inference about one variable, the secondary variable, based upon
knowledge about another variable, the primary. We define monotonicity as a
condition in which an increase in information about the primary variable in
an inference should not result in a decrease in information about the
secondary variable. We show what are the conditions required of a
compatibility relation to lead to monotonic and nonmonotonic inferences.
We provide some examples of nonmonotonic relations.
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