# Grounding LLM Reasoning under Incomplete Graph Evidence

arXiv: https://arxiv.org/abs/2606.30247 · HTML: https://mlsanity.com/paper/2606.30247/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning.
- Builds on 1 of its 25 references that are in the map.
- First posted on arXiv 29 Jun 2026.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)

## Builds on (most cited first, 1 of 1)

- [From Local to Global: A Graph RAG Approach to Query-Focused Summarization](https://mlsanity.com/paper/2404.16130/) (2024)

## Abstract (arXiv)

Knowledge graphs can guide large language models (LLMs) reasoning, but the graph seen by a system is usually a retrieved, linked, temporally scoped, and incomplete evidence state rather than a complete account of truth. We develop a theoretical perspective on grounding observable LLM trajectories under such incomplete graph evidence.The evidence state induces entity anchors, typed relation residuals, path energies, and support regions, while the language model supplies a prior over candidate trajectories. We show that, under open-world incompleteness, no hard rule based only on the observed state can both reject every false unsupported trajectory and retain every true-but-unobserved one.We then characterize soft grounding as a KL-regularized deformation of the LLM prior: finite slack preserves support for unsupported but non-contradicted trajectories, whereas hard conditioning appears as an infinite-penalty limit.The framework also yields stability bounds under evidence perturbations and clarifies the constraint regimes appropriate for GraphRAG, KGQA, graph agents, constrained decoding, and faithful generation. The claims are evidence-relative: KG compatibility is treated as declared support, not factual truth.