  Formal learning theory formalizes the process of inferring a general result
from examples, as in the case of inferring grammars from sentences when
learning a language. Although empirical evidence suggests that children can
learn a language without responding to the correction of linguistic mistakes,
the importance of Teacher in many other paradigms is significant. Instead of
focusing only on learner(s), this work develops a general framework---the
supervised learning game (SLG)---to investigate the interaction between Teacher
and Learner. In particular, our proposal highlights several interesting
features of the agents: on the one hand,Learner may make mistakes in the
learning process, and she may also ignore the potential relation between
different hypotheses; on the other hand, Teacher is able to correct Learner's
mistakes, eliminate potential mistakes and point out the facts ignored by
Learner. To reason about strategies in this game, we develop a modal logic of
supervised learning (SLL). Broadly, this work takes a small step towards
studying the interaction between graph games, logics and formal learning
theory.
