Challenge: First-order logic (FOL) is often used to represent logical entailment, but determining natural language (NL) enanglement using FOL remains a challenge.
Approach: They propose an Entailment-Preserving FOL representations task and a method which trains an NL-to-FOL translator by using the natural language entailment labels as verifiable rewards.
Outcome: The proposed method achieves 1.8–2.7% improvement in EPR and 17.4–20.6% increase in E PR@16 compared to baselines in three datasets.

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Challenge: Existing benchmarks for logical reasoning in large language models lack language naturalness or limited complexity.
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Parsing Natural Language into Propositional and First-Order Logic with Dual Reinforcement Learning (2022.coling-1)

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Challenge: Existing methods to parse natural language into structured logical expressions have limitations due to paucity of labeled data.
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Enhancing Systematic Decompositional Natural Language Inference Using Informal Logic (2024.emnlp-main)

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Challenge: Recent language models allow structured reasoning with text, but lack of a clear protocol for discerning entailment causes noisy datasets and limited performance gains.
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Harnessing the Power of Large Language Models for Natural Language to First-Order Logic Translation (2024.acl-long)

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Challenge: Logic-based approaches to reasoning have lost popularity due to limited scalability and coverage.
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Natural Logic at the Core: Dynamic Rewards for Entailment Tree Generation (2025.findings-acl)

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Challenge: Existing approaches to generating entailment trees lack logical consistency . static reward structures or intricate dependencies within multi-step reasoning are often ignored .
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Challenge: Recent studies have focused on translation of natural language to first-order logical formula (NL-FOL) but these methods face challenges such as inconsistency between training and inference phases and data-intensive finetuning process.
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From the One, Judge of the Whole: Typed Entailment Graph Construction with Predicate Generation (2023.acl-long)

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Challenge: Existing methods to construct entailment graphs suffer from severe sparsity issues due to limited corpora and the long-tail phenomenon of predicate distributions.
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Diagnosing the First-Order Logical Reasoning Ability Through LogicNLI (2021.emnlp-main)

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Challenge: Existing studies have focused on diagnosing LMs' reasoning abilities in natural language understanding tasks.
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PropSegmEnt: A Large-Scale Corpus for Proposition-Level Segmentation and Entailment Recognition (2023.findings-acl)

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Challenge: Existing systems for Natural Language Inference (NLI) only recognize textual entailment relations on sentence-level . however, even a simple sentence often contains multiple propositions, i.e. distinct units of meaning conveyed by the sentence .
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NL2Logic: AST-Guided Translation of Natural Language into First-Order Logic with Large Language Models (2026.findings-eacl)

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Challenge: Structured reasoning approaches that parse first-order logic rules from natural language lack syntax control and semantic faithfulness.
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