Subjective Logic A Formalism for Reasoning under Uncertainty

• Main Author: Jøsang, Audun
• Format: eBook
• Language: English
• Published: Cham Springer International Publishing AG 2016; Springer International Publishing
• Edition: 1
• Series: Artificial Intelligence: Foundations, Theory, and Algorithms
• Subjects: Artificial Intelligence; Computer Science; Logic; Mathematical Logic and Formal Languages; Systems and Data Security

Table of Contents:

• 10.6 The Multinomial Subjective Bayes' Theorem -- 10.6.1 Principles for Inverting Multinomial Conditional Opinions -- 10.6.2 Uncertainty Mass of Inverted Multinomial Conditionals -- 10.6.3 Deriving Multinomial Inverted Conditionals -- 10.7 Multinomial Abduction -- 10.8 Example: Military Intelligence Analysis -- 10.8.1 Example: Intelligence Analysis with Probability Calculus -- 10.8.2 Example: Intelligence Analysis with Subjective Logic -- Chapter 11 Joint and Marginal Opinions -- 11.1 Joint Probability Distributions -- 11.2 Joint Opinion Computation -- 11.2.1 Joint Base Rate Distribution -- 11.2.2 Joint Uncertainty Mass -- 11.2.3 Assembling the Joint Opinion -- 11.3 Opinion Marginalisation -- 11.3.1 Opinion Marginalisation Method -- 11.4 Example: Match-Fixing Revisited -- 11.4.1 Computing the Join Opinion -- 11.4.2 Computing Marginal Opinions -- Chapter 12 Belief Fusion -- 12.1 Interpretation of Belief Fusion -- 12.1.1 Correctness and Consistency Criteria for Fusion Models -- 12.1.2 Classes of Fusion Situations -- 12.1.3 Criteria for Fusion Operator Selection -- 12.2 Belief Constraint Fusion -- 12.2.1 Method of Constraint Fusion -- 12.2.2 Frequentist Interpretation of Constraint Fusion -- 12.2.3 Expressing Preferences with Subjective Opinions -- 12.2.4 Example: Going to the Cinema, First Attempt -- 12.2.5 Example: Going to the Cinema, Second Attempt -- 12.2.6 Example: Not Going to the Cinema -- 12.3 Cumulative Fusion -- 12.3.1 Aleatory Cumulative Fusion -- 12.3.2 Epistemic Cumulative Fusion -- 12.4 Averaging Belief Fusion -- 12.5 Weighted Belief Fusion -- 12.6 Consensus &amp -- Compromise Fusion -- 12.7 Example Comparison of Fusion Operators -- Chapter 13 Unfusion and Fission of Subjective Opinions -- 13.1 Unfusion of Opinions -- 13.1.1 Cumulative Unfusion -- 13.1.2 Averaging Unfusion -- 13.1.3 Example: Cumulative Unfusion of Binomial Opinions
• Intro -- Foreword -- Preface -- Acknowledgements -- Contents -- Chapter 1 Introduction -- Chapter 2 Elements of Subjective Opinions -- 2.1 Motivation for the Opinion Representation -- 2.2 Flexibility of Representation -- 2.3 Domains and Hyperdomains -- 2.4 Random Variables and Hypervariables -- 2.5 Belief Mass Distribution and Uncertainty Mass -- 2.6 Base Rate Distributions -- 2.7 Probability Distributions -- Chapter 3 Opinion Representations -- 3.1 Belief and Trust Relationships -- 3.2 Opinion Classes -- 3.3 Aleatory and Epistemic Opinions -- 3.4 Binomial Opinions -- 3.4.1 Binomial Opinion Representation -- 3.4.2 The Beta Binomial Model -- 3.4.3 Mapping Between a Binomial Opinion and a Beta PDF -- 3.5 Multinomial Opinions -- 3.5.1 The Multinomial Opinion Representation -- 3.5.2 The Dirichlet Multinomial Model -- 3.5.3 Visualising Dirichlet Probability Density Functions -- 3.5.4 Coarsening Example: From Ternary to Binary -- 