فهرست مطالب
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
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
