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Reflexive Structures: An Introduction to Computability Theory is concerned with the foundations of the theory of recursive functions. The approach taken presents the fundamental structures in a fairly general setting, but avoiding the introduction of abstract axiomatic domains. Natural numbers and numerical functions are considered exclusively, which results in a concrete theory conceptually organized around Church's thesis. The book develops the important structures in recursive function theor...

The purpose of this book is to introduce the basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on helping the reader in understanding and constructing proofs and writing clear mathematics. This is achieved by exploring set theory, combinatorics and number theory, topics which include many fundamental ideas which are part of the tool kit of any mathematician. This material illustrates how familiar ideas can be formulated rigorously, provides exampl...

"How often we recall, with regret", wrote Mark Twain about editors, "that Napoleon once shot at a magazine editor and missed him and killed a publisher. But we remember with charity, that his intentions were good. " Fortunately, we live in more forgiving times, and are openly able to express our pleasure at being the editors of this volume containing the papers selected for presentation at the 14th International Conference on Inductive Logic Programming. ILP 2004 was held in Porto from the 6th t...

The author selects 23 of his papers in mathematical logic that pursue definability via priority, forcing, compactness and fine structure applied to classical recursion, hyperarithmetic sets, recursion in objects of finite type, measure, models and E-recursion. His general introduction provides a chronology both personal and technical.

The philosophy of computer science is concerned with issues that arise from reflection upon the nature and practice of the discipline of computer science. This book presents an approach to the subject that is centered upon the notion of computational artefact. It provides an analysis of the things of computer science as technical artefacts. Seeing them in this way enables the application of the analytical tools and concepts from the philosophy of technology to the technical artefacts of computer...

This volume contains thoroughly refereed and revised full papers selected from the presentations at the first workshop held under the auspices of the ESPRIT Basic Research Action 6453 Types for Proofs and Programs in Nijmegen, The Netherlands, in May 1993. As the whole ESPRIT BRA 6453, this volume is devoted to the theoretical foundations, design and applications of systems for theory development. Such systems help in designing mathematical axiomatisation, performing computer-aided logical reaso...

A compilation of papers presented at the 2003 European Summer Meeting of the Association for Symbolic Logic, Logic Colloquium '03 includes tutorials and research articles from some of the world's preeminent logicians. One article is a tutorial on finite model theory and query languages that lie between first order and second order logic. The other articles cover current research topics in all areas of mathematical logic, including Proof Theory, Set Theory, Model Theory, and Computability Theory,...

This book contains the proceedings of the International Symposium on Mathematical Morphology and its Applications to Image and Signal Processing IV, held June 3-5, 1998, in Amsterdam, The Netherlands. The purpose of the work is to provide the image analysis community with a sampling of recent developments in theoretical and practical aspects of mathematical morphology and its applications to image and signal processing. Among the areas covered are: digitization and connectivity, skelet...

This volume constitutes the proceedings of the Third International Conference on the Mathematics of Program Construction, held at Kloster Irsee, Germany in July 1995. Besides five invited lectures by distinguished researchers there are presented 19 full revised papers selected from a total of 58 submissions. The general theme is the use of crisp, clear mathematics in the discovery and design of algorithms and in the development of corresponding software and hardware; among the topics addressed a...

This work relates different approaches for the modelling of parallel processes. On the one hand there are the so-called "process algebras" or "abstract programming languages" with Milner's Calculus of Communicating Systems (CCS) and the theoretical version of Hoare's Communicating Sequential Processes (CSP) as main representatives. On the other hand there are machine models, i.e. the classical finite state automata (transition systems), for which, however, more discriminating notions of equivale...

This is the second of two volumes by Professor Cherlin presenting the state of the art in the classification of homogeneous structures in binary languages and related problems in the intersection of model theory and combinatorics. Researchers and graduate students in the area will find in these volumes many far-reaching results and interesting new research directions to pursue. This volume continues the analysis of the first volume to 3-multi-graphs and 3-multi-tournaments, expansions of graphs...

th The 18 International Conference on Conceptual Structures (ICCS 2010) was the latest in a series of annual conferences that have been held in Europe, A- tralia, and North America since 1993. The focus of the conference has been the representation and analysis of conceptual knowledge for research and practical application. ICCS brings together researchers and practitioners in information and computer sciences as well as social science to explore novel ways that c- ceptual structures can be depl...

For a brief time in history, it was possible to imagine that a sufficiently advanced intellect could, given sufficient time and resources, in principle understand how to mathematically prove everything that was true. They could discern what math corresponds to physical laws, and use those laws to predict anything that happens before it happens. That time has passed. Goedel's undecidability results (the incompleteness theorems), Turing's proof of non-computable values, the formulation of quantum...

This book constitutes the refereed proceedings of the 19th International Conference on Rewriting Techniques and Applications, RTA 2008, held in Hagenberg, Austria, July 15-17, in June 2008 as part of the RISC Summer 2008. The 30 revised full papers presented were carefully reviewed and selected from 57 initial submissions. The papers cover current research on all aspects of rewriting including typical areas of interest such as applications, foundational issues, frameworks, implementations, and s...

The present volume contains the proceedings of the international conference Foundations of Software Science and Computation Structures(FOSSACS)2003, held in Warsaw, Poland, April 7-9, 2003. FOSSACS is an event of the Joint European Conferences on Theory and Practice of Software (ETAPS). The pre- ous ?ve FOSSACS conferences took place in Lisbon (1998), Amsterdam (1999), Berlin (2000), Genoa (2001), and Grenoble (2002). FOSSACS presents original papers on foundational researchwith a clear s- ni?ca...

The papers in this volume were presented at the 6th International Meeting on DNA Based Computers, organized by the Leiden Center for Natural Computing and held from June 13 to June 17, 2000 at The Lorentz Center, University of Leiden, Leiden, The Netherlands. DNA Computing is a novel and fascinating development at the interface of computer science and molecular biology. It has emerged in recent years, not simply as an exciting technology for information processing, but also as a catalyst for kno...

This is a comprehensive book on the life and works of Leon Henkin (1921-2006), an extraordinary scientist and excellent teacher whose writings became influential right from the beginning of his career with his doctoral thesis on "The completeness of formal systems" under the direction of Alonzo Church. Upon the invitation of Alfred Tarski, Henkin joined the Group in Logic and the Methodology of Science in the Department of Mathematics at the University of California Berkeley in 1953. He stayed w...