SATURN: Symbolic Spatial Reasoning for Multi-Perspective Grounding

Vision-Language Models (VLMs) remain unreliable when spatial reasoning requires composing relations whose meanings depend on frames of reference. Existing tool-augmented spatial reasoning methods make reasoning more explicit, but often rely on low-level geometric procedures and hard binary decisions over noisy perception. We propose SATURN, a neuro-symbolic framework for perspective-aware compositional spatial reasoning. SATURN reconstructs an approximate 3D scene, derives soft perspective-aware spatial predicates, and composes them with a training-free Pythonic symbolic executor, separating perception from reasoning while preserving uncertainty through multi-hop inference. We also introduce 3D FORCE, a diagnostic benchmark that controls reasoning depth, view, and perspective composition for spatial arrangement grounding (SAG) and referring expression grounding (REF). On 3D FORCE, VLMs and spatially trained models degrade sharply as depth and perspective complexity increase, whereas SATURN degrades the least and outperforms every baseline at each depth. On the real-world MindCube benchmark, SATURN achieves (78.06%) overall accuracy, outperforming the strongest baseline by (14) percentage points.