The Handbook of Logic in Computer Science is a multi-volume work covering all major areas of application of logic to theoretical computer science.

A thorough, accessible, and rigorous presentation of the central theorems of mathematical logic . . . ideal for advanced students of mathematics, computer science, and logic
Logic of Mathematics combines a full-scale introductory course in mathematical logic and model theory with a range of specially selected, more advanced theorems. Using a strict mathematical approach, this is the only book available that contains complete and precise proofs of all of these important theorems:
* GAdel's theorems of completeness and incompleteness
* The independence of Goodstein's theorem from Peano arithmetic
* Tarski's theorem on real closed fields
* Matiyasevich's theorem on diophantine formulas
Logic of Mathematics also features:
* Full coverage of model theoretical topics such as definability, compactness, ultraproducts, realization, and omission of types
* Clear, concise explanations of all key concepts, from Boolean algebras to Skolem-LAwenheim constructions and other topics
* Carefully chosen exercises for each chapter, plus helpful solution hints
At last, here is a refreshingly clear, concise, and mathematically rigorous presentation of the basic concepts of mathematical logic-requiring only a standard familiarity with abstract algebra. Employing a strict mathematical approach that emphasizes relational structures over logical language, this carefully organized text is divided into two parts, which explain the essentials of the subject in specific and straightforward terms.
Part I contains a thorough introduction to mathematical logic and model theory-including a full discussion of terms, formulas, and other fundamentals, plus detailed coverageof relational structures and Boolean algebras, GAdel's completeness theorem, models of Peano arithmetic, and much more.
Part II focuses on a number of advanced theorems that are central to the field, such as GAdel's first and second theorems of incompleteness, the independence proof of Goodstein's theorem from Peano arithmetic, Tarski's theorem on real closed fields, and others. No other text contains complete and precise proofs of all of these theorems.
With a solid and comprehensive program of exercises and selected solution hints, Logic of Mathematics is ideal for classroom use-the perfect textbook for advanced students of mathematics, computer science, and logic.

Semigroups, Automata, Universal Algebra, Varieties

The requirement to reason logically forms the basis of all mathematics, and hence mathematical logic is one of the most fundamental topics that students will study. Assuming no prior knowledge of the topic, this book provides an accessible introduction for advanced undergraduate students.

Building on fuzzy logic and evolutionary computing, this book introduces fuzzy cooperative coevolution as a novel approach to systems design, conductive to explaining human decision process. Fuzzy cooperative coevolution is a methodology for constructing systems able to accurately predict the outcome of a decision-making process, while providing an understandable explanation of the underlying reasoning.

The central contribution of this work is the use of an advanced evolutionary technique, cooperative coevolution, for dealing with the simultaneous design of connective and operational parameters. Cooperative coevolution overcomes several limitations exhibited by other standard evolutionary approaches.

The applicability of fuzzy cooperative coevolution is validated by modeling the decision processes of three real-world problems, an iris data benchmark problem and two problems from breast cancer diagnosis.

The main subjects of the Developments in Language Theory (DLT) conf- ence series are formal languages, automata, conventional and unconventional computation theory, and applications of automata and language theory. T- ical, but not exclusive, topics of interest include: grammars and acceptors for strings, graphs, and arrays; e?cient text algorithms; combinatorial and al- braic properties of languages; decision problems; relations to complexity theory andlogic;picturedescriptionandanalysis;cryptography;concurrency;andDNA and quantum computing. The members of the steering committee of DLT are: J. Berstel (Paris), M. Ito(Kyoto), W. Kuich(Vienna), G. P? aun(BucharestandSeville), A. Restivo (Palermo), G. Rozenberg (chair, Leiden), A. Salomaa (Turku) and W. Thomas (Aachen). The ?rst DLT conference was organized by G. Rozenberg and A. Salomaa in Turku in 1993. After this, the DLT conferences were held in every odd year: Magdeburg(1995), Thessaloniki(1997), Aachen(1999)andVienna(2001). Since 2001, a DLT conference has been organized in every odd year in Europe and in every even year outside Europe. The last two DLT conferences were organized in Kyoto, Japan in 2002 and Szeged, Hungary in 2003. The titles of the volumes of the past DLT conferences are the following: 1. Developments in Language Theory. At the Crossroads of Mathematics, C- puter Science and Biology (edited by G. Rozenberg and A. Salomaa) (1994) (World Scienti?c) 2. Developments in Language Theory II. At the Crossroads of Mathematics, Computer Science and Biology (edited by J. Dassow, G. Rozenberg and A. Salomaa) (1996) (World Scienti?c) 3. Proceedings of the Third International Conference on Developments in L- guageTheory(edite

This is a softcover reprint of the English translation of 1968 of N. Bourbaki's, Th orie des Ensembles (1970).

