The fundamental ideas concerning computation and recursion naturally find their place at the interface between logic and theoretical computer science. The contributions in this book, by leaders in the field, provide a picture of current ideas and methods in the ongoing investigations into the pure mathematical foundations of computability theory. The topics range over computable functions, enumerable sets, degree structures, complexity, subrecursiveness, domains and inductive inference. A number of the articles contain introductory and background material which it is hoped will make this volume an invaluable resource.

This book constitutes the thoroughly refereed post-proceedings of the 5th International Conference on Developments in Language Theory, DLT 2001, held in Vienna, Austria, in July 2001.The 24 revised full papers presented together with 10 revised invited papers were carefully selected during two rounds of reviewing and revision from a total of 64 papers submitted. Among the topics covered are grammars and acceptors, efficient algorithms for languages, combinatorial and algebraic properties, decision problems, relations to complexity theory, logic, picture description and analysis, DNA computing, cryptography, and concurrency.

This book provides an accessible introduction to the most important features of formal languages and automata theory - core topics on computer science degree schemes worldwide. It focuses on the key concepts, illustrating potentially intimidating material through diagrams and pictorial representations, and this edition will include new and expanded coverage of topics such as: reduction and simplification of material on Turing machines; complexity and O notation; propositional logic and first order predicate logic. Aimed primarily at computer scientists rather than mathematicians, algorithms and proofs are presented informally through examples, and there are numerous exercises (many with solutions) and an extensive glossary. This book will be invaluable to students of computer science but it will also prove essential reading to all practitioners needing to know about formal methods.

This book presents an up-to-date, unified treatment of research in bounded arithmetic and complexity of propositional logic with emphasis on independence proofs and lower bound proofs. The author discusses the deep connections between logic and complexity theory and lists a number of intriguing open problems. An introduction to the basics of logic and complexity is followed by discussion of important results in propositional proof systems and systems of bounded arithmetic. Then more advanced topics are treated, including polynomial simulations and conservativity results, various witnessing theorems, the translation of bounded formulas (and their proofs) into propositional ones, the method of random partial restrictions and its applications, simple independence proofs, complete systems of partial relations, lower bounds to the size of constant-depth propositional proofs, the approximation method and the method of Boolean valuations, combinatorics and complexity theory within bounded arithmetic, and relations to complexity issues of predicate calculus. Students and researchers in mathematical logic and complexity theory will find his comprehensive treatment an excellent guide to this expanding interdisciplinary area.

This book contains a selection of papers presented at the ?rst annual workshop of the TYPES Working Group (Computer-Assisted Reasoning Based on Type Theory, EU IST project 29001), which was held 8th 12th of December, 2000 at the University of Durham, Durham, UK. It was attended by about 80 researchers. The workshop follows a series of meetings organised in 1993, 1994, 1995, 1996, 1998, and 1999 under the auspices of the Esprit BRA6435 and the - prit Working Group 21900 for the previous TYPES projects. Those proceedings were also published in the LNCS series, edited by Henk Barendregt and Tobias Nipkow (Vol. 806, 1993), by Peter Dybjer, Bengt Nordstr]om, and Jan Smith (Vol. 996, 1994), by Stefano Berardi and Mario Coppo (Vol. 1158, 1995), by Christine Paulin-Mohring and Eduardo Gimenez (Vol. 1512, 1996), by Thorsten Altenkirch, Wolfgang Naraschewski, and Bernhard Reus (Vol. 1657, 1998), and by Thierry Coquand, Peter Dybjer, Bengt Nordstr]om, and Jan Smith (Vol. 1956, 1999). The Esprit BRA6453 was itself a continuation of the former Esprit - tion 3245, Logical Frameworks: Design, Implementation, and Experiments. The articles from the annual workshops under that Action were edited by Gerard Huet and Gordon Plotkin in the books Logical Frameworks and Logical En- ronments, both published by Cambridge University Press. Acknowledgements We are very grateful to members of Durham s Computer Assisted Reasoning Group, especially Robert Kiessling, for helping to organise the workshop. Robert s contribution was key to the success of the meeting."

