Table of Contents -- Preface -- Chapter 1 Modeling Agent Epistemic States: An Informal Overview -- 1.1 Models of Agent Epistemic States -- 1.2 Propositional Epistemic Model -- 1.3 Probabilistic Epistemic Model -- 1.4 Possible World Epistemic Model -- 1.5 Comparisons of Models -- 1.6 P3 Model for Decision-Making Agents -- Chapter 2 Mathematical Preliminaries -- 2.1 Usage of Symbols -- 2.2 Sets, Relations, and Functions -- 2.3 Graphs and Trees -- 2.4 Probability -- 2.5 Algorithmic Complexity -- 2.6 Further Readings -- Chapter 3 Classical Logics for the Propositional Epistemic Model -- 3.1 Propositional Logic -- 3.1.1 Axiomatic Theory for Propositional Logic -- 3.1.2 Soundness and Completeness Theorem -- 3.2 First-Order Logic -- 3.2.1 Axiomatic Theory for First-order Logic -- 3.2.2 Soundness and Completeness Theorem -- 3.2.3 Applications -- 3.3 Theorem Proving Procedure -- 3.3.1 Clausal Form -- 3.3.2 Herbrand's theorem -- 3.3.3 Implementation of Herbrand's theorem -- 3.4 Resolution Theorem Proving -- 3.4.1 Resolution principle and unification -- 3.5 Refutation Procedure -- 3.6 Complexity Analysis -- 3.7 Further Readings -- Chapter 4 Logic Programming -- 4.1 The Concept -- 4.2 Program Clauses and Goals -- 4.3 Program Semantics -- 4.4 Definite Programs -- 4.5 Normal Programs -- 4.6 Prolog -- 4.6.1 Prolog Syntax -- 4.6.2 Theoretical Background -- 4.6.3 Backtracking -- 4.6.4 The Cut -- 4.6.5 Special Constructs and Connectives -- 4.6.6 Negation -- 4.6.7 Equality -- 4.6.8 List -- 4.6.9 Arithmetic -- 4.6.10 Input/Output -- 4.6.11 Clause Management -- 4.6.12 Set Evaluation -- 4.6.13 Meta Programming -- 4.7 Prolog Systems -- 4.8 Complexity Analysis -- 4.9 Further Readings -- Chapter 5 Logical Rules for Making Decisions -- 5.1 Evolution of Rules -- 5.2 Bayesian Probability Theory for Handling Uncertainty -- 5.3 Dempster-Shafer Theory for Handling Uncertainty.

5.4 Measuring Consensus -- 5.5 Combining Sources of Varying Confidence -- 5.6 Advantages and Disadvantages of Rule-Based Systems -- 5.7 Background and Further Readings -- Chapter 6 Bayesian Belief Networks -- 6.1 Bayesian Belief Networks -- 6.2 Conditional Independence in Belief Networks -- 6.3 Evidence, Belief, and Likelihood -- 6.4 Prior Probabilities in Networks without Evidence -- 6.5 Belief Revision -- 6.6 Evidence Propagation in Polytrees -- 6.6.1 Upward Propagation in a Linear Fragment -- 6.6.2 Downward Propagation in a Linear Fragment -- 6.6.3 Upward Propagation in a Tree Fragment -- 6.6.4 Downward Propagation in a Tree Fragment -- 6.6.5 Upward Propagation in a Polytree Fragment -- 6.6.6 Downward Propagation in a Polytree Fragment -- 6.6.7 Propagation Algorithm -- 6.7 Evidence Propagation in Directed Acyclic Graphs -- 6.7.1 Graphical Transformation -- 6.7.2 Join Tree Initialization -- 6.7.3 Propagation in Join Tree and Marginalization -- 6.7.4 Handling Evidence -- 6.8 Complexity of Inference Algorithms -- 6.9 Acquisition of Probabilities -- 6.10 Advantages and Disadvantages of Belief Networks -- 6.11 Belief Network Tools -- 6.12 Further Readings -- Chapter 7 Influence Diagrams for Making Decisions -- 7.1 Expected Utility Theory and Decision Trees -- 7.2 Influence Diagrams -- 7.3 Inferencing in Influence Diagrams -- 7.4 Compilation of Influence Diagrams -- 7.5 Inferencing in Strong Junction Tress -- 7.6 Further Readings -- Chapter 8 Modal Logics for the Possible World Epistemic Model -- 8.1 Historical Development of Modal Logics -- 8.2 Systems of Modal Logic -- 8.3 Deductions in Modal Systems -- 8.3.1 Principle of Duality -- 8.3.2 Theorems of K -- 8.3.3 Theorems of D -- 8.3.4 Theorems of T -- 8.3.5 Theorems of S4 -- 8.3.6 Theorems of B -- 8.3.7 Theorems of S5 -- 8.3.8 Theorems of S5' -- 8.4 Modality -- 8.5 Decidability and Matrix Method.

8.6 Relationships among Modal Systems -- 8.7 Possible World Semantics -- 8.8 Soundness and Completeness Results -- 8.9 Complexity and Decidability of Modal Systems -- 8.10 Modal First-Order Logics -- 8.11 Resolution in Modal First-Order Logics -- 8.11.1 Transformation Algorithm -- 8.11.2 Unification -- 8.12 Modal Epistemic Logics -- 8.13 Logic of Agents Beliefs (LAB) -- 8.13.1 Syntax of LAB -- 8.13.2 Axioms of LAB -- 8.13.3 Possible World Semantics of LAB -- 8.13.4 Soundness and Completeness of LAB -- 8.13.5 Rational Extension of LAB -- 8.13.6 Goals in LAB -- 8.13.7 Dempster-Shafer Interpretation of LAB -- 8.14 Further Readings -- Chapter 9 Symbolic Argumentation for Decision-Making -- 9.1 Toulmin's Model of Argumentation -- 9.2 Domino Decision-Making Model for P3 -- 9.3 Knowledge Representation Syntax of P3 -- 9.4 Formalization of P3 via LAB -- 9.5 Aggregation via Dempster-Shafer Theory -- 9.6 Aggregation via Bayesian Belief Networks -- 9.7 Further Readings -- References -- Index.