Default Reasoning about Probabilities

Default reasoning about probabilities is the assignment of subjective probabilities

on the basis of partial information about an uncertain event, and statistical
knowledge about the domain of discourse. In this thesis a logic is developed for representing
probabilistic information about both statistical and subjective probabilities. The question
is explored about how exactly statistical knowledge should influence the formation of
degrees of belief. Strong arguments are presented that justify Cross-Entropy minimization as
the appropriate rule of inference. The minimum cross-entropy principle is implemented in a
preferred model semantics for the representation language. When probabilities are allowed to
take values in real closed fields with a logarithmic function a complete proof system for
the resulting logic is obtained.

November

1995

Siekmann