CICLing2002wasthethirdannualConferenceonIntelligenttextprocessingand Computational Linguistics (hence the name CICLing); see www.CICLing.org. It was intended to provide a balanced view of the cutting edge developments in both theoretical foundations of computational linguistics and practice of natural language text processing with its numerous applications. A feature of CICLing conferences is their wide scope that covers nearly all areas of computational linguistics and all aspects of natural language processing applications. The c- ference is a forum for dialogue between the specialists working in these two areas. This year we were honored by the presence of our invited speakers Ni- lettaCalzolari (Inst. for Computational Linguistics, Italy), Ruslan Mitkov (U.of Wolverhampton, UK), Ivan Sag (Stanford U., USA), Yorick Wilks (U. of She?eld), and Antonio Zampolli (Inst. for Computational Linguistics, Italy). They delivered excellent extended lectures and organized vivid discussions. Of 67 submissions received, after careful reviewing 48 were selected for p- sentation; of them, 35 as full papers and 13 as short papers; by 98 authors from 19countries: Spain (18 authors), Mexico (13), Japan, UK (8each), Israel (7), Germany, Italy, USA (6each), Switzerland (5), Taiwan(4), Ireland (3), A- tralia, China, CzechRep., France, Russia (2each), Bulgaria, Poland, Romania (1 each).

The multiset, as a set with multiplicities associated with its elements in the form of natural numbers, is a notation which has appeared again and again in various areas of mathematics and computer science. As a data structure, multisets stand in-between strings/lists, where a linear ordering of symbols/items is present, and sets, where no ordering and no multiplicity is considered. This book presents a selection of thoroughly reviewed revised full papers contributed to a workshop on multisets held in Curtea de Arges, Romania in August 2000 together with especially commissioned papers. All in all, the book assesses the state of the art of the notion of multisets, the mathematical background, and the computer science and molecular computing relevance.

This book constitutes the refereed proceedings of the Second International Conference of B and Z Users, ZB 2002, held in Grenoble, France in January 2002. The 24 papers presented together with three invited contributions were carefully reviewed and selected for inclusion in the book. The book documents the recent advances for the Z formal specification notion and for the B method; the full scope is covered, ranging from foundational and theoretical issues to advanced applications, tools, and case studies.

Stig Kanger (1924-1988) made important contributions to logic and formal philosophy. Kanger's most original achievements were in the areas of general proof theory, the semantics of modal and deontic logic, and the logical analysis of the concept of rights. But he contributed significantly to action theory, preference logic and the theory of measurement as well. This is the second of two volumes dedicated to the work of Stig Kanger. The first volume is a complete collection of Kanger's philosophical papers. The present volume contains critical essays on the various aspects of Kanger's work as well as some biographical sketches. Lennart A...qvist, Jan Berg, Brian Chellas, Anatoli Degtyarev, Lars Gustafsson, SAren HalldA(c)n, Kaj BA, rge Hansen, Sven Ove Hansson, Risto Hilpinen, Jaakko Hintikka, Ghita HolmstrAm-Hintikka, Lars Lindahl, Sten LindstrAm, Ingmar PArn, Dag Prawitz, Wlodek Rabinowicz, Krister Segerberg, Amartya Sen, SAren Stenlund, GAran Sundholm, and Andrei Voronkov have contributed to this volume.

This volume gives an overview of linear logic in five parts: category theory; complexity and expressivity; proof theory; proof nets; and the geometry of interaction. The book includes a general introduction to linear logic that will ensure this book's use by the novice as well as the expert. Mathematicians and computer scientists will learn much from this book.

This book constitutes the thoroughly refereed post-proceedings of the Second International Conference on Rough Sets and Current Trends in Computing, RSCTC 2000, held in Banff, Canada in October 2000.The 80 revised papers presented together with an introduction and three keynote presentations have gone through two rounds of reviewing and revision. The papers are organized in topical sections on granual computing, rough sets and systems, fuzzy sets and systems, rough sets and data mining, nonclassical logics and reasoning, pattern recognition and image processing, neural networks and genetic algorithms, and current trends in computing.

This book provides a self-contained exposition of the theory of plane Cremona maps, reviewing the classical theory. The book updates, correctly proves and generalises a number of classical results by allowing any configuration of singularities for the base points of the plane Cremona maps. It also presents some material which has only appeared in research papers and includes new, previously unpublished results. This book will be useful as a reference text for any researcher who is interested in the topic of plane birational maps.

