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arxiv: 2605.29687 · v1 · pith:6WWWHJ4Wnew · submitted 2026-05-28 · 💻 cs.AI · cs.LO

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

Pedro Orvalho , Marta Kwiatkowska , Guillem Aleny\`a , Felip Many\`a This is my paper

Pith reviewed 2026-06-29 07:05 UTC · model grok-4.3

classification 💻 cs.AI cs.LO
keywords large language modelsMaxSATpreference optimizationcode generationhybrid reasoningconstraint satisfactionsolution verification
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The pith

LLMs generate code for preference-based MaxSAT problems that exact solvers solve and independent verification confirms as feasible and optimal.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes using large language models to translate natural language descriptions of constrained optimization tasks with user preferences into Python code that sets up a preference-based MaxSAT instance. An exact solver then computes solutions from that code, which are checked against a canonical encoding to confirm they meet the intended feasibility and optimality conditions. Direct LLM answers, chain-of-thought, and program-of-thought methods almost never produce valid results on these tasks, while the MaxSAT pipeline reaches acceptance rates above 80 percent in tested cases. This matters for domains like robotics where problems require balancing hard constraints with soft preferences and where pure language model output lacks reliability. The work demonstrates that externalizing the optimization step to a solver makes the overall reasoning both correct and independently verifiable.

Core claim

Given a natural language problem description, an LLM generates Python code that encodes user-defined constraints and preferences as a preference-based Maximum Satisfiability problem, which is solved by an exact MaxSAT solver; solutions are then independently verified for feasibility and optimality against a canonical MaxSAT encoding, allowing for different encodings and multiple optimal solutions, and this pipeline produces substantially higher acceptance rates than direct-answer, chain-of-thought, or program-of-thought baselines.

What carries the argument

LLM-generated Python code that formulates the input as a preference-based MaxSAT instance, which an exact solver resolves and which is then checked against a canonical encoding for feasibility and optimality.

If this is right

  • LLMs become usable for complex optimization by producing solver-ready encodings rather than final answers.
  • Solutions remain acceptable even when multiple optima exist or encodings differ, provided verification passes.
  • The method applies across open-source and closed-access LLMs on families of preference reasoning tasks.
  • Correctness is measured under independently verified reference semantics instead of surface-level output matching.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The separation of code generation from solving could extend to other exact solvers for different problem classes.
  • Verification against a canonical encoding provides a practical route to trustworthy LLM outputs on structured tasks.
  • The approach suggests testing whether LLMs can also generate the canonical encodings themselves for fully automated pipelines.

Load-bearing premise

The LLM-generated code must correctly encode the natural language constraints and preferences so that its solutions match the reference semantics when verified against the canonical MaxSAT formulation.

What would settle it

A new collection of preference-based tasks on which the MaxSAT pipeline produces verified feasible and optimal solutions at rates no higher than the direct LLM, chain-of-thought, and program-of-thought baselines.

Figures

Figures reproduced from arXiv: 2605.29687 by Felip Many\`a, Guillem Aleny\`a, Marta Kwiatkowska, Pedro Orvalho.

Figure 1
Figure 1. Figure 1: Our pipeline for enabling LLMS to externalise reasoning through vibe coding, delegating formal reasoning and optimisation to a MaxSAT solver via its Python API. LLMS’ solutions are verified against a canonical MaxSAT encoding. Intermediate Planning. We introduce an explicit intermediate planning step. Before generating code, the LLM is asked to produce a structured, symbolic description of the variables, c… view at source ↗
read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The paper proposes a hybrid approach in which LLMs generate Python code to encode natural-language preference-based optimization problems as MaxSAT instances; these are solved by an exact MaxSAT solver and the returned solutions are checked for feasibility and optimality against a canonical MaxSAT encoding (allowing different encodings and multiple optima). On three families of preference-based reasoning tasks the MaxSAT pipeline yields acceptance rates substantially higher than direct-answer, chain-of-thought and program-of-thought baselines, in some cases exceeding 80%.

Significance. If the verification procedure is robust, the work offers a concrete route to solver-verifiable optimization with user preferences, a setting common in robotics and planning. The explicit use of an exact MaxSAT solver together with independent feasibility/optimalty checks against a reference encoding is a methodological strength that supplies falsifiable correctness guarantees not present in pure LLM baselines.

major comments (1)
  1. [Abstract] Abstract: the central claim that the method 'substantially improves correctness under independently verified reference semantics' rests on the canonical MaxSAT encoding serving as an unbiased reference. The manuscript must specify (in the evaluation or method section) how the canonical encodings for the three task families are constructed, whether they were validated by independent parties, and how allowance for 'different encodings' is operationalized in the acceptance metric; without this the high acceptance rates may simply indicate that the LLM matched the authors' chosen encoding rather than solving the underlying preference problem.
minor comments (1)
  1. [Abstract] The abstract should name the three task families and the concrete LLMs used so that readers can immediately assess the scope of the evaluation.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback. The concern about the canonical encodings is valid and we will revise the manuscript to provide the requested details on their construction and the acceptance metric.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the method 'substantially improves correctness under independently verified reference semantics' rests on the canonical MaxSAT encoding serving as an unbiased reference. The manuscript must specify (in the evaluation or method section) how the canonical encodings for the three task families are constructed, whether they were validated by independent parties, and how allowance for 'different encodings' is operationalized in the acceptance metric; without this the high acceptance rates may simply indicate that the LLM matched the authors' chosen encoding rather than solving the underlying preference problem.

    Authors: We agree that explicit details are required. In the revised manuscript we will add a dedicated subsection (Evaluation, §4.2) describing the construction process: for each task family the canonical encoding is derived directly from the formal problem definition by (i) mapping user preferences to a fixed set of hard clauses (feasibility) and soft clauses (optimality) using standard MaxSAT modeling, (ii) assigning a canonical variable ordering and clause representation, and (iii) confirming that the encoding produces the expected optimal cost on a small set of hand-verified instances. These encodings were developed by the authors following the task specifications; no external independent validation was performed, but the verification pipeline itself is solver-independent. The acceptance metric operationalizes 'different encodings' by checking equivalence of the returned solution: after mapping variables via a bijection (when needed), we verify that the LLM-generated solution satisfies all hard clauses of the canonical encoding and attains an identical optimal soft-clause cost; multiple optima are accepted if they share the same cost. This procedure ensures the metric evaluates preference satisfaction rather than syntactic identity with the authors' encoding. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper presents an empirical pipeline where LLMs generate Python code to encode problems as preference-based MaxSAT instances, solved by external exact MaxSAT solvers, with solutions verified for feasibility and optimality against a separately constructed canonical encoding (explicitly allowing different encodings and multiple optima). Acceptance rates are measured by whether generated solutions pass these external checks, then compared to direct/CoT/PoT baselines. No equations, self-definitional reductions, fitted parameters renamed as predictions, or load-bearing self-citations appear in the provided text; the central claims rest on independent solver verification and external benchmarks rather than internal construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on abstract, no free parameters, axioms, or invented entities are introduced; the approach relies on existing MaxSAT solvers and LLMs.

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Reference graph

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