Mathematics Ones and Zeros Understanding Boolean Algebra, Digital Circuits, and the Logic of Sets Ones and Zeros explains, in lay terms, Boolean algebra, the suprisingly simple system of mathematical logic used in digital computer circuitry. Anecdotal in style and often funny, Ones and Zeros follows the development of this logic system from its origins in Victorian England to its rediscovery in this century as the foundation of all modern computing machinery. Readers will learn about the interesting history of the development of symbolic logic in particular, and the often misunderstood process of mathematical invention and scientific discovery, in general. Ones and Zeros also features practical exercises with answers, real-world examples of digital circuit design, and a reading list. This fascinating look at the crucial technology of the twentieth century will be enjoyed by anyone who has a general interest in science, technology, and mathematics. Ones and Zeros will be of particular interest to software engineers who want to gain a comprehensive understanding of computer hardware. Outstanding features include:

• A history of mathematical logic
• An explanation of the logic of digital circuits
• Hands-on exercises and examples

The 8th International Conference on Theory and Applications of Satis?ability Testing(SAT2005)providedaninternationalforumforthemostrecentresearch on the satis?ablity problem (SAT). SAT is the classic problem of determining whether or not a propositional formula has a satisfying truth assignment. It was the ?rst problem shown by Cook to be NP-complete. Despite its seemingly specialized nature, satis?ability testing has proved to extremely useful in a wide range of di?erent disciplines, both from a practical as well as from a theoretical point of view. For example, work on SAT continues to provide insight into various fundamental problems in computation, and SAT solving technology has advanced to the point where it has become the most e?ective way of solving a number of practical problems. The SAT series of conferences are multidisciplinary conferences intended to bring together researchers from various disciplines who are interested in SAT. Topics of interest include, but are not limited to: proof systems and proof c- plexity; search algorithms and heuristics; analysis of algorithms; theories beyond the propositional; hard instances and random formulae; problem encodings; - dustrial applications; solvers and other tools. This volume contains the papers accepted for presentation at SAT 2005. The conference attracted a record number of 73 submissions. Of these, 26 papers were accepted for presentation in the technical programme. In addition, 16 - pers were accepted as shorter papers and were presented as posters during the technicalprogramme.Theacceptedpapersandposterpaperscoverthefullrange of topics listed in the call for papers.

This volume contains the proceedings of the 25th International Conference on Application and Theory of Petri Nets (ICATPN 2004). 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 conferenceshave 100-150participants, one third of these c- ing from industry, whereas the others are from universities and research insti- tions. The conferences always take place in the last week of June. The conference and a number of other activities are coordinated by a ste- ing committee with the following members: Wil van der Aalst (The Neth- lands), JonathanBillington(Australia), JrgDesel(Germany), SusannaDonatelli (Italy), SergeHaddad(France), KurtJensen(Denmark), MaciejKoutny(United Kingdom), Sadatoshi Kumagai(Japan), GiorgioDe Michelis (Italy), Tadao- rata (USA), Carl Adam Petri (Germany, Honorary Member), Wolfgang Reisig (Germany), GrzegorzRozenberg(TheNetherlands, Chairman)andManuelSilva (Spain). The 2004 conference was organized by the Department of Computer Science of the University of Bologna, Italy. We would like to thank the organizing c- mittee, chaired by Roberto Gorrieri, for the e?ort invested in making the event successful. We are also grateful to the following sponsoring institutions and - ganizations: Associazione Italiana per l'Informatica ed il Calcolo Automatico (AICA), Microsoft Research, and Network Project & Solutions (NPS Group). We received a total of 62 submissions from 26 di?erent countries. The p- gramcommittee?nallyselected19regularpapersand5toolpresentationpapers. This volume comprises the papers that were accepted for presentation. Invited lectures were given by Gianfranco Ciardo, Roberto Gorrieri, Thomas A. H- zinger, Wojciech Penczek, Lucia Pomello and William H. Sanders. Their papers are also included in this volume.