This volume contains the revised versions of papers presented at the fourth international Workshop on Implementing Automata (WIA), held 17-19 July, 1999, at Potsdam University, Germany. As for its predecessors, the theme of WIA99 was the implementation of au- mata and grammars of all types and their application in other ?elds. The papers contributed to this volume address, among others, algorithmic issues regarding automata, image and dictionarystorage byautomata, and natural language p- cessing. In addition to the papers presented in these proceedings, the workshop - cluded a paper on quantum computing byC. Calude, E. Calude, and K. Svozil (published elsewhere), an invited lecture byW. Thomas on Algorithmic P- blems in the Theory of ?-Automata, a tutorial byM. Silberztein on the INTEX linguistic development environment, and several demonstrations of systems. The local arrangements for WIA99 were conducted byHelmut Jurgensen, Suna Aydin, Oliver Boldt, Carsten Haustein, Beatrice Mix, and Lynda R- bins. The meeting was held in the Communs building, now the main university building, of the New Palace in the park of Sanssouci, Potsdam. The program committee for WIA99 was: A. Bruggemann-Klein .. Technische Universitat Munc .. hen J.-M. Champarnaud Universit'e de Rouen F. Gun .. thner Universitat Munc .. hen H. Jurgensen .. Universitat Potsdam and Universityof Western Ontario D. Maurel Universit'e de Tours D. Raymond Gateway Group Inc. K. Salomaa Universityof Western Ontario W. Thomas Rheinisch-Westfalische Technische Hochschule Aachen B. Watson Ribbit Software Systems Inc.

This book, written by one of the most distinguished of contemporary philosophers of mathematics, is a fully rewritten and updated successor to the author's earlier The Unprovability of Consistency (1979). Its subject is the relation between provability and modal logic, a branch of logic invented by Aristotle but much disparaged by philosophers and virtually ignored by mathematicians. Here it receives its first scientific application since its invention.

This book constitutes the refereed proceedings of the International Seminar on Proof Theory in Computer Science, PTCS 2001, held in Dagstuhl Castle, Germany, in October 2001.The 13 thoroughly revised full papers were carefully reviewed and selected for inclusion in the book. Among the topics addressed are higher type recursion, lambda calculus, complexity theory, transfinite induction, categories, induction-recursion, post-Turing analysis, natural deduction, implicit characterization, iterate logic, and Java programming.

Diagrams are widely used in reasoning about problems in physics, mathematics and logic, but have traditionally been considered to be only heuristic tools and not valid elements of mathematical proofs. This book challenges this prejudice against visualisation in the history of logic and mathematics and provides a formal foundation for work on natural reasoning in a visual mode. The author presents Venn diagrams as a formal system of representation equipped with its own syntax and semantics and specifies rules of transformation that make this system sound and complete. The system is then extended to the equivalent of a first-order monadic language. The soundness of these diagrammatic systems refutes the contention that graphical representation is misleading in reasoning. The validity of the transformation rules ensures that the correct application of the rules will not lead to fallacies. The book concludes with a discussion of some fundamental differences between graphical systems and linguistic systems. This groundbreaking work will have important influence on research in logic, philosophy and knowledge representation.

As society comes to rely increasingly on software for its welfare and prosperity there is an urgent need to create systems in which it can trust. Experience has shown that confidence can only come from a more profound understanding of the issues, which in turn can come only if it is based on logically sound foundations.
This volume contains contributions from leading researchers in the critical disciplines of computing and information science, mathematics, logic, and complexity. All contributions are self-contained, aiming at comprehensibility as well as comprehensiveness. The volume also contains introductory hints to technical issues, concise surveys, introductions, and various fresh results and new perspectives.

This is a first course in propositional modal logic, suitable for mathematicians, computer scientists and philosophers. Emphasis is placed on semantic aspects, in the form of labelled transition structures, rather than on proof theory. The book covers all the basic material - propositional languages, semantics and correspondence results, proof systems and completeness results - as well as some topics not usually covered in a modal logic course. It is written from a mathematical standpoint. To help the reader, the material is covered in short chapters, each concentrating on one topic. These are arranged into five parts, each with a common theme. An important feature of the book is the many exercises, and an extensive set of solutions is provided.

