Theory-based Bayesian models of inductive reasoning 2 Theory-based Bayesian models of inductive reasoning

Everyday inductive inferences are often guided by rich background knowledge. Formal models of induction should aim to incorporate this knowledge, and should explain how different kinds of knowledge lead to the distinctive patterns of reasoning found in different inductive contexts. We present a Bayesian framework that attempts to meet both goals and describe four applications of the framework: a taxonomic model, a spatial model, a threshold model, and a causal model. Each model makes probabilistic inferences about the extensions of novel properties, but the priors for the four models are defined over different kinds of structures that capture different relationships between the categories in a domain. Our framework therefore shows how statistical inference can operate over structured background knowledge, and we argue that this interaction between structure and statistics is critical for explaining the power and flexibility of human reasoning.

This paper is an analysis of the claim that a universal ban on certain (‘anti-markedness’) grammars is necessary in order to explain their non-occurrence in the languages of the world. To assess the validity of this hypothesis I examine the implications of one sound change (a> �) for learning in a specific phonological domain (stress assignment), making explicit assumptions about the type of data that results, and the learning function that computes over that data. The preliminary conclusion is that restrictions on possible end-point languages are unneeded, and that the most likely outcome of change is a lexicon that is inconsistent with respect to a single generating rule. 1