The very ?rst model of concurrent and distributed systems was introduced by C.A. Petri in his seminal Ph.D. thesis in 1964. Petri nets has remained a central model for concurrentsystemsfor40 years,andthey areoften usedasa yardstick for other models of concurrency. As a matter of fact, many other models have been developed since then, and this research area is ?ourishing today. The goal of the 4th Advanced Course on Petri Nets held in Eichsta ..tt, Germany in September 2003 was to present applications and the theory of Petri Nets in the context of a whole range of other models. We believe that in this way the participants of the course received a broad and in-depth picture of research in concurrent and distributed systems. It is also the goal of this volume to convey this picture. The volume is based on lectures given at the Advanced Course, but in order to provide a balanced p- sentation of the ?eld, some of the lectures are not included, and some material not presented in Eichst. att is covered here. In particular, a series of introductory lectures was not included in this volume, as the material they covered is well - tablishedby now,andwellpresentedelsewhere (e.g.,inW. ReisigandG. Roz- berg, eds., "Lectures on Petri Nets," LNCS 1491, 1492, Springer-Verlag, 1997 - these two volumes are based on the 3rd Advanced Course on Petri Nets).

This book is a specialized monograph on interpolation and definability, a notion central in pure logic and with significant meaning and applicability in all areas where logic is applied, especially computer science, artificial intelligence, logic programming, philosophy of science and natural language. Suitable for researchers and graduate students in mathematics, computer science and philosophy, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism (second edition), J. M. Dunn and G. Hardegree's Algebraic Methods in Philosophical Logic, H. Rott's Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning, P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2, and David J. Pym and Eike Ritter's Reductive Logic and Proof Search: Proof theory, semantics and control.

This book is devoted to the 6th International Conference on Theory and - plications of Satis?ability Testing (SAT 2003) held in Santa Margherita Ligure (Genoa,Italy), during May5-8,2003. SAT 2003followedthe WorkshopsonS- is?ability held in Siena (1996), Paderborn (1998), and Renesse (2000), and the Workshop on Theory and Applications of Satis?ability Testing held in Boston (2001) and in Cincinnati (2002). As in the last edition, the SAT event hosted a SAT solvers competition, and, starting from the 2003 edition, also a Quanti?ed Boolean Formulas (QBFs) solvers comparative evaluation. There were 67 submissions of high quality, authored by researchers from all over the world. All the submissions were thoroughly evaluated, and as a result 42 were selected for oral presentations, and 16 for a poster presentation. The presentations covered the whole spectrum of research in propositional and QBF satis?ability testing, including proof systems, search techniques, probabilistic analysis of algorithms and their properties, problem encodings, industrial app- cations, speci?c tools, case studies and empirical results. Further, the program was enriched by three invited talks, given by Riccardo Zecchina (on "Survey Propagation: from Analytic Results on Random k-SAT to a Message-Passing - gorithm for Satis?ability"), Toby Walsh (on "Challenges in SAT (and QBF)") and Wolfgang Kunz (on "ATPG Versus SAT: Comparing Two Paradigms for Boolean Reasoning"). SAT 2003 thus provided a unique forum for the presen- tion and discussion of research related to the theory and applications of pro- sitional and QBF satis?ability testing.

This volume contains the Proceedings of ICFCA 2004, the 2nd International Conference on Formal Concept Analysis. The ICFCA conference series aims to be the premier forum for the publication of advances in applied lattice and order theory and in particular scienti?c advances related to formal concept analysis. Formal concept analysis emerged in the 1980s from e?orts to restructure lattice theory to promote better communication between lattice theorists and potentialusersoflatticetheory.Sincethen, the?eldhasdevelopedintoagrowing research area in its own right with a thriving theoretical community and an increasing number of applications in data and knowledge processing including data visualization, information retrieval, machine learning, data analysis and knowledge management. In terms of theory, formal concept analysis has been extended into attribute exploration, Boolean judgment, contextual logic and so on to create a powerful general framework for knowledge representation and reasoning. This conference aims to unify theoretical and applied practitioners who use formal concept an- ysis, drawing on the ?elds of mathematics, computer and library sciences and software engineering. The theme of the 2004 conference was 'Concept Lattices" to acknowledge the colloquial term used for the line diagrams that appear in almost every paper in this volume. ICFCA 2004 included tutorial sessions, demonstrating the practical bene?ts of formal concept analysis, and highlighted developments in the foundational theory and standards. The conference showcased the increasing variety of formal concept analysis software and included eight invited lectures from distinguished speakersinthe?eld.Sevenoftheeightinvitedspeakerssubmittedaccompanying papers and these were reviewed and appear in this volume.

