(Visual Computing, University of Konstanz, Germany)
How to Visualize Sets and Set Relations
In his talk he will focus on one particular area of information visualization: the visualization of sets and set relations (known by Venn and Euler diagrams). Unfortunately, such diagrams do not scale, they do not work for larger set numbers. Furthermore, the human ability to understand such data is limited, therefore his group developed perceptually-driven methods to improve these visualizations. Based on a review of existing methods in information visualization he will present new approaches.
CV Oliver Deussen:
Prof. Deussen graduated at Karlsruhe Institute of Technology and is a professor at University of Konstanz, one of the Excellence Universities in Germany. 2008-2020 he was a visiting professor at the Chinese Academy of Science in Shenzhen (SIAT). 2019-2020 he served as President of the Eurographics Association. His areas of interest are modeling and rendering of complex systems in computer graphics, non-photorealistic rendering, sampling theory as well as different methods for Information Visualization. He also contributed papers to geometry processing and image-based modeling methods.
Currently, he is one of the speakers of the Excellence Cluster “Centre for the Advanced Study of Collective Behaviour” at University of Konstanz. In this endeavor animal collectives ranging from insects, fish, birds up to bonobos and humans are measured and quantitatively analyzed to find and formulate rules that constitute swarm behaviour. To this end he creates virtual environments in order to study how animals react to visual signals and visualizes results from various experiments using methods from information visualization.
(Discrete Mathematics, University of Hamburg, Germany)
Tangles: from Wittgenstein to graph minors and back
Tangles, a central notion from the Robertson-Seymour theory of graph minors, have recently been axiomatised in a way that allows us to capture fuzzy phenomena of connectivity and cohesion, such as mindsets in sociology, topics in text analysis, or Wittgenstein’s family resemblances in linguistics, in an entirely formal and precise way.
This talk will offer a non-technical introduction to tangle theory that highlights its various potential applications. Participants interested in trying them out in their own field of interest can obtain well-documented code from us to facilitate this. I look forward to stimulating co-operation with the FCA community!
CV Reinhard Diestel:
After undergraduate studies of Mathematics and Philosophy at Hamburg and Cambridge (UK) Reinhard Diestel did his PhD at Trinity College, Cambridge, under the supervision of Béla Bollobás. From 1986 to 1989 he was a Research Fellow at St. John’s College, Cambridge, habilitating externally at Hamburg in 1987. After a few years at the Sonderforschungsbereich 343 in Bielefeld and a year in Oxford he became a professor at Chemnitz in 1994, from where he moved to Hamburg in 1999.
(Department of Computer Science, Palacký University Olomouc, Czech Republic)
Formal Concept Analysis in Boolean Matrix Factorization: Algorithms and Extensions to Ordinal and Fuzzy-Valued Data
It has been nearly fifteen years since Belohlavek and Vychodil first highlighted the usefulness of Formal Concept Analysis (FCA) in Boolean Matrix Factorization (BMF) and introduced the initial FCA-based algorithms for BMF. This work sparked a thriving research direction within our department that persists to this day. The talk provides an overview of our ongoing research efforts, with a particular emphasis on the application of FCA in the development of algorithms for BMF. Moreover, the progress made in extending these techniques to the factorization of matrices containing ordinal and fuzzy-valued data will be discussed.
CV Jan Konečný:
Jan Konečný is an associate professor at Palacky University in Olomouc, Czech Republic, where he has been a faculty member since 2009. He holds a PhD in Systems Science from Binghamton University, SUNY, and a PhD in Computer Science from Palacky University Olomouc. His research interests include Uncertainty Theories, Data Analysis, Theoretical Computer Science, and Discrete Mathematics, with a particular interest in fuzzy logic, fuzzy sets, and fuzzy relational systems. He has authored and coauthored over 35 journal papers and 20 conference papers, and has worked in both academia and industry.
Manuel Ojeda Aciego
(Department of Applied mathematics, University of Málaga, Spain)
On the φ-degree of inclusion
The notion of inclusion is a cornerstone in set theory and therefore its generalisation in fuzzy set theory is of great interest. The functional degree (or φ-degree) of inclusion is defined to represent the degree of inclusion between two L-fuzzy sets in terms of a mapping that determines the minimal modifications required in one L-fuzzy set to be included in another in the sense of Zadeh. Thus, this notion differs from others existing in the literature because the φ-degree of inclusion is considered as a mapping instead of a value in the unit interval. We show that the φ-degree of inclusion satisfies versions of many common axioms usually required for inclusion measures in the literature.
Considering the relationship between fuzzy entropy and Young’s axioms for measures of inclusion, we also present a measure of entropy based on the φ-degree of inclusion that is consistent with the axioms of De Luca and Termini. We then continue to study the properties of the φ-degree of inclusion and show that, given a fixed pair of fuzzy sets, their φ-degree of inclusion can be linked to a fuzzy conjunction that is part of an adjoint pair. We also show that when this pair is used as the underlying structure to provide a fuzzy interpretation of the modus ponens inference rule, it provides the maximum possible truth value in the conclusion among all those values obtained by fuzzy modus ponens using any other possible adjoint pair. Finally, we will focus on current work on the integration of the φ-degree of inclusion with FCA.