3.5.5 Mapping Between Multinomial Opinion and Dirichlet PDF -- 3.5.6 Uncertainty-Maximisation -- 3.6 Hyper-opinions -- 3.6.1 The Hyper-opinion Representation -- 3.6.2 Projecting Hyper-opinions to Multinomial Opinions -- 3.6.3 The Dirichlet Model Applied to Hyperdomains -- 3.6.4 Mapping Between a Hyper-opinion and a Dirichlet HPDF -- 3.6.5 Hyper-Dirichlet PDF -- 3.7 Alternative Opinion Representations -- 3.7.1 Probabilistic Notation of Opinions -- 3.7.2 Qualitative Opinion Representation -- Chapter 4 Decision Making Under Vagueness and Uncertainty -- 4.1 Aspects of Belief and Uncertainty in Opinions -- 4.1.1 Sharp Belief Mass -- 4.1.2 Vague Belief Mass -- 4.1.3 Dirichlet Visualisation of Opinion Vagueness -- 4.1.4 Focal Uncertainty Mass -- 4.2 Mass-Sum -- 4.2.1 Mass-Sum of a Value -- 4.2.2 Total Mass-Sum -- 4.3 Utility and Normalisation -- 4.4 Decision Criteria -- 4.5 The Ellsberg Paradox -- 4.6 Examples of Decision Making
• 13.2 Fission of Opinions -- 13.2.1 Cumulative Fission -- 13.2.2 Example Fission of Opinion -- 13.2.3 Averaging Fission -- Chapter 14 Computational Trust -- 14.1 The Notion of Trust -- 14.1.1 Reliability Trust -- 14.1.2 Decision Trust -- 14.1.3 Reputation and Trust -- 14.2 Trust Transitivity -- 14.2.1 Motivating Example for Transitive Trust -- 14.2.2 Referral Trust and Functional Trust -- 14.2.3 Notation for Transitive Trust -- 14.2.4 Compact Notation for Transitive Trust Paths -- 14.2.5 Semantic Requirements for Trust Transitivity -- 14.3 The Trust-Discounting Operator -- 14.3.1 Principle of Trust Discounting -- 14.3.2 Trust Discounting with Two-Edge Paths -- 14.3.3 Example: Trust Discounting of Restaurant Advice -- 14.3.4 Trust Discounting for Multi-edge Path -- 14.4 Trust Fusion -- 14.5 Trust Revision -- 14.5.1 Motivation for Trust Revision -- 14.5.2 Trust Revision Method -- 14.5.3 Example: Conflicting Restaurant Recommendations -- Chapter 15 Subjective Trust Networks -- 15.1 Graphs for Trust Networks -- 15.1.1 Directed Series-Parallel Graphs -- 15.2 Outbound-Inbound Set -- 15.2.1 Parallel-Path Subnetworks -- 15.2.2 Nesting Level -- 15.3 Analysis of DSPG Trust Networks -- 15.3.1 Algorithm for Analysis of DSPG -- 15.3.2 Soundness Requirements for Receiving Advice Opinions -- 15.4 Analysing Complex Non-DSPG Trust Networks -- 15.4.1 Synthesis of DSPG Trust Network -- 15.4.2 Criteria for DSPG Synthesis -- Chapter 16 Bayesian Reputation Systems -- 16.1 Computing Reputation Scores -- 16.1.1 Binomial Reputation Score -- 16.1.2 Multinomial Reputation Scores -- 16.2 Collecting and Aggregating Ratings -- 16.2.1 Collecting Ratings -- 16.2.2 Aggregating Ratings with Ageing -- 16.2.3 Reputation Score Convergence with Time Decay -- 16.3 Base Rates for Ratings -- 16.3.1 Individual Base Rates -- 16.3.2 Total History Base Rate
• 16.3.3 Sliding Time Window Base Rate
