# Reliable Reasoning with Large Language Models via Preference-Based Maximum Satisfiability

arXiv: https://arxiv.org/abs/2605.29687 · HTML: https://mlsanity.com/paper/2605.29687/

## 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 20 of its 32 references that are in the map.
- First posted on arXiv 28 May 2026.

## Placed in

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

## Builds on (most cited first, 20 of 20)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [On the Planning Abilities of Large Language Models : A Critical Investigation](https://mlsanity.com/paper/2305.15771/) (2023)
- [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)
- [Leveraging Pre-trained Large Language Models to Construct and Utilize World Models for Model-based Task Planning](https://mlsanity.com/paper/2305.14909/) (2023)
- [ZebraLogic: On the Scaling Limits of LLMs for Logical Reasoning](https://mlsanity.com/paper/2502.01100/) (2025)
- [Multilingual Machine Translation with Large Language Models: Empirical Results and Analysis](https://mlsanity.com/paper/2304.04675/) (2023)
- [SatLM: Satisfiability-Aided Language Models Using Declarative Prompting](https://mlsanity.com/paper/2305.09656/) (2023)
- [A Large-Scale Survey on the Usability of AI Programming Assistants: Successes and Challenges](https://mlsanity.com/paper/2303.17125/) (2023)
- [Large Language Models Can Solve Real-World Planning Rigorously with Formal Verification Tools](https://mlsanity.com/paper/2404.11891/) (2024)
- [Vibe Coding vs. Agentic Coding: Fundamentals and Practical Implications of Agentic AI](https://mlsanity.com/paper/2505.19443/) (2025)
- [Planning Anything with Rigor: General-Purpose Zero-Shot Planning with LLM-based Formalized Programming](https://mlsanity.com/paper/2410.12112/) (2024)
- [Logically Consistent Language Models via Neuro-Symbolic Integration](https://mlsanity.com/paper/2409.13724/) (2024)
- [Aristotle: Mastering Logical Reasoning with A Logic-Complete Decompose-Search-Resolve Framework](https://mlsanity.com/paper/2412.16953/) (2024)
- [MCP-Solver: Integrating Language Models with Constraint Programming Systems](https://mlsanity.com/paper/2501.00539/) (2024)
- [ConstraintLLM: A Neuro-Symbolic Framework for Industrial-Level Constraint Programming](https://mlsanity.com/paper/2510.05774/) (2025)

## Abstract (arXiv)

Large Language Models (LLMs) excel at understanding natural language but struggle with optimisation tasks involving multiple constraints and user-defined preferences, which commonly arise in domains such as robotics. We propose a hybrid reasoning approach in which LLMs externalise reasoning through code generation. Given a natural language problem description, an LLM generates Python code that encodes user-defined constraints and preferences as a preference-based Maximum Satisfiability (MaxSAT) problem, which is then solved by an exact MaxSAT solver. To ensure correctness, solutions returned by the model-generated code are independently verified for feasibility and optimality against a canonical MaxSAT encoding, allowing for different encodings and multiple optimal solutions. We evaluate our approach using both open-source and closed-access LLMs on three families of preference-based reasoning tasks, and compare it against direct-answer, chain-of-thought, and program-of-thought baselines using the same models. While these baselines rarely produce feasible solutions, the MaxSAT-based pipeline achieves substantially higher acceptance rates, in some cases exceeding 80%. Our results demonstrate that LLM-driven code generation combined with preference-based MaxSAT enables solver-verifiable optimisation with respect to generated encodings, and substantially improves correctness under independently verified reference semantics.