We present a model of inductive inference that includes, as special cases, Bayesian reasoning, case-based reasoning, and rule-based reasoning. This unified framework allows us to examine how the various modes of inductive inference can be combined and how their relative weights change...

We suggest a model in which theories are ranked given various databases. Certain axioms on such rankings imply a numerical representation that is the sum of the log-likelihood of the theory and a fixed number for each theory, which may be interpreted as a measure of its complexity. This additive...