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Books > Science & Mathematics > Mathematics > Mathematical foundations > Mathematical logic
This book constitutes the refereed proceedings of the 7th International Conference on Cellular Automata for Research and Industry, ACRI 2006. The book presents 53 revised full papers and 19 revised poster papers together with 6 invited lectures. Topical sections include CA theory and implementation, computational theory, population dynamics, physical modeling, urban, environmental and social modeling, traffic and boolean networks, multi-agents and robotics, as well as crowds and cellular automata, and more.
This book constitutes the refereed proceedings of the 27th International Conference on Applications and Theory of Petri Nets and Other Models of Concurrency, ICATPN 2006, held in Turku, Finland in June 2006. The book presents 16 revised full papers and 6 revised tool papers together with 4 invited papers. All current issues on research and development in the area of Petri nets and modeling of concurrent systems are addressed.
This superb collection of papers focuses on a fundamental question in logic and computation: What is a logical system? With contributions from leading researchers--including Ian Hacking, Robert Kowalski, Jim Lambek, Neil Tennent, Arnon Avron, L. Farinas del Cerro, Kosta Dosen, and Solomon Feferman--the book presents a wide range of views on how to answer such a question, reflecting current, mainstream approaches to logic and its applications. Written to appeal to a diverse audience of readers, What is a Logical System? will excite discussion among students, teachers, and researchers in mathematics, logic, computer science, philosophy, and linguistics.
Biomolecular computing has emerged as an interdisciplinary ?eld that draws - getherchemistry, computerscience, mathematics, molecularbiology, andphysics. Our knowledge of DNA nanotechnology and biomolecular computing increases dramatically with every passing year. The International Meeting on DNA C- puting has been a forum where scientists with di?erent backgrounds, yet sh- ing a common interest in biomolecular computing, meet and present their latest results. Continuing this tradition, the 10th International Meeting on DNA C- puting(DNA10)focusedonthecurrentexperimentalandtheoreticalresultswith the greatest impact. The meeting took place at the University of Milano-Bicocca, Milan, Italy, from June 7 to June 10, 2004, and it was organized by the University of Milano- Bicocca and the Department of Informatics of the University of Milano-Bicocca. Papersandposterpresentationsweresoughtinallareasthatrelatetobiomole- lar computing, including (but not restricted to): demonstrations of biomolecular computing (using DNA and/or other molecules), theoretical models of biomol- ularcomputing, biomolecularalgorithms, computationalprocessesinvitroandin vivo, analysis and theoretical models of laboratory techniques, biotechnological and other applications of DNA computing, DNA nanostructures, DNA devices such as DNA motors, DNA error evaluation and correction, in vitro evolution, molecular design, self-assembled systems, nucleic acid chemistry, and simulation tools. Authors were asked to choose between two di?erent tracks: Track A - Full paper, for authors who wished to submit a full paper for presentation at DNA10 (oral or poster), and publication in the conference p- ceedings. Track B - One-page abstract, for authors submitting experimental results, and who planned to submit their manuscript to a scienti?c journal, rather than publish it in the conference procee
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
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
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:
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.
This is a softcover reprint of the English translation of 1968 of N. Bourbaki's, Th orie des Ensembles (1970).
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.
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.
Higher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory of infinity-categories, higher categories in which all higher morphisms are assumed to be invertible. In "Higher Topos Theory," Jacob Lurie presents the foundations of this theory, using the language of weak Kan complexes introduced by Boardman and Vogt, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language. The result is a powerful theory with applications in many areas of mathematics. The book's first five chapters give an exposition of the theory of infinity-categories that emphasizes their role as a generalization of ordinary categories. Many of the fundamental ideas from classical category theory are generalized to the infinity-categorical setting, such as limits and colimits, adjoint functors, ind-objects and pro-objects, locally accessible and presentable categories, Grothendieck fibrations, presheaves, and Yoneda's lemma. A sixth chapter presents an infinity-categorical version of the theory of Grothendieck topoi, introducing the notion of an infinity-topos, an infinity-category that resembles the infinity-category of topological spaces in the sense that it satisfies certain axioms that codify some of the basic principles of algebraic topology. A seventh and final chapter presents applications that illustrate connections between the theory of higher topoi and ideas from classical topology.
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.
This book constitutes the refereed proceedings of the 5th Italian Conference on Algorithms and Computation, CIAC 2003, held in Rome, Italy in May 2003. The 23 revised full papers presented were carefully reviewed and selected from 57 submissions. Among the topics addressed are complexity, complexity theory, geometric computing, matching, online algorithms, combinatorial optimization, computational graph theory, approximation algorithms, network algorithms, routing, and scheduling. |
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