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Qualitative reasoning in Bayesian networks. (English) Zbl 0861.03015

Write “If \(A\) is true, then typically \(B\) is true” as “\(A|\sim B\)”. This conditional assertion is not defined as \(P(B|A)>P(\neg B|A)\) because this would imply \(P(B|A)>0.5\), “…and this seems too strong a requirement”. (p. 127) If \(P\) is a finitely additive measure on the language \(L\), then there are a number of probabilistically valid rules that can be stated for the relation of typicality. For example, \[ \text{If\;}A\to B,C|\sim A,\text{ and }B\text{ is independent of }C\text{ given }\neg A, \text{ then }C|\sim B. \] The majority of these rules parallel rules in ‘preferential logic’; a number of rules are offered that have no parallels in preferential logic, but which reflect frequently accepted principles of inductive logic. Using these rules, we can read off typicality assertions from a proposed DAG. A further group of qualitative inference rules follow from Jeffrey’s rule applied to marginal probabilities. These correspond to natural inferences such as “if \(A\) becomes more plausible, and \(B\) is a plausible consequence of \(A\), then \(B\) becomes more plausible”. These ideas are applied to the issue of belief revision via expansion, revision, or contraction, discussed by Gärdenfors, Makinson, and others. It is claimed that the modularity provided by the interpretation of typicality claims within Bayesian networks provides computational efficiency for these kinds of changes.

MSC:

03B48 Probability and inductive logic
68T27 Logic in artificial intelligence
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