Dov M. Gabbay

This book constitutes the refereed proceedings of the International Conference on Formal and Applied Practical Reasoning, FAPR '96, held in Bonn, Germany, in June 1996. The 51 revised full papers included in the book together with eight posters were carefully selected for presentation at the conference. The book addresses current aspects of the highly interdisciplinary area of practical reasoning in artificial intelligence, philosophy, psychology, linguistics, software engineering, intelligent systems, and industrial applications. Among the topics addressed are user modeling, belief, legal reasoning, argumentation, dialogue logic, default reasoning, analogy, metareasoning, temporal and procedural reasoning, and many others.

International Conference on Formal and Applied Practical Reasoning, FAPR'96, Bonn, Germany, June (3-7), 1996. Proceedings.

Practical Reasoning

Artur S. D'Avila Garcez

Luís C. Lamb

This book explores why, regarding practical reasoning, humans are sometimes still faster than artificial intelligence systems. It is the first to offer a self-contained presentation of neural network models for many computer science logics.

Neural-Symbolic Cognitive Reasoning

George Metcalfe

Nicola Olivetti

Fuzzy logics are many-valued logics that are well suited to reasoning in the context of vagueness. They provide the basis for the wider field of Fuzzy Logic, encompassing diverse areas such as fuzzy control, fuzzy databases, and fuzzy mathematics. This book provides an accessible and up-to-date introduction to this fast-growing and increasingly popular area. It focuses in particular on the development and applications of "proof-theoretic" presentations of fuzzy logics; the result of more than ten years of intensive work by researchers in the area, including the authors. In addition to providing alternative elegant presentations of fuzzy logics, proof-theoretic methods are useful for addressing theoretical problems (including key standard completeness results) and developing efficient deduction and decision algorithms. Proof-theoretic presentations also place fuzzy logics in the broader landscape of non-classical logics, revealing deep relations with other logics studied in Computer Science, Mathematics, and Philosophy. The book builds methodically from the semantic origins of fuzzy logics to proof-theoretic presentations such as Hilbert and Gentzen systems, introducing both theoretical and practical applications of these presentations.

Proof Theory for Fuzzy Logics

John Woods

Akihiro Kanamori

John Hayden Woods

In designing the Handbook of the History of Logic, the Editors have taken the view that the history of logic holds more than an antiquarian interest, and that a knowledge of logic's rich and sophisticated development is, in various respects, relevant to the research programmes of the present day. Ancient logic is no exception. The present volume attests to the distant origins of some of modern logic's most important features, such as can be found in the claim by the authors of the chapter on Aristotle's early logic that, from its infancy, the theory of the syllogism is an example of an intuitionistic, non-monotonic, relevantly paraconsistent logic. Similarly, in addition to its comparative earliness, what is striking about the best of the Megarian and Stoic traditions is their sophistication and originality.

Sets and Extensions in the Twentieth Century

Franz Guenthner

This eighteenth volume of the acclaimed Handbook of Philosophical Logic includes many contributors who are among the most famous leading figures of applied philosophical logic of our time. Coverage includes deontic logic, practical reasoning, homogeneous and heterogeneous logical proportion, and talmudic logic. Overall, it will appeal to students, practitioners, and researchers looking for an authoritative resource in these areas. The contributors first explore models in terms of dynamic logics for information-driven agency. The paradigm they use is dynamic-epistemic logics for knowledge and belief and their current extensions to the statics and dynamics of agents’ preferences. Next, in the presentation of preference based agency, coverage examines a large number of themes, including interactive social agents and scenarios with long term patterns emerging over time. From here, the book moves on to offer an introduction to homogeneous and heterogeneous logical proportions. Readers will also learn more about the general challenge that the problem of formalizing practical reasoning presents to logical theory. The contributors survey the existing resources that might contribute to the development of such a formalization. They conclude that, while a robust, adequate logic of practical reasoning is not yet in place, the materials for developing such a logic are now available. The last chapter explores topics that deal with the logic of Jewish law and the logic of the Talmud. This includes obligations and prohibitions in Talmudic deontic logic, the handling of loops in Talmudic logic, Temporal Talmudic logic, and quantum states and disjunctive attacks in Talmudic logic. The Talmudic logic system presented are also exported to general logic and to Artificial Intelligence.

