FOL2NS: Generating Natural Sentences from First-Order Logic

TL;DR

FOL2NS is a neurosymbolic framework that generates synthetic first-order logic formulas and converts them into natural language, improving diversity and coverage for NLP applications.

Contribution

The paper introduces FOL2NS, a novel neurosymbolic approach combining rule-based modules and language models to generate and translate complex FOL formulas into natural sentences.

Findings

FOL2NS can reliably produce well-formed logical templates.

The framework generates fluent natural language expressions.

Challenges remain in semantic accuracy with increased structural complexity.

Abstract

Translating formal language into natural language is a foundational challenge in NLP, driving various downstream applications in semantic parsing, theorem validation, and question answering. In this study, we introduce First-Order Logic to Natural Sentence (FOL2NS), a neurosymbolic framework designed to generate synthetic FOL formulas and convert them into natural human expressions. It handles deeply nested structures with varying quantifier depths (QD), which are rarely captured by existing corpora. By combining rule-driven modules with fine-tuned language models, FOL2NS enhances the diversity and coverage of the generated samples. In our experiments, we systematically evaluate the framework's capabilities through both character-level analysis and overall performance metrics. Experimental results show that FOL2NS can reliably produce well-formed templates and fluent statements, but it faces challenges in achieving precise semantic representations and natural generation as structural complexity increases.