However, statements different from the original statement could also be logically consistent with respecttoagivencontext.

Perception and reasoning are two representative abilities of intelligence that are integrated seamlessly during human problem-solving processes.

Each question and answer group has a unique list of corresponding visuals used for image creation. The list of visible objects, which combines the correct-answer objects with an arbitrary'noise' object

SATNet is an award-winning MAXSAT solver that can be used to infer logical rules and integrated as a differentiable layer in a deep neural network. It had been shown to solve Sudoku puzzles visually from examples of puzzle digit images, and was heralded as an impressive achievement towards the longstanding AI goal of combining pattern recognition with logical reasoning. In this paper, we clarify SATNet's capabilities by showing that in the absence of intermediate labels that identify individual Sudoku digit images with their logical representations, SATNet completely fails at visual Sudoku (0% test accuracy). More generally, the failure can be pinpointed to its inability to learn to assign symbols to perceptual phenomena, also known as the symbol grounding problem, which has long been thought to be a prerequisite for intelligent agents to perform real-world logical reasoning. We propose an MNIST based test as an easy instance of the symbol grounding problem that can serve as a sanity check for differentiable symbolic solvers in general.

Logical reasoning is a core challenge in natural language understanding and a fundamental capability of artificial intelligence, underpinning scientific discovery, mathematical theorem proving, and complex decision-making. Despite the remarkable progress of large language models (LLMs), most current approaches still rely on forward reasoning paradigms, generating step-by-step rationales from premises to conclusions. However, such methods often suffer from redundant inference paths, hallucinated steps, and semantic drift, resulting in inefficient and unreliable reasoning. In this paper, we propose a novel framework, Hypothesis-driven Backward Logical Reasoning (HBLR). The core idea is to integrate confidence-aware symbolic translation with hypothesis-driven backward reasoning. In the translation phase, only high-confidence spans are converted into logical form, such as First-Order Logic (FOL), while uncertain content remains in natural language. A translation reflection module further ensures semantic fidelity by evaluating symbolic outputs and reverting lossy ones back to text when necessary. In the reasoning phase, HBLR simulates human deductive thinking by assuming the conclusion is true and recursively verifying its premises. A reasoning reflection module further identifies and corrects flawed inference steps, enhancing logical coherence. Extensive experiments on five reasoning benchmarks demonstrate that HBLR consistently outperforms strong baselines in both accuracy and efficiency.

SA TNet completely fails at visual Sudoku (0% test accuracy).