Kurt Goedel (1906 - 1978) was the most outstanding logician of the twentieth century, famous for his hallmark works on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, and the foundations of computability theory, as well as for the strong individuality of his writings on the philosophy of mathematics. He is less well known for his discovery of unusual cosmological models for Einstein's equations, in theory permitting time travel into the past. The Collected Works is a landmark resource that draws together a lifetime of creative thought and accomplishment. The first two volumes were devoted to Goedel's publications in full (both in original and translation), and the third volume featured a wide selection of unpublished articles and lecture texts found in Goedel's Nachlass. These long-awaited final two volumes contain Goedel's correspondence of logical, philosophical, and scientific interest. Volume IV covers A to G, with H to Z in volume V; in addition, Volume V contains a full inventory of Goedel's Nachlass. All volumes include introductory notes that provide extensive explanatory and historical commentary on each body of work, English translations of material originally written in German (some transcribed from the Gabelsberger shorthand), and a complete bibliography of all works cited. Kurt Goedel: Collected Works is designed to be useful and accessible to as wide an audience as possible without sacrificing scientific or historical accuracy. The only comprehensive edition of Goedel's work available, it will be an essential part of the working library of professionals and students in logic, mathematics, philosophy, history of science, and computer science and all others who wish to be acquainted with one of the great minds of the twentieth century.

Chaitin, the inventor of algorithmic information theory, presents in this book the strongest possible version of Goedel's incompleteness theorem, using an information theoretic approach based on the size of computer programs. One half of the book is concerned with studying the halting probability of a universal computer if its program is chosen by tossing a coin. The other half is concerned with encoding the halting probability as an algebraic equation in integers, a so-called exponential diophantine equation.

Combinatorics and Number Theory of Counting Sequences is an introduction to the theory of finite set partitions and to the enumeration of cycle decompositions of permutations. The presentation prioritizes elementary enumerative proofs. Therefore, parts of the book are designed so that even those high school students and teachers who are interested in combinatorics can have the benefit of them. Still, the book collects vast, up-to-date information for many counting sequences (especially, related to set partitions and permutations), so it is a must-have piece for those mathematicians who do research on enumerative combinatorics. In addition, the book contains number theoretical results on counting sequences of set partitions and permutations, so number theorists who would like to see nice applications of their area of interest in combinatorics will enjoy the book, too. Features The Outlook sections at the end of each chapter guide the reader towards topics not covered in the book, and many of the Outlook items point towards new research problems. An extensive bibliography and tables at the end make the book usable as a standard reference. Citations to results which were scattered in the literature now become easy, because huge parts of the book (especially in parts II and III) appear in book form for the first time.

The aim of contextual logic is to provide a formal theory of elementary logic, which is based on the doctrines of concepts, judgements, and conclusions. Concepts are mathematized using Formal Concept Analysis (FCA), while an approach to the formalization of judgements and conclusions is conceptual graphs, based on Peirce's existential graphs. Combining FCA and a mathematization of conceptual graphs yields so-called concept graphs, which offer a formal and diagrammatic theory of elementary logic.

Expressing negation in contextual logic is a difficult task. Based on the author's dissertation, this book shows how negation on the level of judgements can be implemented. To do so, cuts (syntactical devices used to express negation) are added to concept graphs. As we can express relations between objects, conjunction and negation in judgements, and existential quantification, the author demonstrates that concept graphs with cuts have the expressive power of first-order predicate logic. While doing so, the author distinguishes between syntax and semantics, and provides a sound and complete calculus for concept graphs with cuts. The author's treatment is mathematically thorough and consistent, and the book gives the necessary background on existential and conceptual graphs.

This volume, "Petri Net Technology for Communication-Based Systems," is a state-of-the-artreportin the seriesAdvances in Petri Nets. It showshowvarious well-established and new Petri net notions and techniques can be used for m- elingcommunication-basedsystems, withspecialfocusonwork?owmanagement and business processes. In the last 6 years this topic has been studied by the DFG Forschergruppe Petri Net Technology in Berlin in close cooperation with the international c- munity. The main results of this cooperation were presented at the 1st and 2nd InternationalColloquiaonPetriNetTechnologiesforModelingCommunication- Based Systems, held in Berlin in 1999 and 2001, respectively. A careful selection of contributions by members of the DFG Forschergruppe and by international experts in this ?eld are presented in this volume. Taking into account the fru- ful discussions during the two colloquia and the cross-refereeing process for the accepted papers, a high degree of common understanding was achieved, leading to a highly comprehensive presentation in this volume. The topics of the papers in this volume can be roughly classi?ed into the following two areas: - Petri net technology and - application to communication-based systems. Since most papers comprise aspects of both areas, we chose an alphabetic order. However, in the following we give a rough overview of the contributions in both areas according to the main focus of the corresponding papers.

