Translating natural language to First-Order Logic (NL2FOL) is crucial for logic-based reasoning, but most existing models and benchmarks focus on English, leaving cross-lingual generalization underexplored. In this study, we present the first comprehensive investigation of cross-lingual robustness in NL2FOL. To support this, we introduce Multi-MALLS, the first multilingual benchmark for NL2FOL, which extends the widely-used MALLS dataset with high-quality translations into multiple languages. Using Multi-MALLS, we observe that state-of-the-art models experience a significant performance drop when applied to non-English inputs, highlighting the lack of robustness. To address this, we propose MA-FOL, a multi-agent framework that improves generalization without requiring any training on target languages. By decomposing the task into three modules, a language-agnostic structure generator, a language-specific predicate combiner, and a refinement component, MA-FOL achieves robust zero-shot generalization across diverse linguistic inputs. Additionally, we show that traditional evaluation metrics, such as Exact Match, often fail to assess semantic correctness. To remedy this, we introduce large language models (LLMs)-Judged Semantic Equivalence (SE), a new metric that leverages LLMs to evaluate whether generated formulas preserve the intended meaning. Extensive experiments demonstrate that MA-FOL outperforms strong baselines on Multi-MALLS, without any multilingual fine-tuning. The SE metric further reveals semantic correctness that traditional metrics miss. Overall, our work provides a benchmark to test robustness of NL2FOL, a framework to improve it, and a metric to evaluate it more effectively.

Chain-of-thought (CoT) prompting improves reasoning in large language models (LLMs) by externalizing intermediate computation as discrete text tokens, but this textual interface also introduces redundancy and inference overhead. Latent reasoning offers a promising alternative by carrying part of the computation in continuous representations. However, existing methods typically predefine when latent computation is invoked and how it is allocated during decoding, leaving a key problem unresolved: when to invoke latent computation, what type of computation to perform, and how much budget to allocate. We propose Typed Latent Reasoning(Tyler), a typed and budget-aware framework for latent reasoning during autoregressive decoding. Tyler learns a policy that, at each decoding step, chooses between emitting a visible token and invoking a typed latent operator. Once invoked, an operator maps the current reasoning state into latent tokens that support global planning, local state updates, or reusable procedural abstraction. Across extensive experiments on three backbone LLMs, Tyler improves accuracy by up to 14.49 points over CoT and by up to 4.30 points over the strongest competing baseline. It further generalizes across diverse reasoning domains and achieves the best final-stage performance with the lowest forgetting.