A colleague of mine and I have recently decided to tackle a project which we think has important ramifications for the field of artificial intelligence. We're vaguely aware that relevant work has been done at places like Carnegie Mellon and are hoping to get some guidance.
Our two overarching goals are to discover how models are constructed and to develop a model 'calculus' describing how an agent searches the space of possible hypotheses. We want to examine these questions from a number of different perspectives, studying the means by which both human and artificial agents actually arrive at models that allow them to understand the world, as well as the ways in which they would do so were they performing optimally.
Our motivation is to probe the subtle interchange between inductive and deductive reasoning. When is it that an agent moves from merely noticing patterns in data to reasoning on the basis of an axiomatic, deductive, predictive theory? Does it work differently in different domains? Do these inflection points have common characteristics, and, if so, can we use them to form a general theory of theories?
Does this framing even make any sense?
Along the way we hope to address a number of ancillary questions. Perhaps we can arrive at a formal theory of models, or probe the similarities and differences in how artificial intelligences and humans approach the task of compressing data down into simpler representations. There are obvious connections to Thomas Kuhn, to David Hume's is/ought problem, and to vast swathes of the philosophy of science.
We'd like help locating important books, seminal papers, good overview materials, words or phrases we can Google, theorists that have pushed the field forward, anything like that.