These Transactions publish archival papers in the broad area of Petri nets and other models of concurrency, ranging from theoretical work to tool support and industrial applications. ToPNoC issues are published as LNCS volumes, and hence are widely distributed and indexed. This Journal has its own Editorial Board which selects papers based on a rigorous two-stage refereeing process. ToPNoC contains: - Revised versions of a selection of the best papers from workshops and tutorials at the annual Petri net conferences - Special sections/issues within particular subareas (similar to those published in the Advances in Petri Nets series) - Other papers invited for publication in ToPNoC - Papers submitted directly to ToPNoC by their authors The fifth volume of ToPNoC contains revised versions of selected papers from workshops and tutorials held in conjunction with the 31st International Conference on Application and Theory of Petri Nets and Other Models of Concurrency, as well as a contributed paper selected through the regular submission track of ToPNoC. The 12 papers cover a diverse range of topics including model checking and system verification, synthesis, foundational work on specific classes of Petri nets, and innovative applications of Petri nets and other models of concurrency. Thus, this volume gives a good view of ongoing concurrent systems and Petri nets research.

Formal Logic is an undergraduate text suitable for introductory, intermediate, and advanced courses in symbolic logic. The book's nine chapters offer thorough coverage of truth-functional and quantificational logic, as well as the basics of more advanced topics such as set theory and modal logic. Complex ideas are explained in plain language that doesn't presuppose any background in logic or mathematics, and derivation strategies are illustrated with numerous examples. Translations, tables, trees, natural deduction, and simple meta-proofs are taught through over 400 exercises. A companion website (complimentary for anyone who buys the book) offers supplemental practice software and tutorial videos.

This Brief is an essay at the interface of philosophy and complexity research, trying to inspire the reader with new ideas and new conceptual developments of cellular automata. Going beyond the numerical experiments of Steven Wolfram, it is argued that cellular automata must be considered complex dynamical systems in their own right, requiring appropriate analytical models in order to find precise answers and predictions in the universe of cellular automata.

Indeed, eventually we have to ask whether cellular automata can be considered models of the real world and, conversely, whether there are limits to our modern approach of attributing the world, and the universe for that matter, essentially a digital reality.

This book introduces the notions and methods of formal logic from a computer science standpoint, covering propositional logic, predicate logic, and foundations of logic programming. It presents applications and themes of computer science research such as resolution, automated deduction, and logic programming in a rigorous but readable way.

The style and scope of the work, rounded out by the inclusion of exercises, make this an excellent textbook for an advanced undergraduate course in logic for computer scientists.

This is a short introductory book on the topic of propositional and first-order logic, with a bias towards computer scientistsa ]. SchAning decides to concentrate on computational issues, and gives us a short book (less than 170 pages) with a tight storylinea ]. I found this a nicely written book with many examples and exercises (126 of them). The presentation is natural and easy to followa ]. This book seems suitable for a short course, a seminar series, or part of a larger course on Prolog and logic programming, probably at the advanced undergraduate level. a" SIGACT News

Contains examples and 126 interesting exercises which put the student in an active reading mode.... Would provide a good university short course introducing computer science students to theorem proving and logic programming. a" Mathematical Reviews

This book concentrates on those aspects of mathematical logic which have strong connections with different topics in computer science, especially automated deduction, logic programming, program verification and semantics of programming languages.... The numerous exercises and illustrative examples contribute a great extent to a betterunderstanding of different concepts and results. The book can be successfully used as a handbook for an introductory course in artificial intelligence. a" Zentralblatt MATH

Hodel's 'Introduction to Mathematical Logic' is a comprehensive overview suitable for advanced undergraduates and graduate students. The text covers numerous topics including propositional logic, first-order languages and logic, incompleteness, undecidability and indefinability, recursive functions, computability and Hilbert's tenth problem.

At the heart of the justification for the reasoning used in modern mathematics lies the completeness theorem for predicate calculus. This unique textbook covers two entirely different ways of looking at such reasoning. Topics include:

• the representation of mathematical statements by formulas in a formal language;
• the interpretation of formulas as true or false in a mathematical structure;
• logical consequence of one formula from others;
• formal proof;
• the soundness and completeness theorems connecting logical consequence and formal proof;
• the axiomatization of some mathematical theories using a formal language;
• the compactness theorem and an introduction to model theory.

