Craig interpolation and uniform interpolation have many applications in knowledge representation, including explainability, forgetting, modularization and reuse, and even learning. At the same time, many relevant knowledge representation formalisms do in general not have Craig or uniform interpolation, and computing interpolants in practice is challenging. We have a closer look at two prominent knowledge representation formalisms, description logics and logic programming, and discuss theoretical results and practical methods for computing interpolants.

Democratic societies need reliable information. Misinformation in popular media, such as news articles or videos, threatens to impair civic discourse. Citizens are, unfortunately, not equipped to verify the flood of content consumed daily at increasing rates. This work aims to quantify the scientific accuracy of online media semi-automatically. We investigate the state of the art of climate-related ground truth knowledge representation. By semantifying media content of unknown veracity, their statements can be compared against these ground truth knowledge graphs. We implemented a workflow using LLM-based statement extraction and knowledge graph analysis. Our implementation can streamline content processing towards state-of-the-art knowledge representation and veracity quantification. Developed and evaluated with the help of 27 experts and detailed interviews with 10, the tool evidently provides a beneficial veracity indication. These findings are supported by 43 anonymous participants from a parallel user survey. This initial step, however, is unable to annotate public media at the required granularity and scale. Additionally, the identified state of climate change knowledge graphs is vastly insufficient to support this neurosymbolic fact-checking approach. Further work towards a FAIR (Findable, Accessible, Interoperable, Reusable) ground truth and complementary metrics is required to support civic discourse scientifically.

Visual Language Models (VLMs) are powerful generative tools but often produce factually inaccurate outputs due to a lack of robust reasoning capabilities. While extensive research has been conducted on integrating external knowledge for reasoning in large language models (LLMs), such efforts remain underexplored in VLMs, where the challenge is compounded by the need to bridge multiple modalities seamlessly. This work introduces a framework for knowledge-guided reasoning in VLMs, leveraging structured knowledge graphs for multi-hop verification using image-captioning task to illustrate our framework. Our approach enables systematic reasoning across multiple steps, including visual entity recognition, knowledge graph traversal, and fact-based caption refinement. We evaluate the framework using hierarchical, triple-based and bullet-point based knowledge representations, analyzing their effectiveness in factual accuracy and logical inference. Empirical results show that our approach improves factual accuracy by approximately 31% on preliminary experiments on a curated dataset of mixtures from Google Landmarks v2, Conceptual captions and Coco captions revealing key insights into reasoning patterns and failure modes. This work demonstrates the potential of integrating external knowledge for advancing reasoning in VLMs, paving the way for more reliable and knowledgable multimodal systems.

Retrieval Augmented Generation (RAG) has become the standard approach for equipping Large Language Models (LLMs) with up-to-date knowledge. However, standard RAG, relying on independent passage retrieval, often fails to capture the interconnected nature of information required for complex, multi-hop reasoning. While structured RAG methods attempt to address this using knowledge graphs built from triples, we argue that the inherent context loss of triples (context collapse) limits the fidelity of the knowledge representation. We introduce PropRAG, a novel RAG framework that shifts from triples to context-rich propositions and introduces an efficient, LLM-free online beam search over proposition paths to discover multi-step reasoning chains. By coupling a higher-fidelity knowledge representation with explicit path discovery, PropRAG achieves state-of-the-art zero-shot Recall@5 and F1 scores on 2Wiki, HotpotQA, and MuSiQue, advancing non-parametric knowledge integration by improving evidence retrieval through richer representation and efficient reasoning path discovery.

Graph learning has rapidly evolved into a critical subfield of machine learning and artificial intelligence (AI). Its development began with early graph-theoretic methods, gaining significant momentum with the advent of graph neural networks (GNNs). Over the past decade, progress in scalable architectures, dynamic graph modeling, multimodal learning, generative AI, explainable AI (XAI), and responsible AI has broadened the applicability of graph learning to various challenging environments. Graph learning is significant due to its ability to model complex, non-Euclidean relationships that traditional machine learning struggles to capture, thus better supporting real-world applications ranging from drug discovery and fraud detection to recommender systems and scientific reasoning. However, challenges like scalability, generalization, heterogeneity, interpretability, and trustworthiness must be addressed to unlock its full potential. This survey provides a comprehensive introduction to graph learning, focusing on key dimensions including scalable, temporal, multimodal, generative, explainable, and responsible graph learning. We review state-of-the-art techniques for efficiently handling large-scale graphs, capturing dynamic temporal dependencies, integrating heterogeneous data modalities, generating novel graph samples, and enhancing interpretability to foster trust and transparency. We also explore ethical considerations, such as privacy and fairness, to ensure responsible deployment of graph learning models. Additionally, we identify and discuss emerging topics, highlighting recent integration of graph learning and other AI paradigms and offering insights into future directions. This survey serves as a valuable resource for researchers and practitioners seeking to navigate the rapidly evolving landscape of graph learning.

