Learning and using relational theories: supporting material

We previously considered a Bayesian model based on our complexity measure, but Equations 2 and 3 can also be used to define a Bayesian model based on Goodman’s measure. The left columns show predictions when this model is applied to the inductive tasks in our first experiment. In order to combine Goodman’s model with Equations 2 and 3, each T in these equations must now refer to a candidate extension rather than a string of clauses. To keep matters simple, we did not sum over the space of all possible extensions, but considered only extensions with the lowest possible complexity score that was compatible with the training data. Goodman’s model and our model make similar predictions in four of the six conditions, but the Goodman model does not make accurate predictions about the transitive and exception predicates. Since Goodman’s complexity measure is not sensitive to the structural properties of these predicates, it cannot explain how these properties support inductive projections.