This book is designed for self-study by students, as well as for taught courses, using principles successfully developed by the Open University and used across the world. It includes exercises embedded within the text with full solutions to many of these. In addition there are a number of exercises without answers so that students studying under the guidance of a tutor may be assessed on the basis of what has been taught.

Some experience of axiom-based mathematics is required but no previous experience of logic. Propositional and Predicate Calculus gives students the basis for further study of mathematical logic and the use of formal languages in other subjects.

Derek Goldrei is Senior Lecturer and Staff Tutor at the Open University and part-time Lecturer in Mathematics at Mansfield College, Oxford, UK.

The information age owes its existence to a little-known but crucial development, the theoretical study of logic and the foundations of mathematics. The Great Formal Machinery Works draws on original sources and rare archival materials to trace the history of the theories of deduction and computation that laid the logical foundations for the digital revolution. Jan von Plato examines the contributions of figures such as Aristotle; the nineteenth-century German polymath Hermann Grassmann; George Boole, whose Boolean logic would prove essential to programming languages and computing; Ernst Schroder, best known for his work on algebraic logic; and Giuseppe Peano, cofounder of mathematical logic. Von Plato shows how the idea of a formal proof in mathematics emerged gradually in the second half of the nineteenth century, hand in hand with the notion of a formal process of computation. A turning point was reached by 1930, when Kurt Godel conceived his celebrated incompleteness theorems. They were an enormous boost to the study of formal languages and computability, which were brought to perfection by the end of the 1930s with precise theories of formal languages and formal deduction and parallel theories of algorithmic computability. Von Plato describes how the first theoretical ideas of a computer soon emerged in the work of Alan Turing in 1936 and John von Neumann some years later. Shedding new light on this crucial chapter in the history of science, The Great Formal Machinery Works is essential reading for students and researchers in logic, mathematics, and computer science.

Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.

The last twenty years have witnessed an accelerated development of pure and ap plied logic, particularly in response to the urgent needs of computer science. Many traditional logicians have developed interest in applications and in parallel a new generation of researchers in logic has arisen from the computer science community. A new attitude to applied logic has evolved, where researchers tailor a logic for their own use in the same way they define a computer language, and where auto mated deduction for the logic and its fragments is as important as the logic itself. In such a climate there is a need to emphasise algorithmic logic methodologies alongside any individual logics. Thus the tableaux method or the resolution method are as central to todays discipline of logic as classical logic or intuitionistic logic are. From this point of view, J. Goubault and I. Mackie's book on Proof Theory and Automated Deduction is most welcome. It covers major algorithmic methodolo gies as well as a variety of logical systems. It gives a wide overview for the ap plied consumer of logic while at the same time remains relatively elementary for the beginning student. A decade ago I put forward my view that a logical system should be presented as a point in a grid. One coordinate is its philosphy, motivation, its accepted theorems and its required non-theorems. The other coordinate is the algorithmic methodol ogy and execution chosen for its effective presentation. Together these two aspects constitute a 'logic'."

The logician Kurt Goedel (1906-1978) published a paper in 1931 formulating what have come to be known as his 'incompleteness theorems', which prove, among other things, that within any formal system with resources sufficient to code arithmetic, questions exist which are neither provable nor disprovable on the basis of the axioms which define the system. These are among the most celebrated results in logic today. In this volume, leading philosophers and mathematicians assess important aspects of Goedel's work on the foundations and philosophy of mathematics. Their essays explore almost every aspect of Godel's intellectual legacy including his concepts of intuition and analyticity, the Completeness Theorem, the set-theoretic multiverse, and the state of mathematical logic today. This groundbreaking volume will be invaluable to students, historians, logicians and philosophers of mathematics who wish to understand the current thinking on these issues.