CV Manuel Ojeda Aciego:
Manuel Ojeda-Aciego (MSc in Mathematics, PhD in Computer Science) is currently a Full Professor of Applied Mathematics in the University of Málaga, Spain. He has (co-)authored more than 160 papers in scientific journals and proceedings of international conferences. His current research interests include (fuzzy) formal concept analysis, residuated and multi-adjoint logic programming, and algebraic structures for computer science. He is the president of the Computer Science Committee of the Royal Spanish Mathematical Society, serves the Editorial Board of Fuzzy Sets and Systems, Mathematics, and the Intl J on Uncertainty and Fuzziness in Knowledge-based Systems, and is a member of the Steering Committee of the international conferences Concept Lattices and their Applications (CLA) and Information Processing and Management of Uncertainty (IPMU).
(Department of Ethics, Governance and Society, Vrije Universiteit Amsterdam, Netherlands)
Logical foundations of categorization theory
Categories are cognitive tools that humans use to organize their experience, understand and function in the world, and understand and interact with each other, by grouping things together which can be meaningfully compared and evaluated. They are key to the use of language, the construction of knowledge and identity, and the formation of agents’ evaluations and decisions. Categorization is the basic operation humans perform e.g. when they relate experiences/actions/objects in the present to ones in the past, thereby recognizing them as instances of the same type. This is what we do when we try and understand what an object is or does, or what a situation means, and when we make judgments or decisions based on experience. The literature on categorization is expanding rapidly in fields ranging from cognitive linguistics to social and management science to AI, and the emerging insights common to these disciplines concern the dynamic essence of categories, and the tight interconnection between the dynamics of categories and processes of social interaction. However, these key aspects are precisely those that both the extant foundational views on categorization struggle the most to address. In this lecture, we will discuss a logical approach, semantically based on formal contexts and their associated concept lattices, which aims at creating an environment in which these three cognitive processes can be analyzed in their relationships to one another, and propose several research directions, developing which, novel foundations of categorization theory can be built.
CV Alessandra Palmigiano:
Alessandra Palmigiano holds the Chair of Logic and Management Theory at the Department of Ethics, Governance, and Society of the School of Business and Economics of the Vrije Universiteit Amsterdam, where she leads a research group of 10 PhD students and 2 assistant professors. Her core expertise is in logic, and, in the past ten years (also thanks to a number of grants), her research has been focusing on categories (understood in the Aristotelian sense, and formalized as formal concepts) as the most fundamental cognitive tools humans use for the construction of knowledge and meaning, evaluation, identity-formation and decision-making. With her research group, she is engaging in a research program aimed at building a powerful and far-reaching logical theory of social interaction and its dynamics on the basis of categories and categorization. This research program has direct relevance for a wide range of disciplines which include AI, (especially multimodal machine learning), (computational) linguistics, cognitive and social sciences, management science. Especially working in collaboration with researchers in these disciplines, her strong interest is in using formal tools for representing categorical dynamics to track changes in meaning, analyse the processes of decision-making via persuasion and deliberation, and other aspects of cognition.
William T. Trotter
(School of Mathematics, Georgia Tech Institute, USA)
Modern Concepts of Dimension for Partially Ordered Sets
Partially ordered sets (posets) are useful models for rankings on large data sets where linear orders may fail to exist or may be extremely difficult to determine. Many different parameters have been proposed to measure the complexity of a poset, but by far the most widely studied has been the Dushnik-Miller notion of dimension. Several alternate forms of dimension have been proposed and studied, and the pace of research on this theme has accelerated in the past 10 years. Among these variants are Boolean dimension, local dimension, fractional dimension and fractional local dimension. The last in this list holds promise for applications since it provides an answer to the natural question: How can we determine a partial order given only piecemeal observations made, often independently, and typically with conflicts, on extremely large populations. As an added bonus, this line of research has already produced results that have intrinsic mathematical appeal.
In this talk, I will introduce the several concepts of dimension, outline some key results and applications for each, and close with more detailed comments on fractional local dimension.
CV William T. Trotter:
Professor Trotter was appointed Professor and Chair of the School of Mathematics of the Georgia Institute of Technology in 2002, and served in that capacity until 2009. Previous he served as Department Chair at both Arizona State University, where he was also a Regents’ Professor, and at the University of South Carolina, where he was also a Carolina Research Professor. Professor Trotter has more than 150 refereed journal publications, and he has more than 100 co-authors, including internationally recognized giants such as Endre Szemerédi (2012 Abel Prize), László Lovász (2010 Kyoto Prize and 2021 Abel Prize) and Noga Alon (2000 Pólya Prize and 2008 Gödel Prize). However, among his co-authors are more than 30 assistant professors, five post-docs, and more than 20 graduate students.