| Description |
1 online resource |
| Contents |
Part I Introduction; 1 Introduction; 1.1 Overview; 1.1.1 Purpose and Organisation of the Book; 1.1.2 Concise Overview; 1.1.3 Nonmonotonic Logics; 1.1.4 Basic Definitions -- Chapter 22; 1.1.5 Inheritance Systems -- Chapter 33; 1.1.6 Reiter Defaults -- Chapter 44; 1.1.7 Preferential Structures -- Chapter 55; 1.1.8 Algebraic and Structural Semantics; 1.1.9 Deontic Logic -- Chapter 66; 1.1.10 Theory Revision, Update and Counterfactuals: Chapter 77; 1.1.11 Neurology -- Chapter 88; 1.1.12 Interpolation -- Chapter 99; 1.1.13 Independence -- Chapter 1010; 1.1.14 Formal Construction -- Chapter 1111 |
|
1.1.15 Kal Vachomer -- Chapter 12121.1.16 Equational CTD -- Chapter 1313; 1.2 Introduction to the Main Concepts; 1.2.1 Overview of This Section; 1.2.2 Logic and Neuroscience; 1.2.3 Concepts and Properties; 1.2.4 Language and Language Change; 1.2.5 Modularity and Independence; 1.2.6 Main Concepts and Connections; 1.2.7 Abstract Constructions; 1.3 Previously Published Material; Part II Background Material; 2 Basic Algebraic and Logical Definitions; 2.1 Overview of This Chapter; 2.2 The Definitions; 3 Defeasible Inheritance; 3.1 Summary; 3.2 Conceptual Analysis; 3.3 Basic Discussion |
|
3.3.1 (Defeasible or Nonmonotonic) Inheritance Networks or Diagrams3.3.2 Preclusion; 3.4 Directly Sceptical Split Validity Upward Chaining Off-Path Inheritance; 3.4.1 The Definition of models (i.e. of Validity of Paths); 3.5 Review of Other Approaches and Problems; 3.5.1 Extension-Based Versus Directly Sceptical Definitions; 3.5.2 On-Path Versus Off-Path Preclusion; 3.5.3 Split Validity Versus Total Validity Preclusion; 3.6 Discussion of Their Properties in Our Context; 4 Reiter Defaults and Autoepistemic Logic; 4.1 Reiter Defaults; 4.2 Autoepistemic Logic |
|
4.3 Discussion of the Properties in Our Context5 Preferential Structures and Related Concepts; 5.1 Summary; 5.2 Preferential Structures; 5.2.1 The Minimal Variant; 5.2.2 The Limit Variant; 5.3 Laws About Size; 5.3.1 Defaults as Generalised Quantifiers; 5.3.2 Additive Laws About Size; 5.3.3 Multiplicative Laws About Size; 5.3.4 Hamming Relations and Distances; 5.3.5 Summary of Properties; 5.4 A Short Discussion of Their Abstract Properties in Our Context; 6 Deontic Logic, Contrary-to-Duty Obligations; 6.1 Summary; 6.2 Deontic Logic; 6.3 Contrary-to-Duty Obligations |
|
6.4 calA-Ranked Structures6.4.1 Representation Results for calA-Ranked Structures; 6.5 Application of calA-Ranked Structures to Contrary-to-Duty Conditionals; 6.5.1 Outline of the Solution; 6.5.2 Formal Modelling and Summary of Results; 6.5.3 Overview; 6.5.4 Formal Results and Representation for Hierarchical Conditionals; 7 Theory Revision, Theory Contraction and Conditionals; 7.1 Summary; 7.2 Theory Revision; 7.3 Theory Contraction; 7.3.1 Introduction; 7.3.2 Some of the AGM Axioms for Theory Contraction; 7.3.3 The General Picture of Safe Contraction; 7.3.4 A Modification |
| Summary |
"Logics are like shadows on a wall; to understand why they dance as they do, and how they can be made to move differently, one needs to look at the mathematical structures from which they can be projected. That is a methodology that has long proven its value for classical and other forms of deductive inference; this book manifests its pertinence to logics of uncertain qualitative reasoning. It draws together and refines work from the literature on preferential and other quite different semantics for such reasoning and then, in its central chapter, integrates the leading ideas from them into a single multi-dimensional semantics. It enters new territory with investigations of interpolation and qualitative independence in non-monotonic contexts as well as connections between non-monotonic logic and neuroscience, specifically with Edelman's theory of organization of the brain. Finally, it proposes novel applications such as equational modellings for contrary-to-duty normative reasoning and mathematical analyses of some kinds of casuistic reasoning in the Talmudic tradition. Profusely signposted at every turn, the volume is accessible to readers equipped with a modicum of set theory and abstract algebra. Visitors to the area can come in by the front gate and work their way, in various orders, through as much of the garden as strikes their fancy; specialists will enter at Chap. 11 or at whatever special topic interests them, well assured that they can easily backtrack to whatever bits and pieces are needed from what they skipped. A volume with a clear vision, a book to return to many times." (David Makinson) |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed November 17, 2016) |
| Subject |
Nonmonotonic reasoning.
|
|
Logic, Symbolic and mathematical.
|
|
Philosophy: logic.
|
|
Philosophy of science.
|
|
Mathematical foundations.
|
|
Artificial intelligence.
|
|
Mathematical theory of computation.
|
|
COMPUTERS -- General.
|
|
Logic, Symbolic and mathematical
|
|
Nonmonotonic reasoning
|
| Form |
Electronic book
|
| Author |
Schlechta, Karl, author.
|
| ISBN |
9783319468174 |
|
3319468170 |
|
3319468154 |
|
9783319468150 |
|
