Description 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.
Audience
Libraries and researchers in nonmonotonic and related logics
Contents Foreword (by David Makinson)
Summary
Acknowledgements
CHAPTER 1 : INTRODUCTION
1.1 The main topics of the book
1.1.1 Conceptual
analysis
1.1.2 Generalized modal logic and integration
1.1.3 Formal results
1.1.4 The role of semantics
1.1.5 Various remarks
1.2 Historical remarks
1.3 Organization of the book
1.4 Overview of the chapters
1.5 Specific remarks on propositional
logic
1.6 Basic definitions
CHAPTER 2 : CONCEPTS
2.1 Introduction
2.2 Reasoning types
2.2.1 Traditional nonmonotonic
logics
2.2.2 Prototypical and ideal cases
2.2.3 Extreme cases and interpolation
2.2.4 Clustering
2.2.5 Certainty
2.2.6
Quality of an answer, approximation, and complexity
2.2.7 Useful reasoning
2.2.8 Inheritance and argumentation
2.2.9
Dynamic systems
2.2.10 Theory revision
2.2.11 Update
2.2.12 Counterfactual conditionals
2.3 Basic semantical concepts
2.3.1 Preference
2.3.2 Distance
2.3.3 Size
2.4 Coherence
CHAPTER 3 : PREFERENCES
3.1 Introduction
3.2
General preferential structures
3.2.1 General minimal preferential structures
3.2.2 Transitive minimal preferential structures
3.2.3 One copy version
3.2.4 A very short remark on X-logics
3.3 Smooth minimal preferential structures
3.3.1 Smooth
minimal preferential structures with arbitrarily many copies
3.3.2 Smooth and transitive minimal preferential structures
3.4
The logical characterization of general and smooth preferential models
3.4.1 Simplifications of the general transitive limit case
3.5 A counterexample to the KLM-system
3.5.1 The formal results
3.6 A nonsmooth model of cumulativity
3.6.1 The formal
results
3.7 Plausibility logic - problems without closure under finite union
3.7.1 Introduction
3.7.2 Completeness and
incompleteness results for plausibility logic
3.8 The role of copies in preferential structures
3.9 A new approach to preferential
structures
3.9.1 Introduction
3.9.2 Validity in traditional and in our preferential structures
3.9.3 The disjoint union of
models and the problem of multiple copies
3.9.4 Representation in the finite case
3.10 Ranked preferential structures
3.10.1
Introduction
3.10.2 The minimal variant
3.10.3 The limit variant without copies
CHAPTER 4 : DISTANCES
4.1 Introduction
4.1.1 Theory revision
4.1.2 Counterfactuals
4.1.3 Summary
4.2 Revision by distance
4.2.1 Introduction
4.2.2 The algebraic
results
4.2.3 The logical results
4.2.4 There is no finite characterization
4.2.5 The limit case
4.3 Local and global metrics
for the semantics of counterfactuals
4.3.1 Introduction
4.3.2 The results
CHAPTER 5 : DEFINABILITY PRESERVATION
5.1 Introduction
5.1.1 The problem
5.1.2 The remedy
5.1.3 Basic definitions and results
5.1.4 A remark on definability preservation and modal
logic
5.2 Preferential structures
5.2.1 The algebraic results
5.2.2 The logical results
5.2.3 The general case and the
limit version cannot be characterized
5.3 Revision
5.3.1 The algebraic result
5.3.2 The logical result
CHAPTER 6 : SUMS
6.1 Introduction
6.1.1 The general situation and the Farkas algorithm
6.1.2 Update by minimal sums
6.1.3 Comments on "Belief
revision with unreliable observations"
6.1.4 "Between" and "behind"
6.1.5 Summary
6.2 The Farkas algorithm
6.3 Representation
for update by minimal sums
6.3.1 Introduction
6.3.2 An abstract result
6.3.3 Representation
6.3.4 There is no finite representation
for our type of update possible
6.4 Comments on "Belief revision with unreliable observations"
6.4.1 Introduction
6.4.2 A
characterization of Markov systems (in the finite case)
6.4.3 There is no finite representation possible
6.5 "Between" and "Behind"
6.5.1 There is no finite representation for "between" and "behind"
CHAPTER 7 : SIZE
7.1 Introduction
7.1.1 The details
7.2 Generalized quantifiers
7.2.1 Introduction
7.2.2 Results
7.3 Comparison of three abstract coherent systems based
on size
7.3.1 Introduction
7.3.2 Presentation of the three systems
7.3.3 Comparison of the systems of Ben-David/Ben-Eliyahu
and the author
7.3.4 Comparison of the systems of Ben-David/Ben-Eliyahu and of
Friedman/Halpern
7.4 Theory revision
based on model size
7.4.1 Introduction
7.4.2 Results
CHAPTER 8 : INTEGRATION
8.1 Introduction
8.1.1 Rules or object language?
8.1.2 Various levels of reasoning
8.2 Reasoning types and concepts
8.3 Formal aspects
8.3.1 Classical modal logic
8.3.2 Classical
propositional operators have no unique interpretation
8.3.3 Combining individual completeness results
CHAPTER 9 : CONCLUSION AND OUTLOOK
Bibliography.
Index.
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