CALM: Contextual Analog Logic with Multimodality

In this work, we introduce Contextual Analog Logic with Multimodality (CALM). CALM unites symbolic reasoning with neural generation, enabling systems to make context-sensitive decisions grounded in real-world multi-modal data.Background: Classic bivalent logic systems cannot capture the nuance of human decision-making. They also require human grounding in multi-modal environments, which can be ad-hoc, rigid, and brittle. Neural networks are good at extracting rich contextual information from multi-modal data, but lack interpretable structures for reasoning.Objectives: CALM aims to bridge the gap between logic and neural perception, creating an analog logic that can reason over multi-modal inputs. Without this integration, AI systems remain either brittle or unstructured, unable to generalize robustly to real-world tasks. In CALM, symbolic predicates evaluate to analog truth values computed by neural networks and constrained search.Methods: CALM represents each predicate using a domain tree, which iteratively refines its analog truth value when the contextual groundings of its entities are determined. The iterative refinement is predicted by neural networks capable of capturing multi-modal information and is filtered through a symbolic reasoning module to ensure constraint satisfaction.Results: In fill-in-the-blank object placement tasks, CALM achieved 92.2% accuracy, outperforming classical logic (86.3%) and LLM (59.4%) baselines. It also demonstrated spatial heatmap generation aligned with logical constraints and delicate human preferences, as shown by a human study.Conclusions: CALM demonstrates the potential to reason with logic structure while aligning with preferences in multi-modal environments. It lays the foundation for next-gen AI systems that require the precision and interpretation of logic and the multimodal information processing of neural networks.

@article{jacobson2025_2506.14936,
  title={ CALM: Contextual Analog Logic with Multimodality },
  author={ Maxwell J. Jacobson and Corey J. Maley and Yexiang Xue },
  journal={arXiv preprint arXiv:2506.14936},
  year={ 2025 }
}