Bachelor- und Masterarbeiten
Themen
Die Abschlussarbeiten haben stets einen inhaltlichen Bezug zu aktuellen Forschungsprojekten des Fachgebiets Wissensverarbeitung.
Die Themenstellung erfolgt in Absprache mit den Studierenden; die Ausrichtung und der Umfang der Arbeit richten sich nach dem jeweils angestrebten Anschluss. Prinzipiell liegt der Schwerpunkt bei Abschlussarbeiten auf der Methodik, während er bei Projektarbeiten auf der technischen Umsetzung liegt.
Zu folgenden Themengebieten können wir Arbeiten anbieten; zu konkreten Themen können die jeweiligen Betreuer genauere Auskunft geben:
The Lattice of Relations between Multiple Squares
In the book Conceptual Exploration by Ganter and Obiedkov (2016), Section 4.2.2 gives the example of exploring the different ways of arranging two squares in two dimensions. Later, in Section 6.1.1, the authors also consider part of the problem for the case of three squares. In this mostly theoretical project or thesis, we want to consider the complete case of three squares and, if possible, compute the lattice for the general four square setting.
Inquiries: Tobias Hille
The Truncated Birkhoff Completion
In the Birkhoff completion, certain concepts, especially in the lower part of the lattice, are generated by new objects derived from implications. However, these objects may introduce inconsistent or unrealistic combinations of attributes. Truncating the lattice by eliminating such inconsistencies ensures a more meaningful and applicable structure, particularly in real-world scenarios. This project aims to study the truncated Birkhoff completion as a method for addressing inconsistencies that arise in lattice structures generated through the Birkhoff completion of non-distributive lattices.
Inquiries: Mo Abdulla
To be (distributive) or not to be: Distributivity of Real World Data
In this work, we propose a series of experiments aimed at exploring some structural properties of non-distributive lattices on real-world datasets. Our primary objective is to implement and evaluate methods that measure how far a given lattice deviates from being distributive. These methods will provide a quantitative understanding of non-distributivity . The effectiveness of these techniques will be tested on real datasets from various domains, allowing us to assess their practical applicability.
Inquiries: Mo Abdulla
Formalizing Results of Formal Concept Analysis
Formalization of a large number of definitions and theorems in Algebra, Number Theory and Analysis in the lean prover brings the field of formal theorem proving to the forefront of mathematical research. However, mathematical notions and results from the field of Formal Concept Analysis are not yet included. Thus, the goal of this project (or thesis) is to formally prove the “Basic Theorem on Concept Lattices” (or a comparable result), in order to provide a stepping stone in this direction. Essentially, this involves building core definitions and necessary preliminary results by extending existing ones. We will aim to build a lean blueprint and if you are only interested in a small project, we will find a reasonable partial realization to stop at.
Inquiries: Tobias Hille
Sprechen Sie uns gern zu weiteren Themen an. Informationen zu den einzelnen Themen geben Ihnen gerne vorab die Betreuer.
Aufgabenstellung und Termin
Nach Absprache mit dem jeweiligen Betreuer.
Vorkenntnisse
Informatik Grundstudium bzw. 30 absolvierte Credits des Masterstudiums
Angesprochener Hörendenkreis
Informatik Bachelor und Master, Math. NF Inf. Hauptstudium
Umfang
9 Wochen für Bachelor und 6 Monate für Master
Leistungsnachweis
In der Regel Implementierung, schriftliche Ausarbeitung und Vortrag
Veranstalter
Prof. Dr. Gerd Stumme, Dr. Dominik Dürrschnabel, Mo Abdulla, M.Sc. M.Sc., Tobias Hille, M.Sc.