  Humans can generate reasonable answers to novel queries (Schulz, 2012): if I
asked you what kind of food you want to eat for lunch, you would respond with a
food, not a time. The thought that one would respond "After 4pm" to "What would
you like to eat" is either a joke or a mistake, and seriously entertaining it
as a lunch option would likely never happen in the first place. While
understanding how people come up with new ideas, thoughts, explanations, and
hypotheses that obey the basic constraints of a novel search space is of
central importance to cognitive science, there is no agreed-on formal model for
this kind of reasoning. We propose that a core component of any such reasoning
system is a type theory: a formal imposition of structure on the kinds of
computations an agent can perform, and how they're performed. We motivate this
proposal with three empirical observations: adaptive constraints on learning
and inference (i.e. generating reasonable hypotheses), how people draw
distinctions between improbability and impossibility, and people's ability to
reason about things at varying levels of abstraction.
