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

arXiv: https://arxiv.org/abs/2604.27960 · HTML: https://mlsanity.com/paper/2604.27960/

## 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 16 of its 47 references that are in the map.
- First posted on arXiv 30 Apr 2026.

## Placed in

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

## Builds on (most cited first, 16 of 16)

- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [LLM+P: Empowering Large Language Models with Optimal Planning Proficiency](https://mlsanity.com/paper/2304.11477/) (2023)
- [Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models](https://mlsanity.com/paper/2503.16419/) (2025)
- [Reasoning Models Don't Always Say What They Think](https://mlsanity.com/paper/2505.05410/) (2025)
- [The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity](https://mlsanity.com/paper/2506.06941/) (2025)
- [Is Self-Repair a Silver Bullet for Code Generation?](https://mlsanity.com/paper/2306.09896/) (2023)
- [On the Self-Verification Limitations of Large Language Models on Reasoning and Planning Tasks](https://mlsanity.com/paper/2402.08115/) (2024)
- [Translating Natural Language to Planning Goals with Large-Language Models](https://mlsanity.com/paper/2302.05128/) (2023)
- [Beyond Semantics: The Unreasonable Effectiveness of Reasonless Intermediate Tokens](https://mlsanity.com/paper/2505.13775/) (2025)
- [Sudoku-Bench: Evaluating creative reasoning with Sudoku variants](https://mlsanity.com/paper/2505.16135/) (2025)
- [Exploring LLM Reasoning Through Controlled Prompt Variations](https://mlsanity.com/paper/2504.02111/) (2025)
- [CLMASP: Coupling Large Language Models with Answer Set Programming for Robotic Task Planning](https://mlsanity.com/paper/2406.03367/) (2024)
- [Can LLMs reason over extended multilingual contexts? Towards long-context evaluation beyond retrieval and haystacks](https://mlsanity.com/paper/2504.12845/) (2025)

## Abstract (arXiv)

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.