DIFFUSION REASONING FOR FORMAL LOGIC: CLOSING THE GAP BETWEEN MATHEMATICAL AND DEDUCTIVE CONSISTENCY IN LLMS

Ritika Lamba

Track: tiny / short paper (up to 4 pages)

Keywords: diffusion reasoning, logical reasoning, large language models, neuro-symbolic AI, cross-query consistency, symbolic solvers, belief revision

TL;DR: Diffusion reasoning methods excel at math but fail at formal logic; we propose Solver-Guided Diffusion Reasoning (SGDR), which embeds a symbolic solver inside the denoising loop and adds a belief store for cross-query consistency.

Abstract: Diffusion-based reasoning has recently emerged as a compelling alternative to autoregressive chain-of-thought generation, demonstrating strong results on mathematical benchmarks such as GSM8K and multi-digit arithmetic. However, we argue that mathematical reasoning and formal logical deduction impose fundamentally different constraints on a reasoning system, and that existing diffusion reasoning frameworks have not addressed the latter. Specifically, the challenges of (i) syllogistic and first-order deduction, (ii) maintaining logical consistency across multiple related queries, and (iii) integrating external symbolic solvers remain largely unaddressed by the diffusion reasoning literature. This paper makes the case that these gaps are not merely engineering details but reflect a deeper conceptual mismatch, and proposes a concrete research agenda, Solver-Guided Diffusion Reasoning (SGDR), that pairs iterative latent refinement with a symbolic oracle to enforce deductive validity as a hard constraint during the denoising process. Preliminary simulated experiments on ProntoQA and LogiQA suggest 20+ point gains in cross-query consistency over existing diffusion baselines.

Anonymization: This submission has been anonymized for double-blind review via the removal of identifying information such as names, affiliations, and identifying URLs.

Funding: Yes, the presenting author of this submission falls under ICLR’s funding aims, and funding would significantly impact their ability to attend the workshop in person.

Submission Number: 134