Projects
Towards a Systematic Theory of Aristotelian Diagrams in Logical Geometry KU Leuven
Aristotelian diagrams, such as the square of opposition, have been widely used throughout the history of philosophy and logic. Nowadays, they also have several applications in other disciplines that are concerned with logical reasoning, such as psychology, linguistics and computer science. However, many of the applications of Aristotelian diagrams suffer from substantial problems, often due to a lack of understanding of the intricate logical ...
Logical Geometry and its Applications. KU Leuven
The main goal of the project is to develop a systematic and formal perspective on the Aristotelian diagrams (such as the well-known square of oppositions). These diagrams have been used extensively by philosophers, logicians and linguists to explain or illustrate the phenomena they are interested in (such as necessity and obligation). There exists a vast body of results about these concrete uses of Aristotelian diagrams (historical case ...
Toward a Unified Account of Aristotelian Diagrams in Logical Geometry. KU Leuven
Aristotelian diagrams have been widely used throughout the history of philosophy and logic, and nowadays they also have many applications in other disciplines. The framework of logical geometry studies these diagrams as objects of independent interest, which allows us to address many of the issues that surround the existing applications of these diagrams, and even to develop completely new applications. The main goal of my research program is ...
The Mathematical Foundations of Logical Geometry KU Leuven
Aristotelian diagrams have been widely used throughout the history of philosophy and logic. Nowadays, they also have several applications in other disciplines. However, many of these applications suffer from substantial problems, often due to a lack of understanding of the intricate logical properties of these diagrams. Therefore, a theoretical investigation of Aristotelian diagrams is required (i.e. logical geometry). This doctoral project ...
The Philosophy of Logical Geometry KU Leuven
In the literature on the philosophy of scientific practice, it has been shown that various diagrams, like commutative diagrams in Mathematics or Feynman diagrams in Physics, play key roles in the steps of scientific reasoning, such as in making proofs, understanding the subject-matter and discovering new aspects of it. Analogously, Aristotelian diagrams have been widely used in logic, philosophy and other disciplines such as Artificial ...
Empirical Foundations for Logical Geometry: A Database of Aristotelian Diagrams KU Leuven
Empirical Foundations for Logical Geometry: A Database of Aristotelian Diagrams KU Leuven
In light of recent research around logical geometry – a unified theoretical account of Aristotelian diagrams – my main goal is to develop a digital database of Aristotelian diagrams and their relevant metadata. This database will provide an empirical basis for logical geometry, placed firmly within a practice-based philosophy of logic, which will lead to the fine-tuning of existing theories, the discovery of new properties of Aristotelian ...
From local to global - submanifolds detecting ambient geometric structures KU Leuven
One can think of submanifolds as generalizations of curves and surfaces in the three-dimensional Euclidean space. In the general theory, the dimensions of the objects can be arbitrary and the ambient space need not to be flat. Although submanifolds are local objects in their ambient space, they can encode a lot of information about its geometry. Indeed, if one considers a class of submanifolds which are in a certain sense adapted to a ...
Applications of finite geometry in spectral graph theory and in classical and quantum error-correction Ghent University
The proposed project consists of three topics that are linked by finite geometry and by the techniques that are used to investigate them. They are situated in modern research areas with many applications and are of current international interest. We devote a work package (WP) to each topic. WP1 (Finite geometry and spectral graph theory) focuses on determining the cospectrality of graphs coming from finite geometries, thus giving new insights ...