Volume 18

Handbook of Philosophical Logic

Maarten de Rijke

"Frontiers of Combining Systems 2 includes selected, edited contributions from the Second International Workshop on Frontiers of Combining Systems. - This volume addresses both particular instances of the combination and integration problem and the general issue. - While covering a wide spectrum of disciplines and angles, from systems and constraints to logical aspects, theorem proving and rewriting, there is a clear emphasis on automated tools and logics."--Jacket.

Frontiers of Combining Systems 2

From the point of view of non-classical logics, Heyting's implication is the smallest implication for which the deduction theorem holds. This book studies properties of logical systems having some of the classical connectives and implication in the neighbourhood of Heyt ing's implication. I have not included anything on entailment, al though it belongs to this neighbourhood, mainly because of the appearance of the Anderson-Belnap book on entailment. In the later chapters of this book, I have included material that might be of interest to the intuitionist mathematician. Originally, I intended to include more material in that spirit but I decided against it. There is no coherent body of material to include that builds naturally on the present book. There are some serious results on topological models, second order Beth and Kripke models, theories of types, etc., but it would require further research to be able to present a general theory, possibly using sheaves. That would have postponed pUblication for too long. I would like to dedicate this book to my colleagues, Professors G. Kreisel, M.O. Rabin and D. Scott. I have benefited greatly from Professor Kreisel's criticism and suggestions. Professor Rabin's fun damental results on decidability and undecidability provided the powerful tools used in obtaining the majority of the results reported in this book. Professor Scott's approach to non-classical logics and especially his analysis of the Scott consequence relation makes it possible to present Heyting's logic as a beautiful, integral part of non-classical logics.

Semantical Investigations in Heyting's Intuitionistic Logic

S. Abramsky

T. S. E. Maibaum

This handbook volume covers fundamental topics of semantics in logic and computation. The chapters (some monographic in length), were written following years of co-ordination and follow a thematic point of view. The volume brings the reader up to front line research, and is indispensable to any serious worker in the areas.

Handbook of Logic in Computer Science: Volume 5. Algebraic and Logical Structures

Michael Zakharyaschev

Sergei S. Goncharov

This is an overview of the current state of knowledge along with open problems and perspectives, clarified in such fields as non-standard inferences in description logics, logic of provability, logical dynamics and computability theory. The book includes contributions concerning the role of logic today, including unexpected aspects of contemporary logic and the application of logic. This book will be of interest to logicians and mathematicians in general.

Logics for the XXIst Century

Mathematical Problems from Applied Logic I

This book is intended to serve as an advanced text and reference work on modal logic, a subject of growing importance which has applications to philosophy and linguistics. Although it is based mainly on research which I carried out during the years 1969-1973, it also includes some related results obtained by other workers in the field (see the refer ences in Part 7). Parts 0, 1 and 2, can be used as the basis of a one year graduate course in modal logic. The material which they contain has been taught in such courses at Stanford since 1970. The remaining parts of the book contain more than enough material for a second course in modal logic. The exercises supplement the text and are usually difficult. I wish to thank Stanford University and Bar-Han University for making it possible for me to continue and finish this work, and A. Ungar for correcting the typescript. Bar-Ilan University, Israel Dov M. GABBA Y PART 0 AN INTRODUCTION TO GENERAL INTENSIONAL LOGICS CHAPTER 0 CONSEQUENCE RELATIONS Motivation We introduce the notions of a consequence relation (which is a generalization of the notion of a logical system) and of a semantics. We show that every consequence relation is complete for a canonical semantics. We define the notion of one semantics being Dian in another and study the basic properties of this notion. The concepts of this chapter are generalizations of the various notions of logical system and possible world semantics found in the literature.

Investigations in Modal and Tense Logics with Applications to Problems in Philosophy and Linguistics

Artur S. d'Avila Garcez

Krysia Broda

Augustus de Morgan Professor of Logic Dov M Gabbay

Artificial Intelligence is concerned with producing devices that help or replace human beings in their daily activities. Neural-symbolic learning systems play a central role in this task by combining, and trying to benefit from, the advantages of both the neural and symbolic paradigms of artificial intelligence. This book provides a comprehensive introduction to the field of neural-symbolic learning systems, and an invaluable overview of the latest research issues in this area. It is divided into three sections, covering the main topics of neural-symbolic integration - theoretical advances in knowledge representation and learning, knowledge extraction from trained neural networks, and inconsistency handling in neural-symbolic systems. Each section provides a balance of theory and practice, giving the results of applications using real-world problems in areas such as DNA sequence analysis, power systems fault diagnosis, and software requirements specifications. Neural-Symbolic Learning Systems will be invaluable reading for researchers and graduate students in Engineering, Computing Science, Artificial Intelligence, Machine Learning and Neurocomputing. It will also be of interest to Intelligent Systems practitioners and anyone interested in applications of hybrid artificial intelligence systems.

