D. M. Gabbay, O. Rodrigues, A. Russo
393 pages, Springer, to appear early 2010
| 1 | Background and overview | 1 |
| 1.1 | Introductory discussion | 1 |
| 1.2 | Focusing on "acceptability" rather than "inconsistency" | 5 |
| 1.3 | Overview of this book | 7 |
| 1.4 | Notation used in this book | 8 |
| 1.5 | Basic mathematical notions | 10 |
| References | 11 |
| 2 | Introducing revision theory | 13 |
| 2.1 | AGM belief revision | 13 |
| 2.2 | Katsuno and Mendelzon's characterisation | 20 |
| 2.3 | Counterfactual statements and the Ramsey Test | 21 |
| 2.4 | Grove's systems of spheres | 25 |
| 2.5 | Epistemic entrenchment | 28 |
| 2.6 | Discussion | 30 |
| 2.7 | Action updates | 30 |
| 2.8 | Generalising the concept of revision | 33 |
| 2.9 | Iterating the revision operation | 37 |
| | 2.9.1 | Darwiche and Pearl's postulates for iterated revisions | 37 |
| | 2.9.2 | Lehmann's approach: belief revision, revised | 40 |
| 2.10 | Compromise revision | 41 |
| 2.11 | Controlled revision | 45 |
| 2.12 | Revision by translation | 47 |
| 2.13 | A general setting for algorithmic revision | 49 |
| 2.14 | Outline of this book | 52 |
| References | 52 |
| 3 | Stepwise revision operations | 55 |
| 3.1 | Introduction | 55 |
| 3.2 | Quantitative measurement of change | 55 |
| | 3.2.1 | Minimal change and the function d | 56 |
| 3.3 | Qualitative measurements of change | 63 |
| 3.4 | Representation issues | 65 |
| 3.5 | Revision of formulae | 67 |
| 3.6 | Properties of the revision operator or | 70 |
| 3.7 | Other belief change operators | 77 |
| | 3.7.1 | Belief contraction | 77 |
| | 3.7.2 | Consolidating information on the belief base | 82 |
| 3.8 | Comparison with other belief change operators | 85 |
| 3.9 | Operators for reasoning about the effects of actions | 88 |
| | 3.9.1 | Updates of sentences via distance d | 89 |
| | 3.9.2 | Properties of the action update operator | 93 |
| | 3.9.3 | Action updates of sentences via distance diff | 96 |
| | 3.9.4 | Ambiguous action updates | 98 |
| | 3.9.5 | Taking causality into account | 100 |
| References | 102 |
| 4 | Iterating revision | 105 |
| 4.1 | Introduction | 105 |
| 4.2 | Motivating structure for belief revision | 107 |
| 4.3 | Iteration of the revision operation | 108 |
| 4.4 | Prioritised databases | 111 |
| | 4.4.1 | Properties of the revisions of PDBs | 115 |
| | 4.4.2 | Discussion about iteration of revision | 119 |
| 4.5 | Structured databases | 124 |
| 4.6 | Applications and examples | 126 |
| 4.7 | Related Work | 128 |
| | 4.7.1 | Prioritised base revision | 129 |
| | 4.7.2 | Ordered theory presentations | 131 |
| 4.8 | Using additional information for action updates | 132 |
| References | 136 |
| 5 | Structured revision | 139 |
| 5.1 | Identifying inconsistency | 139 |
| 5.2 | Reasoning with partial priorities | 148 |
| | 5.2.1 | Degree of confidence/reliability of the source | 149 |
| | 5.2.2 | Linearisations | 165 |
| 5.3 | Clustering | 167 |
| 5.4 | Applications in software engineering | 168 |
| | 5.4.1 | Requirements specification | 168 |
| | 5.4.2 | An example with the light control system | 169 |
| References | 175 |
