This article presents a theoretical framework for grounding large language model reasoning trajectories when relying on incomplete knowledge graph evidence rather than complete truth states.

  • The evidence state induces entity anchors, typed relation residuals, path energies, and support regions, while the language model supplies a prior over candidate trajectories.
  • Under open-world incompleteness, no hard rule based solely on the observed state can simultaneously reject every false unsupported trajectory and retain every true-but-unobserved one.
  • Soft grounding is characterized as a KL-regularized deformation of the LLM prior, where finite slack preserves support for unsupported but non-contradicted trajectories.
  • The framework yields stability bounds under evidence perturbations and clarifies constraint regimes for GraphRAG, KGQA, graph agents, constrained decoding, and faithful generation.

The claims are evidence-relative, treating KG compatibility as declared support rather than factual truth.