Foundations and Applications

Neural-Symbolic Learning Systems

With the publication of the present volume, the Handbook of the History of Logic turns its attention to the rise of modern logic. The period covered is 1685-1900, with this volume carving out the territory from Leibniz to Frege. What is striking about this period is the earliness and persistence of what could be called 'the mathematical turn in logic'. Virtually every working logician is aware that, after a centuries-long run, the logic that originated in antiquity came to be displaced by a new approach with a dominantly mathematical character. It is, however, a substantial error to suppose that the mathematization of logic was, in all essentials, Frege's accomplishment or, if not his alone, a development ensuing from the second half of the nineteenth century. The mathematical turn in logic, although given considerable torque by events of the nineteenth century, can with assurance be dated from the final quarter of the seventeenth century in the impressively prescient work of Leibniz. It is true that, in the three hundred year run-up to the Begriffsschrift, one does not see a smoothly continuous evolution of the mathematical turn, but the idea that logic is mathematics, albeit perhaps only the most general part of mathematics, is one that attracted some degree of support throughout the entire period in question. Still, as Alfred North Whitehead once noted, the relationship between mathematics and symbolic logic has been an "uneasy" one, as is the present-day association of mathematics with computing. Some of this unease has a philosophical texture. For example, those who equate mathematics and logic sometimes disagree about the directionality of the purported identity. Frege and Russell made themselves famous by insisting (though for different reasons) that logic was the senior partner. Indeed logicism is the view that mathematics can be re-expressed without relevant loss in a suitably framed symbolic logic. But for a number of thinkers who took an algebraic approach to logic, the dependency relation was reversed, with mathematics in some form emerging as the senior partner. This was the precursor of the modern view that, in its four main precincts (set theory, proof theory, model theory and recursion theory), logic is indeed a branch of pure mathematics. It would be a mistake to leave the impression that the mathematization of logic (or the logicization of mathematics) was the sole concern of the history of logic between 1665 and 1900. There are, in this long interval, aspects of the modern unfolding of logic that bear no stamp of the imperial designs of mathematicians, as the chapters on Kant and Hegcl make clear. Of the two, Hcgel's influence on logic is arguably the greater, serving as a spur to the unfolding of an idealist tradition in logic - a development that will be covered in a further volume, British Logic in the Nineteenth Century.

The Rise of Modern Logic: from Leibniz to Frege

The International Directory of Logicians is a listing of over 260 of the world's most foremost living logicians, representing the most important and influential developments of our day. It provides a compact summary of each entrant's eduction, professional appointments, honours and awards, principal publications, as well as a description of the nature and significance of his or her contributions to logic, and a "vision statement" concerning logic's future prospects. Logic here is understood in its broad sense, encompassing all branches of mathematical logic, philosophical logic and the history of logic. Inclusion in the Directory is by invitation only, following a rigorous selection process guided by a distinguished Advisory Board. The Directory is designed to meet the needs of students and professional logicians alike. It is the most informative single-volume record of logic's present state and will serve as an invaluable historical reference for future generations of scholarship.

Who's who in Logic

The International Directory of Logicians

Philippe Smets

Jürg Kohlas

Serafín Moral

The Handbook of Defeasible Reasoning and Uncertainty Management Systems is unique in its masterly survey of the computational and algorithmic problems of systems of applied reasoning. The various theoretical and modelling aspects of defeasible reasoning were dealt with in the first four volumes, and Volume 5 now turns to the algorithmic aspect. Topics covered include: Computation in valuation algebras; consequence finding algorithms; possibilistic logic; probabilistic argumentation systems, networks and satisfiability; algorithms for imprecise probabilities, for Dempster-Shafer, and network based decisions.

Volume 5: Algorithms for Uncertainty and Defeasible Reasoning

Handbook of Defeasible Reasoning and Uncertainty Management Systems

Modern applications of logic, in mathematics, theoretical computer science, and linguistics, require combined systems involving many different logics working together. In this book the author offers a basic methodology for combining-or fibring-systems. This means that many existing complex systems can be broken down into simpler components, hence making them much easier to manipulate. Using this methodology the book discusses ways of obtaining a wide variety of multimodal, modal intuitionistic, modal substructural and fuzzy systems in a uniform way. It also covers self-fibred languages which allow formulae to apply to themselves. The book also studies sufficient conditions for transferring properties of the component logics into properties of the combined system.