One of the most striking development of the last decades in the study of minimal surfaces, constant mean surfaces and harmonic maps is the discovery that many classical problems in differential geometry - including these examples - are actually integrable systems. This theory grew up mainly after the important discovery of the properties of the Korteweg-de Vries equation in the sixties. After C. Gardner, J. Greene, M. Kruskal et R. Miura 44] showed that this equation could be solved using the inverse scattering method and P. Lax 62] reinterpreted this method by his famous equation, many other deep observations have been made during the seventies, mainly by the Russian and the Japanese schools. In particular this theory was shown to be strongly connected with methods from algebraic geom etry (S. Novikov, V. B. Matveev, LM. Krichever. . . ), loop techniques (M. Adler, B. Kostant, W. W. Symes, M. J. Ablowitz . . . ) and Grassmannian manifolds in Hilbert spaces (M. Sato . . . ). Approximatively during the same period, the twist or theory of R. Penrose, built independentely, was applied successfully by R. Penrose and R. S. Ward for constructing self-dual Yang-Mills connections and four-dimensional self-dual manifolds using complex geometry methods. Then in the eighties it became clear that all these methods share the same roots and that other instances of integrable systems should exist, in particular in differential ge ometry. This led K."

Lattice (Boolean) functions are algebraic functions defined over an arbitrary lattice (Boolean algebra), while lattice (Boolean) equations are equations expressed in terms of lattice (Boolean) functions.This self-contained monograph surveys recent developments of Boolean functions and equations, as well as lattice functions and equations in more general classes of lattices; a special attention is paid to consistency conditions and reproductive general solutions.The contents include:- equational compactness in semilattices and Boolean algebras;- the theory of Post functions and equations (which is very close to that of Boolean functions and equations);- a revision of Boolean fundamentals;- closure operators on Boolean functions;- the decomposition of Boolean functions;- quadratic truth equations;- Boolean differential calculus;- Boolean geometry and other topics.There is also a chapter on equations in a very general sense. Applications refer to graph theory, automata theory, synthesis of circuits, fault detection, databases, marketing and others.

In The Moment of Proof, Benson attempts to convey to general readers the feeling of Eureka, the joy of discovery that mathematicians feel when they first encounter an elegant proof. The book is packed with intriguing puzzles: Loyd's Fifteen Puzzle, the Monty Hall Problem, the Prisoner's Dilemma, and more. Every fan of mathematical puzzles will be enthralled by this book.

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.

Kurt Gödel was the most outstanding logician of the twentieth century, famous for his work 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 computation theory, as well as for the strong individuality of his writings on the philosophy of mathematics. Less well-known is his discovery of unusual cosmological models for Einstein's equations, permitting "time-travel" into the past. This second volume of a comprehensive edition of Gödel's works collects together all his publications from 1938 to 1974. Together with Volume I (Publications 1929-1936), it makes available for the first time in a single source all of his previously published work. Continuing the format established in the earlier volume, the present text includes introductory notes that provide extensive explanatory and historical commentary on each of the papers, a facing English translation of the one German original, and a complete bibliography. Succeeding volumes are to contain unpublished manuscripts, lectures, correspondence, and extracts from the notebooks. Collected Works is designed to be accessible and useful to as wide an audience as possible without sacrificing scientific or historical accuracy. The only complete edition available in English, it will be an essential part of the working library of professionals and students in logic, mathematics, philosophy, history of science, and computer science. These volumes will also interest scientists and all others who wish to be acquainted with one of the great minds of the twentieth century.

The initial volume of a comprehensive edition of Gödel's works, this book makes available for the first time in a single source all his publications from 1929 to 1936. The volume begins with an informative overview of Gödel's life and work and features facing English translations for all German originals, extensive explanatory and historical notes, and a complete biography. Volume 2 will contain the remainder of Gödel's published work, and subsequent volumes will include unpublished manuscripts, lectures, correspondence and extracts from the notebooks.

Kurt Gödel (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 stronger systems, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, the foundations of computation theory, unusual cosmological models, and for the strong individuality of his writings on the philosophy of mathematics. The Collected Works is a landmark resource that draws together a lifetime of creative accomplishment. The first two volumes were devoted to Gödel's publications in full (both in the original and translation). This third volume features a wide selection of unpublished articles and lecture texts found in Gödel's Nachlass, documents that enlarge considerably our appreciation of his scientific and philosophical thought and add a great deal to our understanding of his motivations. Continuing the format of the earlier volumes, the present volume includes introductory notes that provide extensive explanatory and historical commentary on each of the papers, English translations of material originally written in German (some transcribed from Gabelsberger shorthand), and a complete bibliography. A succeeding volume is to contain a comprehensive selection of Gödel's scientific correspondence and a complete inventory of his Nachlass. The books are designed to be accessible and useful to as wide an audience as possible without sacrificing scientific or historical accuracy. The only complete edition available in English, it will be an essential part of the working library of professionals and students in logic, mathematics, philosophy, history of science, and computer science.

