Relational Calculus for Actionable Knowledge

2022_Bookmatter_RelationalCalculusForActionabl
	Preface
	Acknowledgement
	Contents
	About the Authors
	List of Abbreviations
Bossé-Barès2022_Chapter_IntroductionToActionableKnowle
	Chapter 1: Introduction to Actionable Knowledge
		1.1 Actionable Knowledge
		1.2 Our World: Cyber-Physical and Social Systems (CPSS)
		1.3 Societal Behavior Face to Knowledge and Information
		1.4 Informational Situations
		1.5 Mastering and Improving Knowledge
			1.5.1 Toward a Better Mastery of Knowledge
			1.5.2 Universality and Mastering Knowledge
		1.6 Data, Information, and Knowledge
			1.6.1 What Is Data?
			1.6.2 What Is Information?
			1.6.3 What Is Knowledge?
		1.7 Important Notions Related to Actionable Knowledge
			1.7.1 Dynamic Decision-Making Models
			1.7.2 Situation Awareness
			1.7.3 Situations and Situation Analysis
			1.7.4 Analytics and Information Fusion (AIF)
		1.8 Positioning Relational Calculus with Respect to Actionable Knowledge
		1.9 Structure of the Book
		References
Bossé-Barès2022_Chapter_KnowledgeAndItsDimensions
	Chapter 2: Knowledge and Its Dimensions
		2.1 Introduction
		2.2 Structures and Knowledge Structures
			2.2.1 Symbols and Signs: Knowledge Semiotic Basis
			2.2.2 Concepts, Names, and Objects
			2.2.3 Epistemic Structures and Spaces
		2.3 Knowledge Systems
			2.3.1 Knowledge Item, Unit, Quantum, and Element
			2.3.2 Knowledge and Course of Actions
			2.3.3 Domain Knowledge and Knowledge Object
			2.3.4 Representation of Knowledge
		2.4 The Multidimensionality of Knowledge
			2.4.1 Dimensions and Characteristics of Knowledge
			2.4.2 Knowledge Correctness
		2.5 Meaning of Knowledge: The Semantic Dimension
			2.5.1 Production of Sense
			2.5.2 The Semantic Traits or Semes
			2.5.3 Sense and Action
			2.5.4 Connotation and Denotation
			2.5.5 Representations and Manipulations of Sense
			2.5.6 Contexts
		2.6 The Temporal Dimension of Knowledge
			2.6.1 Temporal Dimension and ``Signified´´
			2.6.2 Temporal Dimension Validity
		2.7 The Ontological Dimension of Knowledge
			2.7.1 On Tracing ``Notions´´ in an Ontology
			2.7.2 Domains of Objects
			2.7.3 Implementing the Ontological Dimension
		2.8 A Need for Formalization
			2.8.1 Logical Propositions
			2.8.2 Propositional Transformations
			2.8.3 Predicate Logic Formalization
			2.8.4 Formalization by Graphical Representations
		2.9 Knowledge Reference Dimension: The Use of Quantification
			2.9.1 Order and Scope of the Quantification of a Referent
			2.9.2 Application of Quantification to Referents
			2.9.3 Relational Predicate Applied to Referents
			2.9.4 Converse Property of a Relational Predicate
			2.9.5 Reflexivity Property of a Relational Predicate
			2.9.6 Symmetry and Asymmetry Properties of a Relational Predicate
			2.9.7 Negation Property of a Relational Predicate
			2.9.8 Transitivity Property of a Relational Predicate
		2.10 Conclusion
		References
Bossé-Barès2022_Chapter_TheInfocentricKnowledgeProcess
	Chapter 3: The Infocentric Knowledge Processing Chain
		3.1 Introduction
		3.2 Distinctions Between Data, Information, and Knowledge
			3.2.1 Semantic Status
			3.2.2 Relationships Between Data, Information, and Knowledge (DIK)
			3.2.3 The DIK Semiotic Dimensions
			3.2.4 Infocentricity and the Knowledge Processing Chain
			3.2.5 Actions of Information Computational Processing
		3.3 Quality of Information (QoI) and the Knowledge Chain
			3.3.1 Basic Questions Related to Quality of Information
			3.3.2 Evaluation of Quality of Information
			3.3.3 Frameworks for Evaluation of Quality of Information (QoI)
			3.3.4 Books on Data and Information Quality: A Guided Tour
			3.3.5 Toward an Information Quality Ontology
		3.4 Information, Uncertainty, and Entropy
			3.4.1 Information Theory and Entropy
			3.4.2 Uncertainty and Risk
			3.4.3 Dequech´s Typology of Uncertainty in Economics
			3.4.4 Dubois and Prade´s ``Typology of Defects´´
			3.4.5 Typologies of Uncertainty
			3.4.6 Representations of Uncertainty
			3.4.7 General Uncertainty Principles in Data and Information Transformations
			3.4.8 Quantification: Measures of Uncertainty
		3.5 Conclusion
		References
Bossé-Barès2022_Chapter_PreliminariesOnCrispAndFuzzyRe
	Chapter 4: Preliminaries on Crisp and Fuzzy Relational Calculus
		4.1 Introduction
		4.2 Relations and their Properties
			4.2.1 Binary Relations
			4.2.2 Basic Properties of a Relation: Reflexive, Symmetric, and Transitive
			4.2.3 Closure Properties
				4.2.3.1 Reflexive and Symmetric Closures
