edith@ai.toronto.edu (Edith Fraser) (02/06/90)
Department of Computer Science, University of Toronto
(GB = Gailbraith Building, 35 St. George Street)
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ARTIFICIAL INTELLIGENCE/THEORY SEMINAR
GB305, at 11:00 a.m., Thursday 15 February 1990
Professor Joe Halpern
U of T and IBM Almaden Rsch. Ctr.
"Two views of belief:
Belief as generalized probability and belief as evidence"
Belief functions are mathematical objects defined to satisfy three axioms
that look somewhat similar to the Kolmogorov axioms defining probability
functions. We argue that there are (at least) two useful and quite
different ways of understanding belief functions. The first is as a
generalized probability function (which technically corresponds to the
inner measure induced by a probability function). The second is as a way
of representing evidence. Evidence, in turn, can be understood as a
mapping from probability functions to probability functions. It makes
sense to think of updating a belief if we think of it as a generalized
probability. We provide a way of updating beliefs that is different from
and, we claim, more appropriate than that proposed by Dempster (in terms of
his rule of combination), and argue that it is more appropriate. On the
other hand, it does makes sense to combine two beliefs (using, say,
Dempster's rule of combination) if we think of the belief functions as
representing evidence.
Many researchers have pointed out problems with the belief function
approach; we show how all these problems can be explained as a consequence
of confounding these two views of belief functions.
This is joint work with Ron Fagin. The talk is completely self-contained;
no previous knowledge of belief functions will be assumed.