Doing Model Theory for Learning

Problem Statement

Develop the model theory of learning. What axioms capture important properties of learning? What do models of these properties look like? Are there “correspondences” between axioms and properties of models, as there often are in modal logic?

Things to Try

• First, write a list of properties, including “Polya’s stepwise induction,” “learning curve monotonicity,” “no forgetting.” Think of dynamic logic axioms that should capture these (in general, for any update)
• Go the other way around – dig for axioms, and think of what properties they express. (These may be more well-known…)