• 4.6.1 Decisions with Difference in Projected Probability -- 4.6.2 Decisions with Difference in Sharpness -- 4.6.3 Decisions with Difference in Vagueness and Uncertainty -- 4.7 Entropy in the Opinion Model -- 4.7.1 Outcome Surprisal -- 4.7.2 Opinion Entropy -- 4.8 Conflict Between Opinions -- 4.9 Ambiguity -- Chapter 5 Principles of Subjective Logic -- 5.1 Related Frameworks for Uncertain Reasoning -- 5.1.1 Comparison with Dempster-Shafer Belief Theory -- 5.1.2 Comparison with Imprecise Probabilities -- 5.1.3 Comparison with Fuzzy Logic -- 5.1.4 Comparison with Kleene's Three-Valued Logic -- 5.2 Subjective Logic as a Generalisation of Probabilistic Logic -- 5.3 Overview of Subjective-Logic Operators -- Chapter 6 Addition, Subtraction and Complement -- 6.1 Addition -- 6.2 Subtraction -- 6.3 Complement -- Chapter 7 Binomial Multiplication and Division -- 7.1 Binomial Multiplication and Comultiplication -- 7.1.1 Binomial Multiplication -- 7.1.2 Binomial Comultiplication -- 7.1.3 Approximations of Product and Coproduct -- 7.2 Reliability Analysis -- 7.2.1 Simple Reliability Networks -- 7.2.2 Reliability Analysis of Complex Systems -- 7.3 Binomial Division and Codivision -- 7.3.1 Binomial Division -- 7.3.2 Binomial Codivision -- 7.4 Correspondence with Probabilistic Logic -- Chapter 8 Multinomial Multiplication and Division -- 8.1 Multinomial Multiplication -- 8.1.1 Elements of Multinomial Multiplication -- 8.1.2 Normal Multiplication -- 8.1.3 Justification for Normal Multinomial Multiplication -- 8.1.4 Proportional Multiplication -- 8.1.5 Projected Multiplication -- 8.1.6 Hypernomial Product -- 8.1.7 Product of Dirichlet Probability Density Functions -- 8.2 Examples of Multinomial Product Computation -- 8.2.1 Comparing Normal, Proportional and Projected Products -- 8.2.2 Hypernomial Product Computation -- 8.3 Multinomial Division
• 8.3.1 Elements of Multinomial Division -- 8.3.2 Averaging Proportional Division -- 8.3.3 Selective Division -- Chapter 9 Conditional Reasoning and Subjective Deduction -- 9.1 Introduction to Conditional Reasoning -- 9.2 Probabilistic Conditional Inference -- 9.2.1 Bayes' Theorem -- 9.2.2 Binomial Probabilistic Deduction and Abduction -- 9.2.3 Multinomial Probabilistic Deduction and Abduction -- 9.3 Notation for Subjective Conditional Inference -- 9.3.1 Notation for Binomial Deduction and Abduction -- 9.3.2 Notation for Multinomial Deduction and Abduction -- 9.4 Binomial Deduction -- 9.4.1 Marginal Base Rate for Binomial Opinions -- 9.4.2 Free Base-Rate Interval -- 9.4.3 Method for Binomial Deduction -- 9.4.4 Justification for the Binomial Deduction Operator -- 9.5 Multinomial Deduction -- 9.5.1 Marginal Base Rate Distribution -- 9.5.2 Free Base-Rate Distribution Intervals -- 9.5.3 Constraints for Multinomial Deduction -- 9.5.4 Method for Multinomial Deduction -- 9.6 Example: Match-Fixing -- 9.7 Interpretation of Material Implication in Subjective Logic -- 9.7.1 Truth-Functional Material Implication -- 9.7.2 Material Probabilistic Implication -- 9.7.3 Relevance in Implication -- 9.7.4 Subjective Interpretation of Material Implication -- 9.7.5 Comparison with Subjective Logic Deduction -- 9.7.6 How to Interpret Material Implication -- Chapter 10 Subjective Abduction -- 10.1 Introduction to Abductive Reasoning -- 10.2 Relevance and Dependence -- 10.2.1 Relevance and Irrelevance -- 10.2.2 Dependence and Independence -- 10.3 Binomial Subjective Bayes' Theorem -- 10.3.1 Principles for Inverting Binomial Conditional Opinions -- 10.3.2 Uncertainty Mass of Inverted Binomial Conditionals -- 10.3.3 Deriving Binomial Inverted Conditionals -- 10.3.4 Convergence of Repeated Inversions -- 10.4 Binomial Abduction -- 10.5 Illustrating the Base-Rate Fallacy