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

TL;DR

This paper introduces a flexible neuro-symbolic framework for natural language inference that allows dynamic control over the underlying logic, improving robustness and adaptability across different reasoning domains.

Contribution

It presents a logic-parametric approach embedding various classical and non-classical logics into higher-order logic, enabling systematic comparison and enhancement of reasoning strategies.

Findings

Logic-internal approaches outperform external ones in proof efficiency.

Different logics excel in different reasoning domains, e.g., FOL for commonsense, modal/deontic for ethical reasoning.

Making logic a controllable parameter enhances robustness and modularity in neuro-symbolic NLI.

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.