On the Right Path: A Modal Logic for Supervised Learning

TL;DR

This paper introduces a modal logic framework to model the interaction between Teacher and Learner in supervised learning, accounting for mistakes and corrections, bridging formal learning theory with game and logic perspectives.

Contribution

It develops a novel modal logic for supervised learning that captures complex agent interactions, including mistakes and corrections, within a formal game-theoretic setting.

Findings

Framework models Teacher-Learner interactions in supervised learning.

Logic captures mistakes, corrections, and ignored hypotheses.

Bridges formal learning theory with game and logic approaches.

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.