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This book focuses on one of the major challenges of the newly created scientific domain known as data science: turning data into actionable knowledge in order to exploit increasing data volumes and deal with their inherent complexity. Actionable knowledge has been qualitatively and intensively studied in management, business, and the social sciences but in computer science and engineering, its connection has only recently been established to data mining and its evolution, 'Knowledge Discovery and Data Mining' (KDD). Data mining seeks to extract interesting patterns from data, but, until now, the patterns discovered from data have not always been 'actionable' for decision-makers in Socio-Technical Organizations (STO). With the evolution of the Internet and connectivity, STOs have evolved into Cyber-Physical and Social Systems (CPSS) that are known to describe our world today. In such complex and dynamic environments, the conventional KDD process is insufficient, and additional processes are required to transform complex data into actionable knowledge.  

Readers are presented with advanced knowledge concepts and the analytics and information fusion (AIF) processes aimed at delivering actionable knowledge. The authors provide an understanding of the concept of 'relation' and its exploitation, relational calculus, as well as the formalization of specific dimensions of knowledge that achieve a semantic growth along the AIF processes. This book serves as an important technical presentation of relational calculus and its application to processing chains in order to generate actionable knowledge. It is ideal for graduate students, researchers, or industry professionals interested in decision science and knowledge engineering. 

Relational Calculus for Actionable Knowledge

Chapter 1 Introduction to Actionable Knowledge: Concepts & Definitions 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 Structures and Knowledge Structures 1.5.1 Symbols and Signs 1.5.2 Concepts, Names and Objects 1.6 Mastering and Improving knowledge 1.6.1 Toward a better mastery of knowledge 1.6.2 Universality and mastering knowledge 1.7 Actionable knowledge and decision support 1.7.1 Decision Support in CPSS 1.7.2 Analytics and Information Fusion (AIF) 1.7.3 Situation Awareness and actionable knowledge 1.8 Structure of the book 
Chapter 2 Knowledge and its Dimensions 2.1 Introduction 2.2. Knowledge Systems 2.2.1 Knowledge Item, Unit, Quantum, and Element2.2.2 Epistemic (knowledge) Structures and Spaces 2.2.3 Domain Knowledge and Knowledge Object 2.2.4 Semiotic bases of an 'infocentric' knowledge pipeline 2.2.5 Representation of knowledge 2.3. The multidimensionality of knowledge 2.3.1 Dimensions and characteristics of knowledge 2.3.2 Knowledge correctness2.4. Meaning of knowledge: the semantic dimension 2.4.1 Production of sense 2.4.2 The semantic traits or semes 2.4.3 Sense and Action2.4.4 Connotation and denotation 2.4.5 Representations and manipulations of sense 2.5 The temporal dimension of knowledge 2.5.1 Temporal dimension and "signified' 2.5.2 Temporal dimension validity 2.6 The ontological dimension of knowledge 2.6.1 On tracing 'notions' in an ontology 2.6.2 Domains of objects 2.6.3 Implementing the ontological dimension 2.6.4 Contextual information and knowledge 2.7 Conclusion
Chapter 3 The Knowledge Chain 3.1 Introduction 3.2 Semiotic basis 3.3 Data, Information, and Knowledge 3.3.1 What is data? 3.3.2 What is information? 3.3.3 What is knowledge? 3.3.4 Relationships between information, data, and knowledge. 3.3.5 Semantic status 3.4 Quality of Information (QoI) in the Knowledge Chain 3.4.1 Questions related to quality of information 3.4.2 Evaluation of quality of information 3.4.3 Frameworks to evaluation of quality of information 3.4.4 A guided tour of books on data and information quality 3.4.5 On information quality ontologies 3.5 A need for formalization 3.5.1 Logical propositions 3.5.2 Propositional transformations 3.5.3 Predicate logic formalization 3.5.4 Formalization by graphical representations 3.6 Knowledge reference dimension: the use of quantification 3.6.1 Order and scope of the quantification of a referent 3.6.2 Application of quantification to referents 3.6.3 Relational predicate applied to referents 3.6.4 Converse property of a relational predicate 3.6.5 Reflexivity property of a relational predicate 3.6.6 Symmetry and asymmetry properties of a relational predicate 3.6.7 Negation property of a relational predicate 3.6.8 Transitivity property of a relational predicate 3.7 Knowledge 3.8 Conclusion 
Chapter 4 Preliminaries on Crisp and Fuzzy Relational Calculus 4.1 Introduction 4.2 Relations and their properties4.2.1 Binary relations 4.2.2 Basic properties of a relation: reflexive, symmetric, and transitive 4.2.3 Closure properties 4.2.4 Finitary relations 4.3 Classes of relations 4.3.1 Equivalence relations 4.3.2 Order and partial ordering relations 4.3.3 Lattices 4.4 Crisp relational calculus 4.4.1 Images in crisp relational calculus 4.4.2 Compositions in crisp relational calculus 4.4.3 Characteristic functions of relations 4.4.4 Resolution of forward and inverse problems in crisp relational calculus 4.5 Fundamentals of fuzzy sets 4.5.1 Crisp sets 4.5.2 Fuzzy sets introduction 4.5.3 -cuts 4.5.4 Fuzzified functions 4.5.5 Operations on fuzzy sets. 4.5.5.1 Modifiers 4.5.5.2 Complements 4.5.5.3 Intersections and unions 4.5.5.4 Averaging operations 4.5.5.5 Arithmetic operations 4.6 Basics of Fuzzy relational calculus 4.6.1 Images and compositions for fuzzy relations 4.6.2 Fuzzy relations: matrix representation 4.6.3 Fuzzy Relations and Membership Matrices 4.7 Fuzzy Relational Equations: direct & inverse problems 4.7.1 Direct and inverse problems in fuzzy relational calculus 4.7.2 The role of fuzzy relational equations 4.7.3 Operations on fuzzy relations: inverses, compositions, and joins 4.7.4 Solving fuzzy relation equations4.8 References and further reading 
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 Universe of decision/action 5.3.1 Class of endogenous knowledge 5.3.2 Class of Exogenous Knowledge5.3.3 Typology of knowledge for decision-making and actions 5.3.4 The utility field of knowledge 5.3.5 A closed world assumption 5.4 The knowledge relevance and its impact on the decision-action 5.4.1 Intrinsic relevance 5.4.2 Temporal relevance dimension 5.4.3 Validity of a relevant piece of knowledge5.5 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 possibilities5.6 Towards Efficient Actions for Operational Decision-making Contexts 5.6.1 Interactive Operational Context 5.6.2 Cooperative Operational Context 5.7 Conclusion 
Chapter 6 Relational Calculus for the Generation of Actionable Knowledge 6.1 Introduction 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, 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 
Chapter 7 Conclusion