This volume contains the proceedings of the 22nd International Conference on Application and Theory of Petri Nets. The aim of the Petri net conferences is to create a forum for discussing progress in the application and theory of Petri nets. Typically, the conferences have 100{150 participants { one third of these coming from industry while the rest are from universities and research institutions. The conferences always take place in the last week of June. This year the conference was organized jointly with the 2nd International Conference on Application of Concurrency to System Design (ICACSD 2001). The two conferences shared the invited lectures and the social program. The conference and a number of other activities are co-ordinated by a steering committee with the following members: G. Balbo (Italy), J. Billington (Aust- lia), G. De Michelis (Italy), C. Girault (France), K. Jensen (Denmark), S. - magai (Japan), T. Murata (USA), C.A. Petri (Germany; honorary member), W. Reisig (Germany), G. Rozenberg (The Netherlands; chairman), and M. Silva (Spain). Other activities before and during the 2001 conference included tool dem- strations, a meeting on \XML Based Interchange Formats for Petri Nets," - tensive introductory tutorials, two advanced tutorials on \Probabilistic Methods in Concurrency" and \Model Checking," and two workshops on \Synthesis of Concurrent Systems" and \Concurrency in Dependable Computing." The tu- rial notes and workshop proceedings are not published in these proceedings, but copies are available from the organizers.

This volume contains the papers presented at the Third Discrete Mathematics and Theoretical Computer Science Conference (DMTCS1), which was held at 'Ovidius'University Constantza, Romania in July 2001.The conference was open to all areas of discrete mathematics and theoretical computer science, and the papers contained within this volume cover topics such as: abstract data types and specifications; algorithms and data structures; automata and formal languages; computability, complexity and constructive mathematics; discrete mathematics, combinatorial computing and category theory; logic, nonmonotonic logic and hybrid systems; molecular computing.

This book constitutes the refereed proceedings of the 5th International Conference on Typed Lambda Calculi and Applications, TLCA 2001, held in Krakow, Poland in May 2001. The 28 revised full papers presented were carefully reviewed and selected from 55 submissions. The volume reports research results on all current aspects of typed lambda calculi. Among the topics addressed are type systems, subtypes, coalgebraic methods, pi-calculus, recursive games, various types of lambda calculi, reductions, substitutions, normalization, linear logic, cut-elimination, prelogical relations, and mu calculus.

This book constitutes the thoroughly refereed post-proceedings of the 6th International Workshop on DNA-Based Computers, DNA 2000, held in Leiden, The Netherlands, in June 2000.The 16 revised full papers presented together with two invited papers were carefully reviewed and selected from 33 submissions. All current aspects of DNA computing, ranging from theoretical and foundational issues to algorithms, are addressed, from the computer science point of view as well as from the molecular biology point of view.

This book constitutes the thoroughly refereed post-workshop proceedings of the 15th International Workshop on Algebraic Development Techniques, WADT 2001, held jointly with the General Workshop of the ESPRIT Working Group CoFI in Genova, Italy, in April 2001.The book presents 16 papers selected from 32 workshop presentations. Among the topics addressed are formal specification, specification languages, term rewriting, and proof systems.

This textbook explains the basic principles of categorical type theory and the techniques used to derive categorical semantics for specific type theories. It introduces the reader to ordered set theory, lattices and domains, and this material provides plenty of examples for an introduction to category theory, which covers categories, functors, natural transformations, the Yoneda lemma, cartesian closed categories, limits, adjunctions and indexed categories. Four kinds of formal system are considered in detail, namely algebraic, functional, polymorphic functional, and higher order polymorphic functional type theory. For each of these the categorical semantics are derived and results about the type systems are proved categorically. Issues of soundness and completeness are also considered. Aimed at advanced undergraduates and beginning graduates, this book will be of interest to theoretical computer scientists, logicians and mathematicians specializing in category theory.

This textbook explains the basic principles of categorical type theory and the techniques used to derive categorical semantics for specific type theories. It introduces the reader to ordered set theory, lattices and domains, and this material provides plenty of examples for an introduction to category theory, which covers categories, functors, natural transformations, the Yoneda lemma, cartesian closed categories, limits, adjunctions and indexed categories. Four kinds of formal system are considered in detail, namely algebraic, functional, polymorphic functional, and higher order polymorphic functional type theory. For each of these the categorical semantics are derived and results about the type systems are proved categorically. Issues of soundness and completeness are also considered. Aimed at advanced undergraduates and beginning graduates, this book will be of interest to theoretical computer scientists, logicians and mathematicians specializing in category theory.