Related papers: An Ontology-Based Approach to Optimizing Geometry …
Mathematical thinking is a fundamental aspect of human cognition. Cognitive scientists have investigated the mechanisms that underlie our ability to thinking geometrically and numerically, to take two prominent examples, and developmental…
Ontology embeddings map classes, relations, and individuals in ontologies into $\mathbb{R}^n$, and within $\mathbb{R}^n$ similarity between entities can be computed or new axioms inferred. For ontologies in the Description Logic…
We explore the role of ontologies in enhancing hybrid modeling and simulation through improved semantic rigor, model reusability, and interoperability across systems, disciplines, and tools. By distinguishing between methodological and…
In recent years, data science has evolved significantly. Data analysis and mining processes become routines in all sectors of the economy where datasets are available. Vast data repositories have been collected, curated, stored, and used…
Geometric algebra is the natural outgrowth of the concept of a vector and the addition of vectors. After reviewing the properties of the addition of vectors, a multiplication of vectors is introduced in such a way that it encodes the famous…
AI has made significant progress in solving math problems, but geometry problems remain challenging due to their reliance on both text and diagrams. In the text description, symbolic characters such as "$\triangle$ABC" often serve as a…
System engineering has been shifting from document-centric to model-based approaches, where assets are becoming more and more digital. Although digitisation conveys several benefits, it also brings several concerns (e.g., storage and…
Ontology-based knowledge graph (KG) construction is a core technology that enables multidimensional understanding and advanced reasoning over domain knowledge. Industrial standards, in particular, contain extensive technical information and…
Attack graphs provide a representation of possible actions that adversaries can perpetrate to attack a system. They are used by cybersecurity experts to make decisions, e.g., to decide remediation and recovery plans. Different approaches…
Geometric programming is an important class of optimization problems that enable practitioners to model a large variety of real-world applications, mostly in the field of engineering design. In many real life optimization problem…
This paper wants to show how practical geometry, created to give a concrete help to people involved in trade, in land-surveying and even in astronomy, underwent a transformation that underlined its didactical value and turned it first into…
The limited ability to reason across occupational data from different sources is a long-standing bottleneck for data-driven labour market analytics. Previous research has relied on hand-crafted ontologies that allow such reasoning but are…
Empirical data plays an important role in evolutionary computation research. To make better use of the available data, ontologies have been proposed in the literature to organize their storage in a structured way. However, the full…
Leveraging Large Language Models (LLMs) to automatically formulate and solve optimization problems from natural language has emerged as an efficient paradigm for automated optimization. However, existing methods still exhibit limited…
Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can then be involved in optimization problems, typically as a…
Geometry problems are a crucial testbed for AI reasoning capabilities. Most existing geometry solving systems cannot express problems within a unified framework, thus are difficult to integrate with other mathematical fields. Besides, since…
Geometry problem solving presents a formidable challenge within the NLP community. Existing approaches often rely on models designed for solving math word problems, neglecting the unique characteristics of geometry math problems.…
Developing students as well-rounded professionals is increasingly important for our modern society. Although there is a great consensus that technical and professional ("soft") skills should be developed and intertwined in the core of…
The increasing importance of resource-efficient production entails that manufacturing companies have to create a more dynamic production environment, with flexible manufacturing machines and processes. To fully utilize this potential of…
This is the first paper in a series of eight where in the first three we develop a systematic approach to the geometric algebras of multivectors and extensors, followed by five papers where those algebraic concepts are used in a novel…