A New Perspective on Nonmonotonic Logics

ISBN-13: 9783319468150 / Angielski / Twarda / 2016 / 365 str.

Dov M. Gabbay; Karl Schlechta

Opis

In this book the authors present new results on interpolation for nonmonotonic logics, abstract (function) independence, the Talmudic Kal Vachomer rule, and an equational solution of contrary-to-duty obligations. The chapter on formal construction is the conceptual core of the book, where the authors combine the ideas of several types of nonmonotonic logics and their analysis of 'natural' concepts into a formal logic, a special preferential construction that combines formal clarity with the intuitive advantages of Reiter defaults, defeasible inheritance, theory revision, and epistemic considerations.
It is suitable for researchers in the area of computer science and mathematical logic.

Spis treści

Part I - Introduction.- Part II - Background Material.- Basic Algebraic and Logical Definitions.- Defeasible Inheritance.- Reiter Defaults and Autoepistemic Logic.- Preferential Structures and Related Concepts.- Deontic Logic, Contrary-to-Duty Obligations.- Theory Revision, Theory Contraction, and Conditionals.- Neurology.- Part III - New Results.- Independence and Interpolation.- Probabilistic and Abstract Independence.- Formal Construction.- The Talmudic Kal Vachomer Rule.- Equational CTD.- Conclusion.- Index.

O autorze

Dov Gabbay is the (Emeritus) Augustus de Morgan Professor of Logic at King’s College London, an invited professor at the Université de Luxembourg, a professor at Bar-Ilan University, Israel, and a professor of theoretical computer Science at Ashkelon Academic College, Israel. He is Editor-in-chief of several international journals and handbooks, among them the Handbook of Philosophical Logic. His research interests include logic and computation, proof theory and goal-directed theorem proving, nonclassical logics and nonmonotonic reasoning, labeled deductive systems, fibring logics, and reactive systems. His most recent books include Conditionals and Modularity in General Logics (Springer 2011) and Logical Tools for Handling Change in Agent-Based Systems (Springer 2009).

Karl Schlechta is a retired professor of computer science at Aix-Marseille University in France, and a member of the Laboratoire d’Informatique Fondamentale de Marseille. He works on nonmonotonic logics, theory revision, and related subjects, his main interest being the semantical side of these logics and in particular preferential structures and accompanying representation theorems. His books include Coherent Systems (Elsevier 2004), Logical Tools for Handling Change in Agent-Based Systems (Springer 2009), and Conditionals and Modularity in General Logics (Springer 2011). 

Blurb

"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)