Propositional Argumentation Systems and Symbolic Evidence Theory

CONTENTS
vii
Contents
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Objectives and Overview . . . . . . . . . . . . . . . . . . . . . 2
1.3 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Introduction to Evidence Theory 5
2.1 The Basic Idea . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Quasi–Support and Support . . . . . . . . . . . . . . . . . . . 8
2.3 Doubt and Plausibility . . . . . . . . . . . . . . . . . . . . . . 10
2.4 Basic Arguments, Basic–Support, and Pseudo–Support . . . . 12
2.5 Combining Bodies of Arguments . . . . . . . . . . . . . . . . 14
2.6 Probabilistic Structure . . . . . . . . . . . . . . . . . . . . . . 16
3 Symbolic Theory of Hints 18
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2 The Mathematical Model of Symbolic Hints . . . . . . . . . . 19
3.3 Judging Hypotheses in the Lights of Hints . . . . . . . . . . . 23
3.4 Combining Symbolic Hints . . . . . . . . . . . . . . . . . . . . 27
4 Assumption–Based Systems 32
4.1 Introduction to Propositional Logic . . . . . . . . . . . . . . . 33
4.2 Representing Uncertainty by Propositional Systems . . . . . . 36
4.3 Hypotheses and Arguments in Assumption–Based Systems . . 40
4.4 Representing and Computing Symbolic Arguments . . . . . . 44
4.4.1 Basic–Support and Pseudo–Support . . . . . . . . . . 45
4.4.2 Representing Symbolic Arguments . . . . . . . . . . . 48
4.4.3 Computing Symbolic Arguments . . . . . . . . . . . . 50
4.5 Marginalization, Extension and Combination . . . . . . . . . 52
4.5.1 Marginalization . . . . . . . . . . . . . . . . . . . . . . 52
4.5.2 Extension . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.5.3 Combination . . . . . . . . . . . . . . . . . . . . . . . 56
4.6 Assumptions as Hypotheses . . . . . . . . . . . . . . . . . . . 57
4.7 Assumption–Based Systems versus Hints . . . . . . . . . . . . 58
4.7.1 From Assumption–Based Systems to Hints . . . . . . 59
4.7.2 From Hints to Assumption–Based Systems . . . . . . 60