Large language models (LLMs) and theorem provers (TPs) can be effectively combined for verifiable natural language inference (NLI). However, existing approaches rely on a fixed logical formalism, a feature that limits robustness and adaptability. We propose a logic-parametric framework for neuro-symbolic NLI that treats the underlying logic not as a static background, but as a controllable component. Using the LogiKEy methodology, we embed a range of classical and non-classical formalisms into higher-order logic (HOL), enabling a systematic comparison of inference quality, explanation refinement, and proof behavior. We focus on normative reasoning, where the choice of logic has significant implications. In particular, we compare logic-external approaches, where normative requirements are encoded via axioms, with logic-internal approaches, where normative patterns emerge from the logic's built-in structure. Extensive experiments demonstrate that logic-internal strategies can consistently improve performance and produce more efficient hybrid proofs for NLI. In addition, we show that the effectiveness of a logic is domain-dependent, with first-order logic favouring commonsense reasoning, while deontic and modal logics excel in ethical domains. Our results highlight the value of making logic a first-class, parametric element in neuro-symbolic architectures for more robust, modular, and adaptable reasoning.

翻译：大语言模型（LLM）与定理证明器（TP）的有效结合可用于实现可验证的自然语言推理（NLI）。然而，现有方法依赖于固定的逻辑形式体系，这一特性限制了其鲁棒性与适应性。我们提出了一种用于神经符号NLI的逻辑参数化框架，该框架将底层逻辑视为一个可控组件，而非静态背景。利用LogiKEy方法，我们将一系列经典与非经典形式体系嵌入高阶逻辑（HOL）中，从而能够系统比较推理质量、解释精化与证明行为。我们重点关注规范性推理领域，其中逻辑选择具有重要影响。具体而言，我们比较了逻辑外部方法（通过公理编码规范性要求）与逻辑内部方法（规范性模式从逻辑的内置结构中产生）。大量实验表明，逻辑内部策略能够持续提升性能，并为NLI生成更高效的混合证明。此外，我们发现逻辑的有效性具有领域依赖性：一阶逻辑更适用于常识推理，而道义逻辑与模态逻辑在伦理领域表现更优。我们的研究结果突显了将逻辑作为神经符号架构中一等、参数化元素的价值，以实现更鲁棒、模块化且适应性强的推理。