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.

This is the second volume in a series of well-respected works in temporal science and is by the same authors as the first. Volume one dealt primarily with basic concepts and methods, volume two discuses the more applicable aspects of temporal logics. The first four chapters continue the more theoretical presentations from volume one, covering automata, branching time and labelled deduction. The rest of the book is devoted to discussions of temporal databases, temporal execution and programming, actions and planning. With its inclusion of cutting-edge results and unifying methodologies, this book, and its companion are an indispensable reference for both the pure logician and the theoretical computer scientist.

This book is the second volume exploring the properties of faster than light particles (tachyons). The existence of tachyons has not been proved yet. But the instantaneous nature of Quantum Mechanics and the behavior of particles in Black Holes prove faster than light motion occurs in nature. In volume 1 the author showed that one can derive the form of The Standard Model of elementary particles if neutrinos and down-type quarks are tachyons. In this volume the author shows that these tachyons cause Parity, CP and CPT violation. Also the General Theory of Relativity is extended to Complex General Relativity and its vierbein version. The theory's complex coordinates are mapped to real-valued coordinates (that we observe) using a transformation composed of SU(3) and two SU(2)xU(1) groups - the very groups that appear in The Standard Model. Volume 1 showed that these same groups play a similar role in The Standard Model by mapping complex, faster than light coordinates to real-valued coordinates. Thus the same groups are the basis of Complex General Relativity and The Standard Model. WIMPs (Weakly Interacting Massive Particles - Dark Matter?) appear naturally in this Standard Model. WIMP atoms and chemistry is described. Lastly, the kinetic theory and thermodynamics of systems of tachyons is developed. An appendix is attached with a description of Complex General Relativity that appears in the author's earlier "Quantum Big Bang" book.

Intermediate Logic is an ideal text for anyone who has taken a first course in logic and is progressing to further study. It examines logical theory, rather than the applications of logic, and does not assume any specific technical grounding. The author introduces and explains each concept and term, ensuring that readers have a firm foundation for study. He provides a broad, deep understanding of logic by adopting and comparing a variety of different methods and approaches. In the first section, Bostock covers such fundamental notions as truth, validity, entailment, qualification, and decision procedures. Part Two lays out a definitive introduction to four key logical tools or procedures: semantic tableaux, axiomatic proofs, natural deduction, and sequent calculi. The final section opens up new areas of existence and identity, concluding by moveing from orthodox logic to an examination of free logic'. Intermediate Logic provides an ideal secondary course in logic for university students, and a bridge to advanced study of such subjects as model theory, proof theory, and other specialized areas of mathematical logic. This book is intended for university students from second-year und

This book is designed for readers who know elementary mathematical logic and axiomatic set theory, and who want to learn more about set theory. The primary focus of the book is on the independence proofs. Most famous among these is the independence of the Continuum Hypothesis (CH); that is, there are models of the axioms of set theory (ZFC) in which CH is true, and other models in which CH is false. More generally, cardinal exponentiation on the regular cardinals can consistently be anything not contradicting the classical theorems of Cantor and Konig. The basic methods for the independence proofs are the notion of constructibility, introduced by Godel, and the method of forcing, introduced by Cohen. This book describes these methods in detail, verifi es the basic independence results for cardinal exponentiation, and also applies these methods to prove the independence of various mathematical questions in measure theory and general topology. Before the chapters on forcing, there is a fairly long chapter on "infi nitary combinatorics." This consists of just mathematical theorems (not independence results), but it stresses the areas of mathematics where set-theoretic topics (such as cardinal arithmetic) are relevant. There is, in fact, an interplay between infi nitary combinatorics and independence proofs. Infi nitary combinatorics suggests many set-theoretic questions that turn out to be independent of ZFC, but it also provides the basic tools used in forcing arguments. In particular, Martin's Axiom, which is one of the topics under infi nitary combinatorics, introduces many of the basic ingredients of forcing.