On the Right Path: A Modal Logic for Supervised Learning
Abstract
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.
Cite
@article{arxiv.1909.08559,
title = {On the Right Path: A Modal Logic for Supervised Learning},
author = {Alexandru Baltag and Dazhu Li and Mina Young Pedersen},
journal= {arXiv preprint arXiv:1909.08559},
year = {2019}
}
Comments
The paper was accepted by LORI 2019. But due to the page-limit constraints, that Proceedings version does not include any proofs. In this version, we show the proofs for the results