LLMs as ASP Programmers: Self-Correction Enables Task-Agnostic Nonmonotonic Reasoning

2026-04-30

AI Summary

This work addresses the limitations of large language models (LLMs) in complex reasoning—namely high computational cost, logical inconsistency, and performance degradation—and the inadequacy of existing neuro-symbolic approaches that rely on monotonic logic and fail to capture human-like defeasible reasoning. The paper proposes the first general-purpose LLM+Answer Set Programming (ASP) framework that operates without handcrafted knowledge modules or domain-specific prompts. It automatically translates natural language into ASP and leverages structured feedback from ASP solvers to establish a self-correction loop, enabling unified handling of diverse non-monotonic reasoning tasks. Experiments demonstrate that the approach significantly outperforms SMT-based methods across six benchmarks, with the self-correction mechanism identified as key to performance gains. Moreover, streamlined context mitigates “context corruption,” validating the efficacy of default rules with exceptions and the framework’s task-agnostic generalization capability.

Abstract

Recent large language models (LLMs) have achieved impressive reasoning milestones but continue to struggle with high computational costs, logical inconsistencies, and sharp performance degradation on high-complexity problems. While neuro-symbolic methods attempt to mitigate these issues by coupling LLMs with symbolic reasoners, existing approaches typically rely on monotonic logics (e.g., SMT) that cannot represent defeasible reasoning -- essential components of human cognition. We present "LLM+ASP," a framework that translates natural language into Answer Set Programming (ASP), a nonmonotonic formalism based on stable model semantics. Unlike prior "LLM+ASP" approaches that require manually authored knowledge modules, domain-specific prompts, or evaluation restricted to single problem classes, our framework operates without any per-task engineering and applies uniformly across diverse reasoning tasks. Our system utilizes an automated self-correction loop where structured feedback from the ASP solver enables iterative refinement. Evaluating across six diverse benchmarks, we demonstrate that: (1) stable model semantics allow LLMs to naturally express default rules and exceptions, outperforming SMT-based alternatives by significant margins on nonmonotonic tasks; (2) iterative self-correction is the primary driver of performance, effectively replacing the need for handcrafted domain knowledge; (3) compact in-context reference guides substantially outperform verbose documentation, revealing a "context rot" phenomenon where excessive context hinders constraint adherence.

Problem

• nonmonotonic reasoning
• large language models
• defeasible reasoning
• logical inconsistency
• computational cost

Innovation

• Answer Set Programming
• nonmonotonic reasoning
• self-correction
• neuro-symbolic integration
• stable model semantics