Research Tools & Code·arXiv cs.CL·May 18

FOL2NS: Generating Natural Sentences from First-Order Logic

Researchers have developed FOL2NS, a neurosymbolic system that bridges formal logic and natural language by generating synthetic first-order logic formulas and converting them to human-readable text. The framework tackles a persistent gap in NLP: most training corpora lack deeply nested logical structures with variable quantifier depths, limiting downstream performance in semantic parsing and theorem validation. By combining symbolic rule engines with fine-tuned language models, FOL2NS expands dataset diversity and coverage, addressing a bottleneck that affects reasoning-heavy applications across question answering and formal verification pipelines.

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Explainer

FOL2NS doesn't just generate more training data; it systematically produces the logical complexity patterns (variable quantifier nesting, scope depth) that real corpora omit. The insight is that diversity in data structure, not just volume, is what downstream reasoning tasks actually need.

This connects directly to the pattern we saw in the GA-S2S work from mid-May: language models trained on flattened representations miss relational structure that matters for reasoning. FOL2NS inverts that problem by starting with formal structure and converting to text, ensuring the synthetic corpus preserves the logical topology that semantic parsing and theorem validation require. Where GA-S2S adds graph attention to recover lost structure, FOL2NS prevents the loss upfront through generation. Both papers converge on the same diagnosis: standard text-only training leaves reasoning capabilities on the table.

If FOL2NS-trained models outperform baselines specifically on deeply nested quantifier problems (3+ levels of nesting) while showing no advantage on shallow logical structures, that confirms the synthetic data is actually targeting the right gap. If performance gains vanish when tested on real semantic parsing benchmarks outside the synthetic domain, the approach is solving a training artifact rather than a real bottleneck.

Coverage we drew on

Leveraging Graph Structure in Seq2Seq Models for Knowledge Graph Link Prediction · arXiv cs.CL

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MentionsFOL2NS · First-Order Logic · Natural Sentence

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