Linear Logic is a branch of proof theory which provides refined tools for the study of the computational aspects of proofs. These tools include a duality-based categorical semantics, an intrinsic graphical representation of proofs, the introduction of well-behaved non-commutative logical connectives, and the concepts of polarity and focalisation. These various aspects are illustrated here through introductory tutorials as well as more specialised contributions, with a particular emphasis on applications to computer science: denotational semantics, lambda-calculus, logic programming and concurrency theory. The volume is rounded-off by two invited contributions on new topics rooted in recent developments of linear logic. The book derives from a summer school that was the climax of the EU Training and Mobility of Researchers project "Linear Logic in Computer Science." It is an excellent introduction to some of the most active research topics in the area.

The refereed proceedings of the 24th International Conference on Applications and Theory of Petri Nets, ICATPN 2003, held in Eindhoven, The Netherlands, in June 2003. The 25 revised full papers presented together with 6 invited contributions were carefully reviewed and selected from 77 submissions. All current issues on research and development in the area of Petri nets are addressed, in particular concurrent systems design and analysis, model checking, networking, business process modeling, formal methods in software engineering, agent systems, systems specification, systems validation, discrete event systems, protocols, and prototyping.

Kurt Gödel is regarded as one of the most outstanding logician of the twentieth century, famous for his work on logic and number theory. This third volume of a comprehensive edition of Godel's works comprises a selection of previously unpublished manuscripts and lectures. It includes introductory notes that provide extensive explanations and historical commentary on each of the papers. This book is accessible to a wide audience without sacrificing historical or scientific accuracy and will be an essential part of the working library of both professionals and students.

Biomolecular computing is an interdisciplinary ?eld that draws together mol- ular biology, DNA nanotechnology, chemistry, physics, computer science and mathematics. Theannualinternationalmeeting onDNA-based computationhas been an exciting forum where scientists of di?erent backgrounds who share a common interest in biomolecular computing can meet and discuss their latest results. The central goal of this conference is to bring together experimentalists and theoreticians whose insights can calibrate each others' approaches. The 9th Annual International Meeting on DNA Based Computers was held during June 1-4, 2003 in the University of Wisconsin, Madison, USA. The meeting had 106 registered participants from 12 countries around the world. On the ?rst day of the meeting, we had three tutorials: the ?rst was on self-assembly of DNA nano structures which focused on the basic techniques of using designed DNA nano molecules to be self-assembled onto larger structures for computational purposes. This tutorial was given by Hao Yan of Duke U- versity. The second tutorial was given by Chengde Mao of Purdue University in which Dr. Mao presented basic DNA biochemistry that was designed for non experimentalists. The third tutorial was given by Max Garzon of the Univ- sity of Memphis. Dr. Garzon gave a lecture on computational complexity which was tailored for non-computer scientists. The next three days were for invited plenary lectures, and regular oral and poster presentations. Invited plenary l- turesweregivenbyHelenBermanofRutgersUniversity(USA), GiancarloMauri of the University of Milan (Italy), Guenter von Kiedrowski of Ruhr University (Germany), and Sorin Istrail of Celera/Applied Biosystems. Theorganizerssoughtto attractthemostsigni?cantrecentresearchwith the highestimpactonthedevelopmentofthediscipline.

Logic languages are free from the ambiguities of natural languages, and are therefore specially suited for use in computing. Model theory is the branch of mathematical logic which concerns the relationship between mathematical structures and logic languages, and has become increasingly important in areas such as computing, philosophy and linguistics. As the reasoning process takes place at a very abstract level, model theory applies to a wide variety of structures. It is also possible to define new structures and classify existing ones by establishing links between them. These links can be very useful since they allow us to transfer our knowledge between related structures. This book provides a clear and readable introduction to the subject, and is suitable for both mathematicians and students from outside the subject. It includes some historically relevant information before each major topic is introduced, making it a useful reference for non-experts. The motivation of the subject is constantly explained, and proofs are also explained in detail.

Proof complexity is a rich subject drawing on methods from logic, combinatorics, algebra and computer science. This self-contained book presents the basic concepts, classical results, current state of the art and possible future directions in the field. It stresses a view of proof complexity as a whole entity rather than a collection of various topics held together loosely by a few notions, and it favors more generalizable statements. Lower bounds for lengths of proofs, often regarded as the key issue in proof complexity, are of course covered in detail. However, upper bounds are not neglected: this book also explores the relations between bounded arithmetic theories and proof systems and how they can be used to prove upper bounds on lengths of proofs and simulations among proof systems. It goes on to discuss topics that transcend specific proof systems, allowing for deeper understanding of the fundamental problems of the subject.