| 6 | Algorithmic context revision | 177 |
| 6.1 | Introduction | 177 |
| 6.2 | Abductive revision | 177 |
| | 6.2.1 | Introducing LDS for-> | 180 |
| | 6.2.2 | Goal-directed algorithm for-> | 183 |
| | 6.2.3 | Discussion on the abduction procedure | 187 |
| | 6.2.4 | Abduction algorithm for-> | 192 |
| | 6.2.5 | Abduction for intuitionistic logic | 194 |
| 6.3 | Compromise revision | 197 |
| | 6.3.1 | Introducing compromise revision for-> | 197 |
| | 6.3.2 | Comparison with AGM revision | 209 |
| 6.4 | Controlled revision | 214 |
| | 6.4.1 | Proof theory | 215 |
| | 6.4.2 | Policies for inconsistency | 217 |
| | 6.4.3 | Conclusions | 220 |
| References | 221 |
| 7 | Revision by translation | 223 |
| 7.1 | Introduction | 223 |
| 7.2 | Belief revision for modal logic | 225 |
| | 7.2.1 | An overview of propositional modal logics | 225 |
| | 7.2.2 | Hilbert Systems for Modal Logics | 230 |
| | 7.2.3 | Translation of the modal logic K into classical logic | 233 |
| 7.3 | Revising in Lukasiewiczs finitely many-valued logic Ln | 235 |
| | 7.3.1 | Lukasiewiczs finitely many-valued logic Ln | 235 |
| | 7.3.2 | Translating Lukasiewiczs many-valued logic Ln into classical logic | 241 |
| | 7.3.3 | Revision in Lukasiewiczs many-valued logic (Ln) | 244 |
| 7.4 | Revising in algebraic logics | 246 |
| | 7.4.1 | Translating algebraic logic into classical logic | 246 |
| | 7.4.2 | Revision in algebraic logics | 248 |
| 7.5 | Introducing Belnap's four-valued logic | 248 |
| | 7.5.1 | Belief revision in Belnap's four-valued logic | 249 |
| 7.6 | Belnap's four-valued Logic | 251 |
| | 7.6.1 | Axiomatising Belnap's four-valued Logic | 251 |
| | 7.6.2 | Entailment in Belnap's four-valued logic | 253 |
| | 7.6.3 | Generalising Belnap's notion of entailment to infinite theories | 255 |
| | 7.6.4 | Translating Belnap's logic into classical logic | 259 |
| | 7.6.5 | Revising in Belnap's four-valued logic | 265 |
| 7.7 | Conclusions and discussions | 268 |
| References | 269 |
| 8 | Object-level deletion | 271 |
| 8.1 | Introduction | 271 |
| 8.2 | Object level × meta-level operations | 271 |
| 8.3 | The need for object level deletion | 274 |
| 8.4 | Strategy of the technique | 279 |
| 8.5 | Substructural logics | 281 |
| | 8.5.1 | Hilbert and Gentzen formulations | 282 |
| | 8.5.2 | Goal directed proof theory | 288 |
| | 8.5.3 | Semantics | 297 |
| 8.6 | Introducing anti-formulae in concatenation and linear logic | 305 |
| | 8.6.1 | Analysis | 305 |
| | 8.6.2 | Introducing anti-formulae into logics with -> and e | 310 |
| | 8.6.3 | Anti-formulae and negation | 315 |
| 8.7 | The notion of failure in resource logics | 321 |
| 8.8 | Deletion in resource unbounded logics | 325 |
| 8.9 | Logical deletion in LDS | 327 |
| 8.10 | Introducing N-Prolog with negation as failure | 336 |
| 8.11 | Exploring deletion via addition | 344 |
| 8.12 | A formal system for deletion via addition | 353 |
| 8.13 | Concluding remarks | 356 |
| References | 358 |
| 9 | Conclusions and discussions | 361 |
| 9.1 | Concluding remarks | 361 |
| 9.2 | Discussions | 366 |
| References | 376 |
| List of Symbols | 377 |
| Subject Index | 379 |
