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Table of Contents
Intro; Preface; Organization; Reasoning Web 2019 Sponsors; Contents; Classical Algorithms for Reasoning and Explanation in Description Logics; 1 Introduction; 2 Description Logics; 2.1 Syntax; 2.2 Semantics; 2.3 Reasoning Problems; 2.4 Reductions Between Reasoning Problems; 3 Tableau Procedures; 3.1 Deciding Concept Satisfiability; 3.2 TBox Reasoning; 4 Axiom Pinpointing; 4.1 Computing One Justification; 4.2 Computing All Justifications; 4.3 Computing All Repairs; 4.4 Computing Justifications and Repairs Using SAT Solvers; 5 Summary and Outlook; A Appendix; A.1 Computational Complexity
A.2 Propositional Logic and SATReferences; Explanation-Friendly Query Answering Under Uncertainty; 1 Introduction; 2 The Datalog+/- Family of Ontology Languages; 2.1 Preliminary Concepts and Notations; 2.2 Syntax and Semantics of Datalog+/-; 2.3 Conjunctive Query Answering; 2.4 Datalog+/- Fragments: In Search of Decidability and Tractability; 3 Query Answering over Probabilistic Knowledge Bases; 3.1 Brief Overview of Basic Probabilistic Graphical Models; 3.2 Probabilistic Datalog+/-; 3.3 Towards Explainable Probabilistic Ontological Reasoning
4 Inconsistency-Tolerant Query Answering with Datalog+/-4.1 Relationship with (Classical) Consistent Answers; 4.2 Relationship with IAR Semantics; 4.3 Lazy Answers; 4.4 Towards Explainable Inconsistency-Tolerant Query Answering; 5 Discussion and Future Research Directions; References; Provenance in Databases: Principles and Applications; 1 Introduction; 2 Provenance; 3 Example Applications; 4 Beyond Relational Provenance; 5 Outlook; References; Knowledge Representation and Rule Mining in Entity-Centric Knowledge Bases; 1 Introduction; 1.1 Knowledge Bases; 1.2 Applications
1.3 Knowledge Representation and Rule Mining2 Knowledge Representation; 2.1 Entities; 2.2 Classes; 2.3 Relations; 2.4 Knowledge Bases; 2.5 The Semantic Web; 2.6 Challenges in Knowledge Representation; 3 Rule Mining; 3.1 Rules; 3.2 Rule Mining; 3.3 Rule Mining Approaches; 3.4 Related Approaches; 3.5 Challenges in Rule Mining; 4 Representation Learning; 4.1 Embedding; 4.2 Neural Networks; 4.3 Knowledge Base Embeddings; 4.4 Challenges in Representation Learning; 5 Conclusion; A Computation of Support and Confidence; References; Explaining Data with Formal Concept Analysis; 1 Introduction; 2 TL
DR
Formal Concept Analysis in a Nutshell3 Concept Lattices; 3.1 Formal Contexts and Cross Tables; 3.2 The Derivation Operators; 3.3 Formal Concepts, Extent and Intent; 3.4 Conceptual Hierarchy; 3.5 Concept Lattice Diagrams; 3.6 Supremum and Infimum; 3.7 Complete Lattices; 3.8 The Basic Theorem of FCA; 3.9 Computing All Concepts of a Context; 3.10 Drawing Concept Lattices; 3.11 Clarifying and Reducing a Formal Context; 3.12 Additive and Nested Line Diagrams; 4 Closure Systems; 4.1 Definition and Examples; 4.2 The Next Closure Algorithm; 5 Implications; 5.1 Implications of a Formal Context
A.2 Propositional Logic and SATReferences; Explanation-Friendly Query Answering Under Uncertainty; 1 Introduction; 2 The Datalog+/- Family of Ontology Languages; 2.1 Preliminary Concepts and Notations; 2.2 Syntax and Semantics of Datalog+/-; 2.3 Conjunctive Query Answering; 2.4 Datalog+/- Fragments: In Search of Decidability and Tractability; 3 Query Answering over Probabilistic Knowledge Bases; 3.1 Brief Overview of Basic Probabilistic Graphical Models; 3.2 Probabilistic Datalog+/-; 3.3 Towards Explainable Probabilistic Ontological Reasoning
4 Inconsistency-Tolerant Query Answering with Datalog+/-4.1 Relationship with (Classical) Consistent Answers; 4.2 Relationship with IAR Semantics; 4.3 Lazy Answers; 4.4 Towards Explainable Inconsistency-Tolerant Query Answering; 5 Discussion and Future Research Directions; References; Provenance in Databases: Principles and Applications; 1 Introduction; 2 Provenance; 3 Example Applications; 4 Beyond Relational Provenance; 5 Outlook; References; Knowledge Representation and Rule Mining in Entity-Centric Knowledge Bases; 1 Introduction; 1.1 Knowledge Bases; 1.2 Applications
1.3 Knowledge Representation and Rule Mining2 Knowledge Representation; 2.1 Entities; 2.2 Classes; 2.3 Relations; 2.4 Knowledge Bases; 2.5 The Semantic Web; 2.6 Challenges in Knowledge Representation; 3 Rule Mining; 3.1 Rules; 3.2 Rule Mining; 3.3 Rule Mining Approaches; 3.4 Related Approaches; 3.5 Challenges in Rule Mining; 4 Representation Learning; 4.1 Embedding; 4.2 Neural Networks; 4.3 Knowledge Base Embeddings; 4.4 Challenges in Representation Learning; 5 Conclusion; A Computation of Support and Confidence; References; Explaining Data with Formal Concept Analysis; 1 Introduction; 2 TL
DR
Formal Concept Analysis in a Nutshell3 Concept Lattices; 3.1 Formal Contexts and Cross Tables; 3.2 The Derivation Operators; 3.3 Formal Concepts, Extent and Intent; 3.4 Conceptual Hierarchy; 3.5 Concept Lattice Diagrams; 3.6 Supremum and Infimum; 3.7 Complete Lattices; 3.8 The Basic Theorem of FCA; 3.9 Computing All Concepts of a Context; 3.10 Drawing Concept Lattices; 3.11 Clarifying and Reducing a Formal Context; 3.12 Additive and Nested Line Diagrams; 4 Closure Systems; 4.1 Definition and Examples; 4.2 The Next Closure Algorithm; 5 Implications; 5.1 Implications of a Formal Context