A new perspective on nonmonotonic logics. (2016)

• Record Type: Book
• Further Information: Note: Dov M. Gabbay, Karl Schlechta.
• Authors: Gabbay, Dov M, 1945-; Schlechta, Karl
• 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.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2016
• Extent: 1 online resource
• Subjects: 006.3; Computer science; Nonmonotonic reasoning; Logic, Symbolic and mathematical; Logic; Science -- Philosophy; Artificial intelligence; COMPUTERS -- General; Logic, Symbolic and mathematical; Nonmonotonic reasoning; Philosophy -- Logic; Science -- Philosophy & Social Aspects; Mathematics -- Logic; Computers -- Intelligence (AI) & Semantics; Philosophy: logic; Philosophy of science; Mathematical foundations; Artificial intelligence; Mathematical theory of computation; Computer Science; Mathematical Logic and Formal Languages; Logic; Philosophy of Science; Mathematical Logic and Foundations; Artificial Intelligence (incl. Robotics); Electronic books
• Languages: English
• ISBNs: 9783319468174; 3319468170; 3319468154; 9783319468150
• Related ISBNs: 9783319468150
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (SpringerLink, viewed November 17, 2016).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.