AN INDUCTIVE METHOD FOR INEXACT REASONING

A notion of nondeterministic inference on inexact information is intro duced. The model is characterized by a second order probability distri bution on beliefs together with an updating procedure. Such nondetermi nistic inference processes naturally generate a corresponding determin istic process which essentially involves calculating the expected resp onse of the nondeterministic process. Given that the number of proposi tional variables in the relevant language may vary, it is natural to c onsider hierarchies of inference processes, these being characterized by hierarchies of prior distributions. A number of logical principles are considered which in the presence of certain smoothness assumptions restrict the choice of hierarchies to hierarchies of symmetric Dirich let priors where each prior is defined up to a parameter lambda which is constant over the whole hierarchy A principle of maximal expected d ependency between propositional variables is then introduced which res tricts lambda to a particular value. (C) 1997 Elsevier Science Inc.