Revision, Acceptability and Context - Theoretical and Algorithmic Aspects

Preface

Contents

1 Background and Overview

1.1 Introductory Discussion

1.2 Focusing on `Acceptability' Rather than `Inconsistency'

1.3 Overview of This Book

1.4 Notation Used in This Book

1.5 Basic Mathematical Notions

References

2 Introducing Revision Theory

2.1 AGM Belief Revision

2.2 Katsuno and Mendelzon's Characterisation

2.3 Counterfactual Statements and the Ramsey Test

2.4 Grove's Systems of Spheres

2.5 Epistemic Entrenchment

2.6 Discussion

2.7 Action Updates

2.8 Generalising the Concept of Revision

2.9 Iterating the Revision Operation

2.9.1 Darwiche and Pearl's Postulates for Iterated Revisions

2.9.2 Lehmann's Approach: Belief Revision, Revised

2.10 Compromise Revision

2.11 Controlled Revision

2.12 Revision by Translation

2.13 A General Setting for Algorithmic Revision

2.14 Outline of This Book

References

3 Stepwise Revision Operations

3.1 Introduction

3.2 Quantitative Measurement of Change

3.2.1 Minimal Change and the Function d

3.3 Qualitative Measurements of Change

3.4 Representation Issues

3.5 Revision of Formulae

3.6 Properties of the Revision Operator r

3.7 Other Belief Change Operators

3.7.1 Belief Contraction

3.7.2 Consolidating Information on the Belief Base

3.8 Comparison with Other Belief Change Operators

3.9 Operators for Reasoning About the Effects of Actions

3.9.1 Updates of Sentences via Distance d

3.9.2 Properties of the Action Update Operator

3.9.3 Action Updates of Sentences via Distance diff

3.9.4 Ambiguous Action Updates

3.9.5 Taking Causality into Account

References

4 Iterating Revision

4.1 Introduction

4.2 Motivating Structure for Belief Revision

4.3 Iteration of the Revision Operation

4.4 Prioritised Databases

4.4.1 Properties of the Revisions of PDBs

4.4.2 Discussion about Iteration of Revision

4.5 Structured Databases

4.6 Applications and Examples

4.7 Related Work

4.7.1 Prioritised Base Revision

4.7.2 Ordered Theory Presentations

4.8 Using Additional Information for Action Updates

References

5 Structured Revision

5.1 Identifying Inconsistency

5.2 Reasoning with Partial Priorities

5.2.1 Degree of Confidence/Reliability of the Source

5.2.2 Linearisations

5.3 Clustering

5.4 Applications in Software Engineering

5.4.1 Requirements Specification

5.4.2 An Example with the Light Control System

References

6 Algorithmic Context Revision

6.1 Introduction

6.2 Abductive Revision

6.2.1 Introducing LDS for

6.2.2 Goal-Directed Algorithm for

6.2.3 Discussion on the Abduction Procedure

6.2.4 Abduction Algorithm for

6.2.5 Abduction for Intuitionistic Logic

6.3 Compromise Revision

6.3.1 Introducing Compromise Revision for

6.3.2 Comparison with AGM Revision

6.4 Controlled Revision

6.4.1 Proof Theory

6.4.2 Policies for Inconsistency

6.4.3 Conclusions

References

7 Revision by Translation

7.1 Introduction

7.2 Belief Revision for Modal Logic

7.2.1 An Overview of Propositional Modal Logics

7.2.2 Hilbert Systems for Modal Logics

7.2.3 Translation of the Modal Logic K into Classical Logic

7.3 Revising in ukasiewicz' Finitely Many-Valued Logic n

7.3.1 ukasiewicz' Finitely Many-Valued Logic n

7.3.2 Translating ukasiewicz' Many-Valued Logic n into Classical Logic

7.3.3 Revision in ukasiewicz' Many-Valued Logic ( n)

7.4 Revising in Algebraic Logics

7.4.1 Translating Algebraic Logic into Classical Logic

7.4.2 Revision in Algebraic Logics

7.5 Introducing Belnap's Four-Valued Logic

7.5.1 Belief Revision in Belnap's Four-Valued Logic

7.6 Belnap's Four-Valued Logic

7.6.1 Axiomatising Belnap's Four-Valued Logic

7.6.2 Entailment in Belnap's Four-Valued Logic

7.6.3 Generalising Belnap's Notion of Entailment to Infinite Theories

7.6.4 Translating Belnap's Logic into Classical Logic

7.6.5 Revising in Belnap's Four-Valued Logic

7.7 Conclusions and Discussions

References

8 Object-Level Deletion

8.1 Introduction

8.2 Object-Level Meta-Level Operations

8.3 The Need for Object-Level Deletion

8.4 Strategy of the Technique

8.5 Substructural Logics

8.5.1 Hilbert and Gentzen Formulations

8.5.2 Goal-Directed Proof Theory

8.5.3 Semantics

8.6 Introducing Anti-formulae in Concatenation and Linear Logic

8.6.1 Analysis

8.6.2 Introducing Anti-formulae into Logics with and e

8.6.3 Anti-formulae and Negation

8.7 The Notion of Failure in Resource Logics

8.8 Deletion in Resource-Unbounded Logics

8.9 Logical Deletion in LDS

8.10 Introducing N-Prolog with Negation as Failure

8.11 Exploring Deletion via Addition

8.12 A Formal System for Deletion via Addition

8.13 Concluding Remarks

References

9 Conclusions and Discussions

9.1 Concluding Remarks

9.2 Discussions

References

List of Symbols

Subject Index