Formal Reasoning Meets LLMs: Toward AI for Mathematics and Verification

Overview

Syllabus

• Introduction to Formal Reasoning and Large Language Models (LLMs)
Overview of formal reasoning in AI
Introduction to Large Language Models (LLMs)
Applications of AI in mathematics and verification
• Theorem Proving
Basics of formal logic and theorem proving
Overview of automated theorem proving systems
Hands-on exercises with theorem provers
• Autoformalization
Understanding autoformalization and its challenges
Techniques for autoformalization
Case studies on successful formalizations
• AI for Inequality Problems
Analysis of inequality problem domains
Implementation of AI solutions for inequality problems
Project: Developing an AI-based system for solving inequality problems
• Formalization of Euclidean Geometry
Introduction to Euclidean geometry concepts
Challenges in formalizing geometry using AI
Project: Formalizing Euclidean geometry theorems with AI systems
• Integrating LLMs in Formal Reasoning
Role of LLMs in enhancing formal reasoning capabilities
Techniques for integrating LLMs with theorem provers
Examples of LLM-enhanced formal reasoning systems
• Research and Challenges in AI for Mathematics
Current research in AI-driven mathematics
Key challenges and open problems
Future directions for AI in formal mathematics and verification
• Project Presentations and Feedback
Final project presentations
Peer review and feedback sessions
Course reflections and concluding discussions

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Subjects

Computer Science