Related papers: An Ontology-Based Approach to Optimizing Geometry …

Despite rapid progress, most of the educational technologies today lack a strong instructional design knowledge basis leading to questionable quality of instruction. In addition, a major challenge is to customize these educational…

In recent years, knowledge graph embeddings have achieved great success. Many methods have been proposed and achieved state-of-the-art results in various tasks. However, most of the current methods present one or more of the following…

An important problem in geometric reasoning is to find the configuration of a collection of geometric bodies so as to satisfy a set of given constraints. Recently, it has been suggested that this problem can be solved efficiently by…

Ontology matching is a core task when creating interoperable and linked open datasets. In this paper, we explore a novel structure-based mapping approach which is based on knowledge graph embeddings: The ontologies to be matched are…

The current learning systems typically lack the level of metacognitive awareness, self-directed learning, and time management skills. Most of the ontologically based learning management systems are in the proposed phase and those which are…

Ontologies are known for their ability to organize rich metadata, support the identification of novel insights via semantic queries, and promote reuse. In this paper, we consider the problem of automated planning, where the objective is to…

Ontology revision aims to seamlessly incorporate a new ontology into an existing ontology and plays a crucial role in tasks such as ontology evolution, ontology maintenance, and ontology alignment. Similar to repair single ontologies,…

Ontologies have been widely used in numerous and varied applications, e.g., to support data modeling, information integration, and knowledge management. With the increasing size of ontologies, ontology understanding, which is playing an…

Large language models (LLMs) struggle with formal domains that require rigorous logical deduction and symbolic reasoning, such as mathematical proof generation. We propose a neuro-symbolic approach that combines LLMs' generative strengths…

Enterprises are creating domain-specific knowledge graphs by curating and integrating their business data from multiple sources. The data in these knowledge graphs can be described using ontologies, which provide a semantic abstraction to…

This is an attempt to present axioms for Euclidean geometry, aiming at the following goals: to work with geometric notions (thus not merely identify points with pairs of numbers, giving a special status to a particular coordinate system);…

In the last decade or so, we have witnessed deep learning reinvigorating the machine learning field. It has solved many problems in the domains of computer vision, speech recognition, natural language processing, and various other tasks…

Mathematical models and algorithms are an essential part of mathematical research data, as they are epistemically grounding numerical data. In order to represent models and algorithms as well as their relationship semantically to make this…

When ontologies reach a certain size and complexity, faults such as inconsistencies, unsatisfiable classes or wrong entailments are hardly avoidable. Locating the incorrect axioms that cause these faults is a hard and time-consuming task.…

Ontologies provide formal representation of knowledge shared within Semantic Web applications. Ontology learning involves the construction of ontologies from a given corpus. In the past years, ontology learning has traversed through shallow…

We introduce ontology-mediated planning, in which planning problems are combined with an ontology. Our formalism differs from existing ones in that we focus on a strong separation of the formalisms for describing planning problems and…

Knowledge representation and reasoning has a long history of examining how knowledge can be formalized, interpreted, and semantically analyzed by machines. In the area of automated vehicles, recent advances suggest the ability to formalize…

One of the main current challenges in Educational Data Mining and Learning Analytics is the portability or transferability of predictive models obtained for a particular course so that they can be applied to other different courses. To…

In the era of foundation models and Large Language Models (LLMs), Euclidean space has been the de facto geometric setting for machine learning architectures. However, recent literature has demonstrated that this choice comes with…

Mathematics olympiads are prestigious competitions, with problem proposing and solving highly honored. Building artificial intelligence that proposes and solves olympiads presents an unresolved challenge in automated theorem discovery and…