The logical study of language is becoming more interdisciplinary, playing a role in fields such as computer science, artificial intelligence, cognitive science and game theory. This new edition, written by the leading experts in the field, presents an overview of the latest developments at the interface of logic and linguistics as well as a historical perspective. It is divided into three parts covering Frameworks, General Topics and Descriptive Themes. - Completely revised and updated - includes over 25% new material - Discusses the interface between logic and language - Many of the authors are creators or active developers of the theories

Logic is, and should be, the core subject area of modern mathemat ics. The blueprint for twentieth century mathematical thought, thanks to Hilbert and Bourbaki, is the axiomatic development of the subject. As a result, logic plays a central conceptual role. At the same time, mathematical logic has grown into one of the most recondite areas of mathematics. Most of modern logic is inaccessible to all but the special ist. Yet there is a need for many mathematical scientists-not just those engaged in mathematical research-to become conversant with the key ideas of logic. The Handbook of Mathematical Logic, edited by Jon Bar wise, is in point of fact a handbook written by logicians for other mathe maticians. It was, at the time of its writing, encyclopedic, authoritative, and up-to-the-moment. But it was, and remains, a comprehensive and authoritative book for the cognoscenti. The encyclopedic Handbook of Logic in Computer Science by Abramsky, Gabbay, and Maibaum is a wonderful resource for the professional. But it is overwhelming for the casual user. There is need for a book that introduces important logic terminology and concepts to the working mathematical scientist who has only a passing acquaintance with logic. Thus the present work has a different target audience. The intent of this handbook is to present the elements of modern logic, including many current topics, to the reader having only basic mathe matical literacy.

A one-stop reference, self-contained, with theoretical topics presented in conjunction with implementations for which code is supplied.

The Handbook of the Logic of Argument and Inference is an authoritative reference work in a single volume, designed for the attention of senior undergraduates, graduate students and researchers in all the leading research areas concerned with the logic of practical argument and inference. After an introductory chapter, the role of standard logics is surveyed in two chapters. These chapters can serve as a mini-course for interested readers, in deductive and inductive logic, or as a refresher. Then follow two chapters of criticism; one the internal critique and the other the empirical critique. The first deals with objections to standard logics (as theories of argument and inference) arising from the research programme in philosophical logic. The second canvasses criticisms arising from work in cognitive and experimental psychology. The next five chapters deal with developments in dialogue logic, interrogative logic, informal logic, probability logic and artificial intelligence. The last chapter surveys formal approaches to practical reasoning and anticipates possible future developments. Taken as a whole the Handbook is a single-volume indication of the present state of the logic of argument and inference at its conceptual and theoretical best. Future editions will periodically incorporate significant new developments.

The papers presented in this volume examine topics of central interest in contemporary philosophy of logic. They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, many-valued logic, relevance and paraconsistent logic, free logics, extensional v. intensional logics, the logic of fiction, epistemic logic, formal logical and semantic paradoxes, the concept of truth, the formal theory of entailment, objectual and substitutional interpretation of the quantifiers, infinity and domain constraints, the Löwenheim-Skolem theorem and Skolem paradox, vagueness, modal realism v. actualism, counterfactuals and the logic of causation, applications of logic and mathematics to the physical sciences, logically possible worlds and counterpart semantics, and the legacy of Hilbert's program and logicism. The handbook is meant to be both a compendium of new work in symbolic logic and an authoritative resource for students and researchers, a book to be consulted for specific information about recent developments in logic and to be read with pleasure for its technical acumen and philosophical insights.- Written by leading logicians and philosophers- Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic- Clear, in-depth expositions of technical detail- Progressive organization from general considerations to informal to symbolic logic to nonclassical logics- Presents current work in symbolic logic within a unified framework- Accessible to students, engaging for experts and professionals- Insightful philosophical discussions of all aspects of logic- Useful bibliographies in every chapter

This book represents the attempt to provide the student in the one semester introductory course in logic with 1. a handbook of the fundamentals of the science, brief and succinct enough to be practical and yet substantial enough to provide him with the solid foundation of the traditional from which to approach the “mysteries” of modern developments in the field. 2. A working knowledge of the science, out of which there may be built the personal equipment with which the student may be able to solve for himself the problems posed by the impact of the new on the old in the field of logic. 3. Sufficient problem material to enable the student to learn the use of logic, so that in reconciling in his own mind the new and the old, the modern and the traditional, he may do this logically.

Epistemic logic and, more generally, logics of knowledge and belief, originated with philosophers such as Jaakko Hintikka and David Lewis in the early 1960s. Since then, such logics have played a significant role not only in philosophy, but also in computer science, artificial intelligence, and economics. This handbook reports significant progress in a field that, while more mature, continues to be very active. This book should make it easier for new researchers to enter the field, and give experts a chance to appreciate work in related areas. The book starts with a gentle introduction to the logics of knowledge and belief; it gives an overview of the area and the material covered in the book. The following eleven chapters, each written by a leading researcher (or researchers), cover the topics of only knowing, awareness, knowledge and probability, knowledge and time, the dynamics of knowledge and of belief, model checking, game theory, agency, knowledge and ability, and security protocols. The chapters have been written so that they can be read independently and in any order. Each chapter ends with a section of notes that provides some historical background, including references, and a detailed bibliography.