Reason Popper-ly: Patching In-Context Reasoning with Inductive Logic Programming

2026-07-24

AI Summary

This work addresses the limitations of large language models in multi-hop reasoning, where unreliable intermediate steps in chain-of-thought reasoning often degrade performance. The authors propose the first integration of Inductive Logic Programming (ILP) into chain-of-thought reasoning, enabling online learning of relational composition rules and iterative verification and repair of reasoning trajectories. This neuro-symbolic approach preserves the model’s semantic comprehension while precisely correcting verifiable logical errors and providing fine-grained error categorization. Evaluated on the CLUTRR benchmark, the method significantly improves accuracy across tasks involving 2 to 10 reasoning hops, yielding gains of up to 48 and 15 percentage points for smaller and state-of-the-art models, respectively. It outperforms purely symbolic baselines, demonstrating particularly strong performance in complex reasoning scenarios.

Abstract

Chain-of-thought (CoT) prompting enables large language models (LLMs) to tackle multi-step reasoning tasks, yet the generated intermediate steps are not guaranteed to be logically sound. We present Reason Popper-ly, a neurosymbolic framework that uses inductive logic programming (ILP) to learn relation composition rules from reasoning traces and deploys them as an online verifier for step-level correction. Given an LLM-generated trace, the method checks each inferred step against the learned rule table, diagnoses the violation type, rewrites incorrect steps with symbolically derived repairs, and regenerates the remaining suffix so that the model can produce its final answer conditioned on a verified trace. We evaluate on CLUTRR, a multi-hop kinship reasoning benchmark, using five language models over reasoning chains of 2 to 10 hops. Across all models, Reason Popper-ly consistently improves terminal accuracy over standard CoT, with gains of up to 48 percentage points for small models and 15 points for frontier models on the longest chains. Compared with a fully exogenous symbolic pipeline, our method performs better on harder instances by preserving the model's successful grounding while correcting only verifiable reasoning failures. In addition, step-level ILP verification yields a fine-grained error taxonomy that provides diagnostic insight beyond final-answer accuracy.

Problem

• chain-of-thought
• logical soundness
• reasoning errors
• large language models
• multi-step reasoning

Innovation

• inductive logic programming
• neurosymbolic reasoning
• chain-of-thought verification
• step-level correction
• reasoning trace repair