Because it is not always possible to get complete infor- mation
or knowledge about the evidence, so the uncertainty problems
arise. One of the characteristics of human reasoning is the
ability to draw inferences under uncertain circumstance. This
ability is quite useful and intuitive, but sometimes it may not
be able to form useful conclusions especially when a large
amount of hypotheses are presented. In rule-based expert
systems, the knowledge is represented in the form of the
production rules. The knowledge rules may have many exceptions
which cannot afford to enumerate. One way to summarize
exceptions is to assign to each proposition a numerical measure
of uncertainty and then combine these measures according to
some principles. This approach has been adopted by first-
generation expert systems such as MYCIN [Shortliffe 1975] and
PROSPECTOR [Duda et al. 1978]. Such an approach does not alter
the modularity of inference rules in classical logic, and the
modularity can not be sustained in problems of uncertainty. To
draw inferences under uncertain circumstance, we should
consider the source of evidence and the causal relations
between evidence. The causal relations can be represented in
conditional probabilities, and the subjective Bayesian view of
uncertainty can provide many of the features demanded by expert
systems [Spiegelhalter 1986]. The main purposes of this thesis
are : . to explicit the difficulties in plausible reasoning, .
to represent and establish the knowledge for reasoning under
uncertain circumstance, . to combine the impact of evidence
rationally, and . to establish the Bayesian scheme for
evidential reasoning. The Polytree algorithm is a Bayesian
method for evidential reasoning [Kim and Pearl 1983; Pearl
1986; Pearl 1988]. It is adopted to combine and propagate the
impact of evidence in this thesis.