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

2026-01-09

arXiv.org

AI Summary

Existing neural-symbolic approaches to natural language inference (NLI) are constrained by fixed logical formalisms, struggling to balance robustness and adaptability. This work proposes a logic-parameterized framework that, for the first time, treats logical forms as first-class tunable parameters within a neural-symbolic architecture. By integrating the LogiKEy methodology, the framework uniformly embeds diverse classical and non-classical logics—including deontic and modal logics—into higher-order logic, while synergistically combining large language models with automated theorem provers. The approach distinguishes between reasoning strategies external and internal to the logic, substantially enhancing modularity, verifiability, and hybrid proof efficiency. Empirical results demonstrate that different logics exhibit distinct strengths: first-order logic excels in commonsense reasoning, whereas deontic and modal logics prove more effective in ethical reasoning tasks.

Technology Category

• Knowledge Representation and Reasoning: Logic Programming
• Machine Learning: Statistical Relational/Logic Learning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

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.

Problem

• neuro-symbolic NLI
• logical formalism
• verifiable reasoning
• normative reasoning
• logic adaptability

Innovation

• logic-parametric
• neuro-symbolic reasoning
• natural language inference
• LogiKEy
• deontic logic