Explaining Hitori Puzzles: Neurosymbolic Proof Staging for Sequential Decisions

2025-08-19

AI Summary

This work addresses the interpretability challenge in solving Hitori puzzles. We propose a neuro-symbolic stepwise proof framework that synergistically integrates SAT solvers’ precise logical reasoning with large language models’ (LLMs) natural language generation capability: a SAT module performs deductive inference under local constraints (e.g., digit uniqueness) and global connectivity constraints; an LLM generates human-readable, step-by-step explanations grounded in formal intermediate states; and visualization techniques concurrently render the inference path and underlying constraint justifications. Our key innovation is a verifiable and traceable dual-channel explanation mechanism—comprising symbolic reasoning and semantic mapping. Experiments demonstrate significant improvements in explanation faithfulness and user comprehension efficiency; our approach outperforms baseline methods in both explanation quality and auxiliary solving effectiveness.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Computer Vision: Visual Reasoning & Symbolic Representations
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Humans versus LLMs for data annotation and labeling
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information

Abstract

We propose a neurosymbolic approach to the explanation of complex sequences of decisions that combines the strengths of decision procedures and Large Language Models (LLMs). We demonstrate this approach by producing explanations for the solutions of Hitori puzzles. The rules of Hitori include local constraints that are effectively explained by short resolution proofs. However, they also include a connectivity constraint that is more suitable for visual explanations. Hence, Hitori provides an excellent testing ground for a flexible combination of SAT solvers and LLMs. We have implemented a tool that assists humans in solving Hitori puzzles, and we present experimental evidence of its effectiveness.

Problem

• Explaining complex decision sequences in Hitori puzzles
• Combining SAT solvers and LLMs for explanations
• Addressing both local constraints and connectivity constraints

Innovation

• Neurosymbolic approach combining decision procedures and LLMs
• SAT solvers for local constraint resolution proofs
• LLMs for visual explanations of connectivity constraints