Fibring Logics

John Symons

Shahid Rahman

Jean Paul van Bendegem

The first volume in this new series explores, through extensive co-operation, new ways of achieving the integration of science in all its diversity. The book offers essays from important and influential philosophers in contemporary philosophy, discussing a range of topics from philosophy of science to epistemology, philosophy of logic and game theoretical approaches. It will be of interest to philosophers, computer scientists and all others interested in the scientific rationality.

Logic, Epistemology, and the Unity of Science

Daniel Lehmann

Kurt Engesser

Quantum mechanics is said to be the most successful physical theory ever. It is, in fact, unique in its success when applied to concrete physical problems. On the other hand, however, it raises profound conceptual problems that are equally unprecedented. Quantum logic, the topic of this volume, can be described as an attempt to cast light on the puzzle of quantum mechanics from the point of view of logic. Since its inception in the famous 1936 paper by Birkhoff and von Neumann entitled, “The logic of quantum mechanics, quantum logic has undergone an enormous development. Various schools of thought and approaches have emerged, and there are a variety of technical results. The chapters of this volume constitute a comprehensive presentation of the main schools, approaches and results in the field of quantum logic. • Authored by eminent scholars in the field • Material presented is of recent origin representing the frontier of the subject. • Provides the most comprehensive and varied discussion of Quantum Mechanics available.

Quantum Logic

Handbook of Quantum Logic and Quantum Structures

The fourteenth volume of the Second Edition covers central topics in philosophical logic that have been studied for thousands of years, since Aristotle: Inconsistency, Causality, Conditionals, and Quantifiers. These topics are central in many applications of logic in central disciplines and this book is indispensable to any advanced student or researcher using logic in these areas. The chapters are comprehensive and written by major figures in the field.

Heinrich Wansing

The notion of negation is one of the central logical notions. It has been studied since antiquity and has been subjected to thorough investigations in the development of philosophical logic, linguistics, artificial intelligence and logic programming. The properties of negation-in combination with those of other logical operations and structural features of the deducibility relation-serve as gateways among logical systems. Therefore negation plays an important role in selecting logical systems for particular applications. At the moment negation is a 'hot topic', and there is an urgent need for a comprehensive account of this logical key concept. We therefore have asked leading scholars in various branches of logic to contribute to a volume on "What is Negation?". The result is the present neatly focused collection of re search papers bringing together different approaches toward a general characteri zation of kinds of negation and classifications thereof. The volume is structured into four interrelated thematic parts. Part I is centered around the themes of Models, Relevance and Impossibility. In Chapter 1 (Negation: Two Points of View), Arnon Avron develops two characteri zations of negation, one semantic the other proof-theoretic. Interestingly and maybe provokingly, under neither of these accounts intuitionistic negation emerges as a genuine negation. J. Michael Dunn in Chapter 2 (A Comparative Study of Various Model-theoretic Treatments of Negation: A History of Formal Negation) surveys a detailed correspondence-theoretic classifcation of various notions of negation in terms of properties of a binary relation interpreted as incompatibility.

What is Negation?

It is with great pleasure that we are presenting to the community the second edition of this extraordinary handbook. It has been over 15 years since the publication of the first edition and there have been great changes in the landscape of philosophical logic since then. The first edition has proved invaluable to generations of students and researchers in formal philosophy and language, as well as to consumers of logic in many applied areas. The main logic article in the Encyclopaedia Britannica 1999 has described the first edition as 'the best starting point for exploring any of the topics in logic'. We are confident that the second edition will prove to be just as good,! The first edition was the second handbook published for the logic commu nity. It followed the North Holland one volume Handbook of Mathematical Logic, published in 1977, edited by the late Jon Barwise. The four volume Handbook of Philosophical Logic, published 1983-1989 came at a fortunate temporal junction at the evolution of logic. This was the time when logic was gaining ground in computer science and artificial intelligence circles. These areas were under increasing commercial pressure to provide devices which help and/or replace the human in his daily activity. This pressure required the use of logic in the modelling of human activity and organisa tion on the one hand and to provide the theoretical basis for the computer program constructs on the other.

Dov M. Gabbay

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