A New Perspective on Nonmonotonic Logics

Description

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. Content: 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.