Towards a Common Framework for Autoformalization

2025-09-11

AI Summary

Current automated formalization research is fragmented across subfields—including mathematical theorem proving and natural language-to-logic translation—hampered by inconsistent terminology, absent standardized benchmarks, and theoretical isolation, which severely impede method reuse and collaborative advancement. To address this, we propose the first unified framework that systematically integrates both explicit formalization tasks (e.g., translating mathematical statements into formal logic) and implicit formalization tasks (e.g., extracting latent logical structure from informal text). We establish a cross-domain terminology taxonomy and principled benchmark design guidelines. Furthermore, we introduce a formalization pipeline that synergistically combines large language models with interactive theorem provers. This framework bridges theoretical divides, enables cross-task method transfer, and fosters integration of AI capabilities across reasoning, knowledge representation, and planning—laying foundational groundwork for next-generation verifiable AI systems.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Natural Language Processing: (Large) Language Models
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Large language models for search
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Autoformalization has emerged as a term referring to the automation of formalization - specifically, the formalization of mathematics using interactive theorem provers (proof assistants). Its rapid development has been driven by progress in deep learning, especially large language models (LLMs). More recently, the term has expanded beyond mathematics to describe the broader task of translating informal input into formal logical representations. At the same time, a growing body of research explores using LLMs to translate informal language into formal representations for reasoning, planning, and knowledge representation - often without explicitly referring to this process as autoformalization. As a result, despite addressing similar tasks, the largely independent development of these research areas has limited opportunities for shared methodologies, benchmarks, and theoretical frameworks that could accelerate progress. The goal of this paper is to review - explicit or implicit - instances of what can be considered autoformalization and to propose a unified framework, encouraging cross-pollination between different fields to advance the development of next generation AI systems.

Problem

• Creating unified autoformalization framework across disciplines
• Bridging independent research areas for shared methodologies
• Translating informal inputs into formal logical representations

Innovation

• Using large language models for formalization
• Proposing unified autoformalization framework across fields
• Translating informal inputs into logical representations