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

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


Libraries and researchers in nonmonotonic and related logics

Table of 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 Sm


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© 2004
Elsevier Science
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About the author

Karl Schlechta

Affiliations and Expertise

K. Schlechta Université de Provence and Laboratoire d'Informatique Fondamentale (CNRS UMR 6166), Marseille, France