The rapid growth of research output in control engineering calls for new approaches to structure and formalize domain knowledge. This paper briefly describes an LLM-supported method for semi-automated generation of formal knowledge representations that combine human readability with machine interpretability and increased expressiveness. Based on the Imperative Representation of Knowledge (PyIRK) framework, we demonstrate how language models can assist in transforming natural-language descriptions and mathematical definitions (available as LaTeX source code) into a formalized knowledge graph. As a first application we present the generation of an ``interactive semantic layer'' to enhance the source documents in order to facilitate knowledge transfer. From our perspective this contributes to the vision of easily accessible, collaborative, and verifiable knowledge bases for the control engineering domain.

Traditional knowledge graphs are constrained by fixed ontologies that organize concepts within rigid hierarchical structures. The root cause lies in treating domains as implicit context rather than as explicit, reasoning-level components. To overcome these limitations, we propose the Domain-Contextualized Concept Graph (CDC), a novel knowledge modeling framework that elevates domains to first-class elements of conceptual representation. CDC adopts a C-D-C triple structure - - where domain specifications serve as dynamic classification dimensions defined on demand. Grounded in a cognitive-linguistic isomorphic mapping principle, CDC operationalizes how humans understand concepts through contextual frames. We formalize more than twenty standardized relation predicates (structural, logical, cross-domain, and temporal) and implement CDC in Prolog for full inference capability. Case studies in education, enterprise knowledge systems, and technical documentation demonstrate that CDC enables context-aware reasoning, cross-domain analogy, and personalized knowledge modeling - capabilities unattainable under traditional ontology-based frameworks.

Retrieval-Augmented Generation (RAG) significantly improves the performance of Large Language Models (LLMs) on knowledge-intensive tasks. However, varying response quality across LLMs under RAG necessitates intelligent routing mechanisms, which select the most suitable model for each query from multiple retrieval-augmented LLMs via a dedicated router model. We observe that external documents dynamically affect LLMs' ability to answer queries, while existing routing methods, which rely on static parametric knowledge representations, exhibit suboptimal performance in RAG scenarios. To address this, we formally define the new retrieval-augmented LLM routing problem, incorporating the influence of retrieved documents into the routing framework. We propose RAGRouter, a RAG-aware routing design, which leverages document embeddings and RAG capability embeddings with contrastive learning to capture knowledge representation shifts and enable informed routing decisions. Extensive experiments on diverse knowledge-intensive tasks and retrieval settings, covering open and closed-source LLMs, show that RAGRouter outperforms the best individual LLM and existing routing methods. With an extended score-threshold-based mechanism, it also achieves strong performance-efficiency trade-offs under low-latency constraints. The code and data are available at https://github.com/OwwO99/RAGRouter.

Inductive Knowledge Graph Reasoning (KGR) aims to discover facts in open-domain KGs containing unknown entities and relations, which poses a challenge for KGR models in comprehending uncertain KG components. Existing studies have proposed Knowledge Graph Foundation Models (KGFMs) that learn structural invariances across KGs to handle this uncertainty. Recently, Large Language Models (LLMs) have demonstrated strong capabilities for open-domain knowledge reasoning. As a result, the latest research has focused on LLM-based KGFMs that integrate LLM knowledge with KG context for inductive KGR. However, the intrinsic knowledge of LLMs may be overshadowed by sparse KG context, leading to LLM knowledge distortion, which can cause irreversible damage to model reasoning. Moreover, existing LLM-based KGR methods still struggle to fully constrain generative hallucinations in LLMs, severely limiting the credibility of reasoning results. To address these limitations, we propose a Knowledge Reasoning Language Model (KRLM) that achieves unified coordination between LLM knowledge and KG context throughout the KGR process. Specifically, we design a Knowledge Reasoning Language (KRL) instruction format and a KRL tokenizer to align LLM knowledge with KG representations. Then, we propose a KRL attention layer that coordinates intrinsic LLM knowledge with additional KG context through a dynamic knowledge memory mechanism. Finally, a structure-aware next-entity predictor is proposed, which strictly constrains the reasoning results within a trustworthy knowledge domain. Extensive experimental results on 25 real-world inductive KGR datasets demonstrate the significant superiority of the proposed KRLM\footnote{Our source codes are available at https://anonymous.4open.science/r/KRLM-EA36 in both zero-shot reasoning and fine-tuning scenarios.