Louis Mozart Kamdem Teyou

Louis Mozart Kamdem Teyou, Caglar Demir, Axel-Cyrille Ngonga Ngomo

We introduce a novel embedding method diverging from conventional approaches by operating within function spaces of finite dimension rather than finite vector space, thus departing significantly from standard knowledge graph embedding techniques. Initially employing polynomial functions to compute embeddings, we progress to more intricate representations using neural networks with varying layer complexities. We argue that employing functions for embedding computation enhances expressiveness and allows for more degrees of freedom, enabling operations such as composition, derivatives and primitive of entities representation. Additionally, we meticulously outline the step-by-step construction of our approach and provide code for reproducibility, thereby facilitating further exploration and application in the field.

Louis Mozart Kamdem Teyou, Caglar Demir, Axel-Cyrille Ngonga Ngomo

Concept learning is a form of supervised machine learning that operates on knowledge bases in description logics. State-of-the-art concept learners often rely on an iterative search through a countably infinite concept space. In each iteration, they retrieve instances of candidate solutions to select the best concept for the next iteration. While simple learning problems might require a few dozen instance retrieval calls to find a fitting solution, complex learning problems might necessitate thousands of calls. We alleviate the resulting runtime challenge by presenting a semantics-aware caching approach. Our cache is essentially a subsumption-aware map that links concepts to a set of instances via crisp set operations. Our experiments on 5 datasets with 4 symbolic reasoners, a neuro-symbolic reasoner, and 5 popular pagination policies demonstrate that our cache can reduce the runtime of concept retrieval and concept learning by an order of magnitude while being effective for both symbolic and neuro-symbolic reasoners.

Louis Mozart Kamdem Teyou, Luke Friedrichs, N'Dah Jean Kouagou et al.

Concept learning exploits background knowledge in the form of description logic axioms to learn explainable classification models from knowledge bases. Despite recent breakthroughs in neuro-symbolic concept learning, most approaches still cannot be deployed on real-world knowledge bases. This is due to their use of description logic reasoners, which are not robust against inconsistencies nor erroneous data. We address this challenge by presenting a novel neural reasoner dubbed EBR. Our reasoner relies on embeddings to approximate the results of a symbolic reasoner. We show that EBR solely requires retrieving instances for atomic concepts and existential restrictions to retrieve or approximate the set of instances of any concept in the description logic $\mathcal{SHOIQ}$. In our experiments, we compare EBR with state-of-the-art reasoners. Our results suggest that EBR is robust against missing and erroneous data in contrast to existing reasoners.