KELPS: A Framework for Verified Multi-Language Autoformalization via Semantic-Syntactic Alignment

2025-07-11

AI Summary

To address the scarcity and low quality of parallel corpora for automatic formalization of informal mathematics into proof assistants (e.g., Lean, Coq, Isabelle), this paper introduces KELPS—a knowledge-enhanced neural-symbolic framework. It employs Knowledge Equations (KEs) as a semantic–syntactic alignment intermediate representation, integrating assertion logic theory to construct a verifiable neural-symbolic system. Formalization proceeds via KE translation, formal rule mapping, and iterative data synthesis and filtering—ensuring semantic fidelity. We curate a high-quality multilingual parallel corpus comprising 62,000 problems and achieve 88.9% syntactic accuracy on MiniF2F, substantially outperforming state-of-the-art models including DeepSeek-V3 and Herald. The core contributions are: (1) the KE intermediate representation, which bridges informal mathematical statements and formal syntax through logically grounded equations; and (2) a novel neural-symbolic co-generation paradigm for verified formalization, unifying deductive reasoning with learned translation.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Natural Language Processing: Sentence-level Semantics, Textual Inference, etc.
• Machine Learning: Neuro-Symbolic Learning

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Large pretrained models with web data
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Modern large language models (LLMs) show promising progress in formalizing informal mathematics into machine-verifiable theorems. However, these methods still face bottlenecks due to the limited quantity and quality of multilingual parallel corpora. In this paper, we propose a novel neuro-symbolic framework KELPS (Knowledge-Equation based Logical Processing System) to address these problems. KELPS is an iterative framework for translating, synthesizing, and filtering informal data into multiple formal languages (Lean, Coq, and Isabelle). First, we translate natural language into Knowledge Equations (KEs), a novel language that we designed, theoretically grounded in assertional logic. Next, we convert them to target languages through rigorously defined rules that preserve both syntactic structure and semantic meaning. This process yielded a parallel corpus of over 60,000 problems. Our framework achieves 88.9% syntactic accuracy (pass@1) on MiniF2F, outperforming SOTA models such as Deepseek-V3 (81%) and Herald (81.3%) across multiple datasets. All datasets and codes are available in the supplementary materials.

Problem

• Addressing limited multilingual parallel corpora for autoformalization
• Translating natural language to formal languages accurately
• Improving syntactic accuracy in theorem formalization across datasets

Innovation

• Uses Knowledge Equations for semantic-syntactic alignment
• Converts equations to formal languages via strict rules
• Generates large parallel corpus for multi-language formalization