				4.2.3.2 Transitive Closure
			4.2.4 Finitary Relations
		4.3 Classes of Relations
			4.3.1 Equivalence Relations
			4.3.2 Order and Partial Ordering Relations
		4.4 Lattices
		4.5 Crisp Relational Calculus
			4.5.1 Images in Crisp Relational Calculus
			4.5.2 Compositions in Crisp Relational Calculus
			4.5.3 Characteristic Functions of Relations
			4.5.4 Resolution of Forward and Inverse Problems in Crisp Relational Calculus
		4.6 Fundamentals of Fuzzy Sets
			4.6.1 Crisp Sets
			4.6.2 Fuzzy Sets Introduction
			4.6.3 α-Cuts
			4.6.4 Fuzzified Functions
			4.6.5 Operations on Fuzzy Sets
				4.6.5.1 Modifiers
				4.6.5.2 Complements
				4.6.5.3 Intersections and Unions
				4.6.5.4 Averaging Operations
				4.6.5.5 Arithmetic Operations
		4.7 Basics of Fuzzy Relational Calculus
			4.7.1 Images and Compositions for Fuzzy Relations
			4.7.2 Fuzzy Relations: Matrix Representation
			4.7.3 Fuzzy Relations and Membership Matrices
		4.8 Fuzzy Relational Equations: Direct and Inverse Problems
			4.8.1 Direct and Inverse Problems in Fuzzy Relational Calculus
			4.8.2 The Role of Fuzzy Relational Equations
			4.8.3 Operations on Fuzzy Relations: Inverses, Compositions, and Joins
			4.8.4 Solving Fuzzy Relation Equations
		4.9 Conclusion
		References
Bossé-Barès2022_Chapter_ActionableKnowledgeForEfficien
	Chapter 5: Actionable Knowledge for Efficient Actions
		5.1 Introduction
		5.2 The Couple (Knowledge, Action)
			5.2.1 Influence of the Accessibility of K on the Parameter M
			5.2.2 Availability of Parameter K
		5.3 The Universe of Decision/Action
			5.3.1 Context Awareness
			5.3.2 Class of Endogenous Knowledge
			5.3.3 Class of Exogenous Knowledge
			5.3.4 Typology of Knowledge for Decision-Making and Actions
			5.3.5 The Utility Field of Knowledge
			5.3.6 A Closed World Assumption
		5.4 The Knowledge Relevance and Its Impact on the Couple (Decision, Action)
			5.4.1 Intrinsic Relevance
			5.4.2 Temporal Relevance Dimension
			5.4.3 Validity of a Relevant Piece of Knowledge
		5.5 Notion of Semantic Enrichment
			5.5.1 Semantic Enrichment by ``Symbolic Fusion´´
			5.5.2 Semantic Enrichment with Compatibility Model
			5.5.3 Semantic Enrichment with Distribution of Possibilities
		5.6 Efficient Actions in Interactive Operational Contexts
			5.6.1 Set I of Interaction Channels
			5.6.2 Set M of Modalities
			5.6.3 Set C of Constraints
		5.7 Efficient Actions in Cooperative Operational Contexts
			5.7.1 The Concept of Cooperability
			5.7.2 The Concept of System Openness
			5.7.3 Openness Structure of a Coalition
			5.7.4 Definition of an Interoperability Space
				5.7.4.1 Interoperability Competence Relation
				5.7.4.2 Fuzzy Representation of an Interoperable Action
				5.7.4.3 Fuzzy Matrices of Interoperability
			5.7.5 Definition of a Cooperability Space
				5.7.5.1 Matrix of Cooperability-System
				5.7.5.2 Matrix of Cooperability-Action
		5.8 Conclusion
		References
Bossé-Barès2022_Chapter_RelationalCalculusToSupportAna
	Chapter 6: Relational Calculus to Support Analytics and Information Fusion
		6.1 Introduction
			6.1.1 Archetypal Dynamics: An AIF Integrating Framework
			6.1.2 Generic AIF Core Processes
		6.2 A Brief Recall of Relational Calculus
			6.2.1 Relations Represented By Cuts
			6.2.2 Typology and Characterization of Relations
			6.2.3 Properties Common to Operations: Idempotence, Absorption, and Involution
			6.2.4 Usefulness of Morgan´s Laws
			6.2.5 Interest of Transitivity in AIF Processes
			6.2.6 Importance of Relations ``Closure´´
		6.3 Various Notions of Order Relations in AIF Processes
			6.3.1 Notion of Order on an Ensemble of Signals
			6.3.2 Useful Relations for the AIF Alignment Process
			6.3.3 Preorder Relations Applied to the AIF Detection Process
			6.3.4 Relations and Equivalence Relations
			6.3.5 Applying the Equivalence Relation to AIF Processes
			6.3.6 A Quotient Set of Sensors
			6.3.7 Order Relation Induced on a Quotient Set
		6.4 Formal Notion of Partition
			6.4.1 Partitioning of a Situation by an Observer
			6.4.2 Modalities of Classifying Partitions
			6.4.3 Refinement on an Observed Situation
			6.4.4 Refining Limits on a Situation
			6.4.5 Application to Electronic Warfare
		6.5 Composition of Relations for the Fusion/Merging AIF Process
			6.5.1 Properties of a Composition of Relations
			6.5.2 Application to the Formalization of Parentage
		6.6 Conclusion
		References
Bossé-Barès2022_Chapter_Conclusion
	Chapter 7: Conclusion
		References
2022_Bookmatter_RelationalCalculusForActionabl (1)
	Index