Knowledge graphs represent information as structured triples and serve as the backbone for a wide range of applications, including question answering, link prediction, and recommendation systems. A prominent line of research for exploring knowledge graphs involves graph embedding methods, where entities and relations are represented in low-dimensional vector spaces that capture underlying semantics and structure. However, most existing methods rely on assumptions such as the Closed World Assumption or Local Closed World Assumption, treating missing triples as false. This contrasts with the Open World Assumption underlying many real-world knowledge graphs. Furthermore, while explicitly stated negative statements can help distinguish between false and unknown triples, they are rarely included in knowledge graphs and are often overlooked during embedding training.

With the recent surge in popularity of Large Language Models (LLMs), there is the rising risk of users blindly trusting the information in the response. Nevertheless, there are cases where the LLM recommends actions that have potential legal implications and this may put the user in danger. We provide an empirical analysis on multiple existing LLMs showing the urgency of the problem. Hence, we propose a first short-term solution, consisting in an approach for isolating these legal issues through prompt engineering. We prove that this solution is able to stem some risks related to legal implications, nonetheless we also highlight some limitations. Hence, we argue on the need for additional knowledge-intensive resources and specifically Knowledge Graphs for fully solving these limitations. For the purpose, we draw our proposal aiming at designing and developing a solution powered by a legal Knowledge Graph (KG) that, besides capturing and alerting the user on possible legal implications coming from the LLM answers, is also able to provide actual evidence for them by supplying citations of the interested laws. We conclude with a brief discussion on the issues that may be needed to solve for building a comprehensive legal Knowledge Graph

Knowledge Graphs are used in various domains to represent knowledge about entities and their relations.In the vast majority of cases, they capture what is known to be true about those entities, i.e., positive statements, while the Open World Assumption implicitly states that everything not expressed in the graph may or may not be true.This makes it difficult and less frequent to capture information explicitly known not to be true, i.e., negative statements.Moreover, while those negative statements could bear the potential to learn more useful representations in knowledge graph embeddings, that direction has been explored only rarely.However, in many domains, negative information is particularly interesting, for example, in recommender systems, where negative associations of users and items can help in learning better user representations, or in the biomedical domain, where the knowledge that a patient does exhibit a specific symptom can be crucial for accurate disease diagnosis.In this paper, we argue that negative statements should be given more attention in knowledge graph embeddings.Moreover, we investigate how they can be used in knowledge graph embedding methods, highlighting their potential in some interesting use cases.We discuss some existing works and preliminary results that incorporate explicitly declared negative statements in walk-based knowledge graph embedding methods.Finally, we outline promising avenues for future research in this area.