Coherent Systems
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Table of contents
- Contentsix
- Forewordv
- Summaryxv
- Acknowledgementsxix
- Chapter 1. Introduction1
- 1.1 The main topics of the book1
- 1.2 Historical remarks12
- 1.3 Organization of the book15
- 1.4 Overview of the chapters15
- 1.5 Specific remarks on propositional logic24
- 1.6 Basic definitions26
- Chapter 2. Concepts37
- 2.1 Introduction37
- 2.2 Reasoning types39
- 2.3 Basic semantical concepts70
- 2.4 Coherence92
- Chapter 3. Preferences101
- 3.1 Introduction101
- 3.2 General preferential structures111
- 3.3 Smooth minimal preferential structures125
- 3.4 The logical characterization of general and smooth Preferential Models138
- 3.5 A counterexample to the KLM-system146
- 3.6 A nonsmooth model of cumulativity151
- 3.7 Plausibility logic157
- 3.8 The role of copies in preferential structures174
- 3.9 A new approach to preferential structures176
- 3.10 Ranked preferential structures191
- Chapter 4. Distances223
- 4.1 Introduction223
- 4.2 Revision by distance232
- 4.3 Local and global metrics for the semantics of counterfactuals261
- Chapter 5. Definability Preservation271
- 5.1 Introduction271
- 5.2 Preferential structures284
- 5.3 Revision312
- Chapter 6. Sums319
- 6.1 Introduction319
- 6.2 The Farkas algorithm327
- 6.3 Representation for update by minimal sums329
- 6.4 Comments on "Belief revision with unreliable observations"349
- 6.5 "Between" and "Behind"361
- Chapter 7. Size367
- 7.1 Introduction367
- 7.2 Generalized quantifiers372
- 7.3 Comparison of three abstract coherent systems based on size379
- 7.4 Theory revision based on model size396
- Chapter 8. Integration411
- 8.1 Introduction411
- 8.2 Reasoning types and concepts416
- 8.3 Formal aspects422
- Chapter 9. Conclusion and Outlook433
- Bibliography435
- Index440
One aspect of common sense reasoning is reasoning about normal cases, e.g. a physician will first try to interpret symptoms by a common disease, and will take more exotic possibilities only later into account. Such "normality" can be encoded, e.g. by
a relation, where case A is considered more normal than case B. This gives a standard semantics or interpretation to nonmonotonic reasoning (a branch of common sense reasoning), or, more formally, to nonmonotonic logics. We consider in this book the repercussions such normality relations and similar
constructions have on the resulting nonmonotonic logics, i.e. which types of logic are adequate for which kind of relation, etc.
We show in this book that some semantics correspond nicely to some logics, but also that other semantics do not correspond to any logics of the usual form.
Key features:
· provides a coherent picture of several formalisms of nonmonotonic logics.
· gives completeness and incompleteness results for many variants of preferential, distance based, and other semantics.
· gives probably the first systematic investigation of definability preservation and its consequences.
· gives new proof techniques for completeness results.
· is centered on semantics
a relation, where case A is considered more normal than case B. This gives a standard semantics or interpretation to nonmonotonic reasoning (a branch of common sense reasoning), or, more formally, to nonmonotonic logics. We consider in this book the repercussions such normality relations and similar
constructions have on the resulting nonmonotonic logics, i.e. which types of logic are adequate for which kind of relation, etc.
We show in this book that some semantics correspond nicely to some logics, but also that other semantics do not correspond to any logics of the usual form.
Key features:
· provides a coherent picture of several formalisms of nonmonotonic logics.
· gives completeness and incompleteness results for many variants of preferential, distance based, and other semantics.
· gives probably the first systematic investigation of definability preservation and its consequences.
· gives new proof techniques for completeness results.
· is centered on semantics