Formal Concept Analysis: 17th International Conference, ICFCA 2023, Kassel, Germany, July 17–21, 2023, Proceedings

Description

This book constitutes the proceedings of the 17th International Conference on Formal Concept Analysis, ICFCA 2023, which took place in Kassel, Germany, in July 2023. The 13 full papers presented in this volume were carefully reviewed and selected from 19 submissions. The International Conference on Formal Concept Analysis serves as a platform for researchers from FCA and related disciplines to showcase and exchange their research findings. The papers are organized in two topical sections, first "Theory" and second "Applications and Visualization". Preface Organization Abstracts of Invited Talks How to Visualize Sets and Set Relations Tangles: from Wittgenstein to Graph Minors and Back Formal Concept Analysis in Boolean Matrix Factorization: Algorithms and Extensions to Ordinal and Fuzzy-Valued Data On the -Degree of Inclusion Logical Foundations of Categorization Theory Modern Concepts of Dimension for Partially Ordered Sets Latebreaking Result Talk Breaking the Barrier: A Computation of the Ninth Dedekind Number Contents Theory Approximating Fuzzy Relation Equations Through Concept Lattices 1 Introduction 2 Preliminaries 3 Approximating Fuzzy Relation Equations 4 Selecting the Best Approximation 5 Conclusions and Future Work References Doubly-Lexical Order Supports Standardisation and Recursive Partitioning of Formal Context 1 Introduction 2 Jointly Reverse Lectic Order 2.1 Lectic and Reverse Lectic Orders 2.2 Maxmod-Partition and Reverse Lectic Order 2.3 Doubly-Lexical Order 2.4 Jointly Reverse Lectic Order 2.5 JRL Order and Carve 3 Carve Identifies Nested Blocks in JRL-Ordered Matrix 3.1 Connected Components are Blocks 3.2 Blocks are Nested 4 Coordinated Browsing 5 Context Standardisation and Restoration 6 Discussion References Graph-FCA Meets Pattern Structures 1 Introduction 2 Preliminaries 2.1 Pattern Structures (PS) 2.2 Graph-FCA 3 Graph-PS: Extending Graph-FCA with Pattern Structures 3.1 Graph Context 3.2 Projected Graph Patterns (PGP) 3.3 Graph Concepts 4 Application to RDFS Graphs 5 Conclusion and Perspectives References On the Commutative Diagrams Among Galois Connections Involved in Closure Structures 1 Introduction 2 Preliminaries 3 Crisp Closure Systems 4 A Study on Commutativity of Diagrams 5 Conclusions and Further Work References Scaling Dimension 1 Introduction 2 Formal Concepts Derived from Data Tables 2.1 Pre-scalings 2.2 Interordinal Plain Scaling 2.3 Scale Measures and Views 3 Measurability 4 Small Case Study 5 Discussion and Future Work 6 Conclusion References Three Views on Dependency Covers from an FCA Perspective 1 Introduction and Motivation 2 The Relevance of the Implication Problem 3 Definitions 4 Algorithms to Compute the Closure of a Set of Attributes 4.1 The Closure Algorithm 4.2 The Linclosure Algorithm 4.3 Experimental Evaluation of Closure and Linclosure 5 Covers of Dependencies 5.1 Four Main Characteristics of Covers 5.2 The Minimal Cover in the RDBM and Its Variations 5.3 The Canonical-Direct Basis 5.4 The Duquenne-Guigues basis 6 Discussion and Conclusion References A Triadic Generalisation of the Boolean Concept Lattice 1 Introduction 2 Formal and Triadic Concept Analysis 2.1 Formal Concept Analysis 2.2 Triadic Concept Analysis 3 The Loss of Duality in Triadic Concept Analysis 4 A Triadic Generalisation of the Boolean Concept Lattice 5 On the Minimum Number of Objects in a Bn,m Tricontext 6 Discussion and Conclusion References Applications and Visualization Computing Witnesses for Centralising Monoids on a Three-Element Set 1 Introduction 2 Preliminaries 3 Finding Witness-Complete Sets 4 Computing All Centralising Monoids on {0,1,2} References Description Quivers for Compact Representation of Concept Lattices and Ensembles of Decision Trees 1 Introduction 2 Theoretical Background 2.1 Formal Concept Analysis 2.2 Difference Generators 3 Description Quivers for Unsupervised Setting 3.1 Description Quiver 3.2 Path in Quiver 4 Decision Quivers for Supervised Setting 4.1 Target-based Decision Quiver 4.2 Arrow-Based Decision Quiver 4.3 Summation of Arrow-Based Decision Quivers 4.4 Conversion of Target-Based Quivers to Arrow-Based Quivers 5 Experiments 5.1 Datasets 5.2 Sizes of Difference Generators 5.3 Summation of Decision Trees 6 Conclusion References Examples of Clique Closure Systems 1 Introduction 2 Maximal Cliques 3 Closed Cliques 4 Examples References On the Maximal Independence Polynomial of the Covering Graph of the Hypercube up to n=6 1 Introduction 2 Problem Statement and Basic Facts 2.1 Graphs and Independent Sets 2.2 Formal Concept Analysis and Symmetric Concepts 2.3 Conceptual Representation of Qn 3 Algorithm 4 Results 4.1 Level-Union MIS 4.2 Lattice-Based Results 4.3 Spectral-Based Results 5 Conclusions References Relational Concept Analysis in Practice: Capitalizing on Data Modeling Using Design Patterns 1 Introduction 2 Background and Motivation 3 Design Patterns 3.1 Describing a Design Pattern 3.2 The Design Pattern Separate/Gather Views 3.3 The Design Pattern Level Relations 4 Perspectives 5 Conclusion References Representing Concept Lattices with Euler Diagrams 1 Introduction 2 Rounded Rectangular Euler Diagrams 3 Reducing Concept Lattices 4 Two Examples of Constructing Euler Diagrams 5 Conclusion References Author Index