Modeling analogy as probabilistic grammar∗

Formal implemented models of analogy face two opposing challenges. On the one hand, they must be powerful and flexible enough to handle gradient and probabilistic data. This requires an ability to notice statistical regularities at many different levels of generality, and in many cases, to adjudicate between multiple conflicting patterns by assessing the relative strength of each, and to generalize them to novel items based on their relative strength. At the same time, when we examine evidence from language change, child errors, psycholinguistic experiments, we find that only a small fraction of the logically possible analogical inferences are actually attested. Therefore, an adequate model of analogy must also be restrictive enough to explain why speakers generalize certain statistical properties of the data and not others. Moreover, in the ideal case, restrictions on possible analogies should follow from intrinsic properties of the architecture of the model, and not need to be stipulated post hoc.