Scalable Uncertainty Reasoning in Knowledge Graphs

Large language models (LLMs) have demonstrated remarkable capabilities in natural language processing. However, LLMs often suffer from hallucinations and lack of relevant knowledge when dealing with question answering (QA) tasks. To mitigate these issues, knowledge graphs (KGs) have been utilized to enhance LLM reasoning. Nevertheless, KGs often contain noise and errors, while existing KG-enhanced LLM approaches are generally unable to identify and filter such noisy and erroneous content, which can instead amplify hallucinations and pose challenges for reliable reasoning. Uncertain knowledge graphs (UKGs), which associate each triple with a confidence score to quantify uncertainty, offer a promising direction to address this challenge. Compared with prior work, we investigate how to leverage UKGs to support LLMs for QA. We propose Debate-on-Graph (DoG), a new framework that enables LLMs and UKGs to collaborate adaptively for reliable reasoning. Specifically, we first design a heuristic search algorithm tailored for UKGs to extract reliable and question-relevant subgraphs, thereby reducing noise and errors in retrieved knowledge. We then introduce a Multi-Agent Debate mechanism, which yields reliable answers through adaptive adversarial debates, aiming to fully exploit the knowledge in UKGs while preserving the reliability of retrieved evidence. Extensive experiments on four benchmark QA datasets show that DoG achieves state-of-the-art performance over existing LLM reasoning methods and KG-based baselines, while enabling reliable and adaptive reasoning. Our code is available at https://github.com/seucoin/Debate-on-Graph.

This book presents a comprehensive and systematic survey of graph theory under uncertainty, with particular emphasis on the unifying role of the uncertain graph framework. It reviews fundamental concepts, structural properties, graph classes, and graph parameters within fuzzy, neutrosophic, and related models, while also introducing a wide range of extensions such as uncertain digraphs, hypergraphs, superhypergraphs, and dynamic graphs. In addition to theoretical developments, the book explores practical applications, including uncertain molecular graphs, decision-making systems, graph neural networks, knowledge graphs, and cognitive maps. By organizing diverse uncertainty-aware graph models within a common perspective, this work provides a coherent framework for understanding their relationships, capabilities, and applications in complex systems.

Knowledge Graph-based Question Answering (KGQA) plays a pivotal role in complex reasoning tasks but remains constrained by two persistent challenges: the structural heterogeneity of Knowledge Graphs(KGs) often leads to semantic mismatch during retrieval, while existing reasoning path retrieval methods lack a global structural perspective. To address these issues, we propose Structure-Tracing Evidence Mining (STEM), a novel framework that reframes multi-hop reasoning as a schema-guided graph search task. First, we design a Semantic-to-Structural Projection pipeline that leverages KG structural priors to decompose queries into atomic relational assertions and construct an adaptive query schema graph. Subsequently, we execute globally-aware node anchoring and subgraph retrieval to obtain the final evidence reasoning graph from KG. To more effectively integrate global structural information during the graph construction process, we design a Triple-Dependent GNN (Triple-GNN) to generate a Global Guidance Subgraph (Guidance Graph) that guides the construction. STEM significantly improves both the accuracy and evidence completeness of multi-hop reasoning graph retrieval, and achieves State-of-the-Art performance on multiple multi-hop benchmarks.