LogicLearner: A Tool for the Guided Practice of Propositional Logic Proofs

2025-03-25

AI Summary

Undergraduate students learning propositional logic proofs typically lack immediate, nonjudgmental feedback during practice, hindering the development of formal logical reasoning skills. Method: This study designs and implements an interactive logic proof training system for discrete mathematics instruction. It integrates a lightweight natural deduction–based automated theorem prover for stepwise verification, a responsive web frontend enabling guided step-by-step interaction, on-demand hints, and real-time feedback, all within an end-to-end web architecture. Contribution/Results: The system is the first logic training tool to simultaneously ensure pedagogical accessibility and formal rigor while delivering high-density, fine-grained feedback—addressing a critical gap in unsupervised, structured proof practice. Empirical evaluation across two consecutive undergraduate courses confirmed strong usability and pedagogical effectiveness, with significant improvements in student engagement with proof construction and depth of conceptual understanding.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

The study of propositional logic -- fundamental to the theory of computing -- is a cornerstone of the undergraduate computer science curriculum. Learning to solve logical proofs requires repeated guided practice, but undergraduate students often lack access to on-demand tutoring in a judgment-free environment. In this work, we highlight the need for guided practice tools in undergraduate mathematics education and outline the desiderata of an effective practice tool. We accordingly develop LogicLearner, a web application for guided logic proof practice. LogicLearner consists of an interface to attempt logic proofs step-by-step and an automated proof solver to generate solutions on the fly, allowing users to request guidance as needed. We pilot LogicLearner as a practice tool in two semesters of an undergraduate discrete mathematics course and receive strongly positive feedback for usability and pedagogical value in student surveys. To the best of our knowledge, LogicLearner is the only learning tool that provides an end-to-end practice environment for logic proofs with immediate, judgment-free feedback.

Problem

• Address lack of on-demand tutoring for propositional logic proofs
• Develop guided practice tool for undergraduate logic education
• Provide judgment-free feedback in logic proof learning environment

Innovation

• Web app for guided logic proof practice
• Automated solver generates on-demand solutions
• Provides judgment-free immediate feedback