Concept Lattice Based Topological Data Analysis and Reasoning
( 03. Jan – 05. Jan, 2023 )
- Bernhard Ganter (TU Dresden, DE)
- Tom Hanika (Universität Kassel, DE)
- Friedrich Martin Schneider (TU Bergakademie Freiberg, DE)
- Karl Erich Wolff (Ernst-Schröder-Zentrum Darmstadt, DE)
- Heike Clemens (für administrative Fragen)
Based on the tradition of human centered sciences as propagated by Rudolf Wille (1939 - 2017), this Dagstuhl project meeting aims at developing new approaches for human-comprehensible artificial intelligence. Well-founded in the areas of formal concept analysis (FCA) and topological data analysis (TDA), the goal is to explore the confluence of both towards novel methods of lattice based reasoning. The fundamental idea to link FCA and TDA, an approach we call relational TDA (rTDA), was developed in an earlier Dagstuhl workshop on the applications of formal sciences in 2021. Exploiting this connection, rTDA enables linking other AI research fields to TDA, such as description logics, symbolic and neuro-symbolic machine learning, as well as ontologies.
The methods of TDA aim to detect and compensate the influence of erroneous or artificially imposed metric representations of data. Despite being extensive, the toolkit of TDA is still based on a metric data representation. However, in many practical applications, the respective data universes do not have an intrinsic (i.e., natural) notion of distance.
Within the workshop several approaches for extending TDA towards relational data representations will be investigated. This extension is intended, on the one hand, to take into account the requirements of classical symbolic AI and, at the same time, to provide it with an interface to topological methods. In this context, the methods of formal concept analysis, in particular the induced lattices and implication structures, represent the core of the approach to be studied. This is complemented by the methodological apparatus for scaling data, which is extensively elaborated in the works of FCA.
In order to take a significant step in the envisioned research direction, this Dagstuhl workshop brings together experts from the fields of symbolic AI, formal concept analysis and mathematics. The ideas will be investigated in close cooperation by a mixed team of young and senior researchers, some of whom in particular have worked with Rudolf Wille.
We hope that the discussions towards relational TDA (rTDA) at the Dagstuhl workshop do result in three outcomes. First, we hope to derive a preliminary consistent and sound formulation of rTDA that may serve as a foundation for future research. Second, we want to derive from said foundation first insights on how human-comprehensible knowledge can be attained through rTDA. Third, we aim at identifying goal-oriented future research questions as well as a meaningful sequence for addressing them, in order to establish a new line of research with rTDA.
- Forschungstreffen 21353: Applications of Formal Sciences: Explainable AI (2021-09-01 - 2021-09-03) (Details)
- Artificial Intelligence
- Computational Geometry
- Machine Learning