edited by
Bob Coecke / Free University of Brussels, Dept. of Mathematics, FUND, Belgium
David Moore / University of Geneva, Dept. of Theoretical Physics, Switzerland
Alexander Wilce / Juniata College, Dept. of Mathematics and Computer Science, Huntingdon, PA, USA

Current Research in Operational QuantumLogic
Algebras, Categories, Languages

FUNDAMENTAL THEORIES OF PHYSICS Volume 111

This edited volume gives an overview of the concepts and methods used in current research in quantum logic, viewed both as an operational physical theory and in terms of purely mathematical structure. Far from being simply a collation of research papers, it consists of 11 specially commissioned essays that, taken together, provide both an introduction to quantum logic and an overview of current research in this subject. The contributors, who include some of the most distinguished names in the field, discuss topics ranging from
the algebraic theory of orthomodular lattices to recent applications of category-theoretic methods and connections with theoretical computer science. Moreover, an historical overview of the field and an extensive
citation and concept index are included.

Audience: This volume, dedicated to D.J. Foulis in honour of his seminal contributions to quantum logic, should interest pure mathematicians, theoretical physicists, computer scientists and philosophers of science.

Contents and Contributors
Introduction. Operational quantum logic: An overview; B. Coecke, et al. I:
Algebras. Algebraic aspects of orthomodular lattices; G. Bruns, J. Harding.
Observables in the logico-algebraic approach; P. Pt?k. Test spaces and
orthoalgebras; A. Wilce. Representations on unigroups; D.J. Foulis. Free
extensions of group actions, induced representations, and the foundations of
physics; D.J. Foulis, A. Wilce. II: Categories. Short introduction to enriched
categories; F. Borceux, I. Stubbe. Operational Galois adjunctions; B. Coecke,
D. Moore. Operational axiomatics and compound systems; F. Valckenborgh.
Quantales; J. Paseka, J. Rosick?. III: Languages. Quantales and
observational semantics; P. Resende. Quantum languages; S. Gudder. Indices.
Concept index. Citation index.

Hardbound, ISBN 0-7923-6258-6
March 2000, 328 pp.

Frank O. Wagner
Institut Girard Desargues, Universit? Claude Bernard (Lyon-1), Villeurbanne, France

Simple Theories

MATHEMATICS AND ITS APPLICATIONS Volume 503

Simplicity theory is an extension of stability theory to a wider class of structures, containing, among others, the random graph, pseudo-finite fields, and fields with a generic automorphism. Following Kim's proof of `forking
symmetry' which implies a good behaviour of model-theoretic independence, this area of model theory has been a field of intense study. It has necessitated the development of some important new tools, most notably the model-theoretic treatment of hyperimaginaries (classes modulo type-definable equivalence relations). It thus provides a general notion of independence (and of rank in the supersimple case) applicable to a wide class
of algebraic structures.

The basic theory of forking independence is developed, and its properties in a simple structure are analyzed. No prior knowledge of stability theory is assumed; in fact many stability-theoretic results follow either from more general propositions, or are developed in side remarks.

Audience: This book is intended both as an introduction to simplicity theory accessible to graduate students with some knowledge of model theory, and as a reference work for research in the field.

Contents
Preface. Acknowledgements. 1. Preliminaries. 2. Simplicity. 3. Hyperimaginaries. 4. Groups. 5. Supersimple Theories. 6. Miscellaneous. Bibliography. Index.

Hardbound, ISBN 0-7923-6221-7
March 2000, 272 pp.

Steffen Holldobler (eds.)
Dept. of Computer Science, Dresden University of Technology, Germany

Intellectics and Computational Logic
Papers in Honor of Wolfgang Bibel

APPLIED LOGIC SERIES Volume 19

`Intellectics' seeks to understand the functions, structure and operation of the human intellect and to test artificial systems to see the extent to which they can substitute or complement such functions. The word itself was introduced in the early 1980s by Wolfgang Bibel to describe the united fields of artificial intelligence and cognitive science.

The book collects papers by distinguished researchers, colleagues and former students of Bibel's, all of whom have worked together with him, and who present their work to him here to mark his 60th birthday. The papers discuss significant issues in intellectics and computational logic, ranging across automated deduction, logic programming, the logic-based approach to intellectics, cognitive robotics, knowledge representation and reasoning. Each paper contains new, previously unpublished, reviewed results. The collection is a state of the art account of the current capabilities and limitations of a computational-logic-based approach to intellectics.

Readership: Researchers who are convinced that the intelligent behaviour of machines should be based on a rigid formal treatment of knowledge representation and reasoning.

Contents and Contributors
Preface; S. H?lldobler. Prologue; C. Kreitz. A Confluent Connection Calculus; P. Baumgartner, et al. Prioritizing Default Logic; G. Brewka, T. Eiter. A Connection Calculus for Handling Incomplete Information; S. Br?ning, T.
Schaub. The Connection Method, Co straints and Model Building; R. Caferra, N. Peltier. Towards a Logical Characterisation of Sentences of the Kindv`Sentence p is About Object c'; R. Demolombe, L.F. del Cerro. The Cut Rule in Theorem Proving; E. Eder. Some Strengths of Nonmonotonic Reasoning; Uwe Egly, H. Tompits. Composing Re-usable Synthesis Methods through Graph-based Viewpoints; J. Eusterbrock. Proof Structures and Matrix Graphs; B. Fronh?fer. AI and Cognitive Science: Feedback Leads to a New Neural Concept; C. Herrmann. Matrix-based Constructive Theorem Proving; C. Kreitz, et al. Complex Plans in the Fluent Calculus; S. H?lldobler, H.-P. St?rr. Querying AOL Knowledge Bases; G. Lakemeyer, H.J. Levesque. Properties and Relations of Tableau and Connection Calculi; R. Letz. Concepts in Proof Planning; E. Melis, J.H. Siekmann. Proof = Guarantee + Explanation; J.A. Robinson. Automated Theorem Proving in High-Quality Software Design; J. Schumann. A Complete Neural Network Algorithm for HORN-SAT; A. Strohmaier. Nondeterministic Acions in the Fluent Calculus: Disjunctive State Update Axioms; M. Thielscher. The Illusion of Knowledge; C. Wagner. Criteria for Termination; C. Walther. Epilogue; C. Kreitz.

Hardbound, ISBN 0-7923-6261-6
April 2000, 408 pp.

edited by
Da Ruan / Belgian Nuclear Research Centre (SCK.CEN), Mol, Belgium
Etienne E. Kerre / Applied Mathematics and Computer Science, University of Ghent, Belgium

Fuzzy If-Then Rules in Computational Intelligence
Theory and Applications

THE KLUWER INTERNATIONAL SERIES IN ENGINEERING AND COMPUTER SCIENCE Volume 553

During the last three decades, interest has increased significantly in the representation and manipulation of imprecision and uncertainty. Perhaps the most important technique in this area concerns fuzzy logic or the logic of fuzziness initiated by L. A. Zadeh in 1965. Since then, fuzzy logic has been incorporated into many areas of fundamental science and into the applied sciences. More importantly, it has been successful in the areas of expert systems and fuzzy control. The main body of this book consists of so-called IF-THEN rules, on which experts express their knowledge with respect to a certain domain of expertise.

Fuzzy IF-THEN Rules in Computational Intelligence: Theory and Applications brings together contributions from leading global specialists who work in the domain of representation and processing of IF-THEN rules. This work gives