# Logic-Parametric Neuro-Symbolic NLI: Controlling Logical Formalisms for Verifiable LLM Reasoning

arXiv: https://arxiv.org/abs/2601.05705 · HTML: https://mlsanity.com/paper/2601.05705/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 7 of its 57 references that are in the map.
- First posted on arXiv 9 Jan 2026.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 7 of 7)

- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [DeepSeek LLM: Scaling Open-Source Language Models with Longtermism](https://mlsanity.com/paper/2401.02954/) (2024)
- [Social Chemistry 101: Learning to Reason about Social and Moral Norms](https://mlsanity.com/paper/2011.00620/) (2020)
- [Logical Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2502.09100/) (2025)
- [Empowering LLMs with Logical Reasoning: A Comprehensive Survey](https://mlsanity.com/paper/2502.15652/) (2025)
- [The Dark Side of ChatGPT: Legal and Ethical Challenges from Stochastic Parrots and Hallucination](https://mlsanity.com/paper/2304.14347/) (2023)
- [Adaptive LLM-Symbolic Reasoning via Dynamic Logical Solver Composition](https://mlsanity.com/paper/2510.06774/) (2025)

## Abstract (arXiv)

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.