Download or read book Recursion on the Countable Functionals written by D. Normann and published by Springer. This book was released on 2006-12-08 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Recursion Theory on the Countable Functionals written by J. M. E. Hyland and published by . This book was released on 1975 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Recursive Functionals written by L.E. Sanchis and published by Elsevier. This book was released on 1992-05-18 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is a self-contained elementary exposition of the theory of recursive functionals, that also includes a number of advanced results. Although aiming basically at a theory of higher order computability, attention is restricted to second order functionals, where the arguments are numerical functions and the values, when defined, are natural numbers. This theory is somewhat special, for to some extent it can be reduced to first order theory, but when properly extended and relativized it requires the full machinery of higher order computations. In the theory of recursive monotonic functionals the author formulates a reasonable notion of computation which provides the right frame for what appears to be a convincing form of the extended Church's thesis. At the same time, the theory provides sufficient room to formulate the classical results that are usually derived in terms of singular functionals. Presented are complete proofs of Gandy's selector theorem, Kleene's theorem on hyperarithmetical predicates, and Grilliot's theorem on effectively discontinuous functionals.
Download or read book Provability Computability and Reflection written by Lev D. Beklemishev and published by Elsevier. This book was released on 2000-04-01 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provability, Computability and Reflection
Download or read book Formalized Recursive Functionals and Formalized Realizability written by Stephen Cole Kleene and published by American Mathematical Soc.. This book was released on 1969 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph carries out the program which the author formulated in earlier work, the formalization of the theory of recursive functions of type 0 and 1 and of the theory of realizability.
Download or read book Classical Recursion Theory written by P. Odifreddi and published by Elsevier. This book was released on 1992-02-04 with total page 667 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1988 marked the first centenary of Recursion Theory, since Dedekind's 1888 paper on the nature of number. Now available in paperback, this book is both a comprehensive reference for the subject and a textbook starting from first principles. Among the subjects covered are: various equivalent approaches to effective computability and their relations with computers and programming languages; a discussion of Church's thesis; a modern solution to Post's problem; global properties of Turing degrees; and a complete algebraic characterization of many-one degrees. Included are a number of applications to logic (in particular Gödel's theorems) and to computer science, for which Recursion Theory provides the theoretical foundation.
Download or read book Recursion Theoretic Hierarchies written by Peter G. Hinman and published by Cambridge University Press. This book was released on 2017-03-02 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory set out in this book results from the meeting of descriptive set theory and recursion theory.
Download or read book Automata Languages and Programming written by Peter Widmayer and published by Springer. This book was released on 2003-08-03 with total page 1089 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 29th International Colloquium on Automata, Languages and Programming, ICALP 2002, held in Malaga, Spain, in July 2002.The 83 revised full papers presented together with 7 invited papers were carefully reviewed and selected from a total of 269 submissions. All current aspects of theoretical computer science are addressed and major new results are presented.
Download or read book Logic Colloquium 2000 written by René Cori and published by Cambridge University Press. This book was released on 2017-03-30 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the nineteenth publication in the Lecture Notes in Logic series, collects the proceedings of the European Summer Meeting of the Association for Symbolic Logic, held in Paris, France in July 2000. This meeting marked the centennial anniversary of Hilbert's famous lecture and was held in the same hall at La Sorbonne where Hilbert presented his problems. Three long articles, based on tutorials given at the meeting, present accessible expositions of developing research in model theory, computability, and set theory. The eleven subsequent papers present work from the research frontier in all areas of mathematical logic.
Download or read book Logic Colloquium 03 written by Viggo Stoltenberg-Hansen and published by Cambridge University Press. This book was released on 2017-03-30 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the twenty-fourth publication in the Lecture Notes in Logic series, contains the proceedings of the European Summer Meeting of the Association for Symbolic Logic, held in Helsinki, Finland, in August 2003. These articles include an extended tutorial on generalizing finite model theory, as well as seventeen original research articles spanning all areas of mathematical logic, including proof theory, set theory, model theory, computability theory and philosophy.
Download or read book Higher Order Computability written by John Longley and published by Springer. This book was released on 2015-11-06 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a self-contained exposition of the theory of computability in a higher-order context, where 'computable operations' may themselves be passed as arguments to other computable operations. The subject originated in the 1950s with the work of Kleene, Kreisel and others, and has since expanded in many different directions under the influence of workers from both mathematical logic and computer science. The ideas of higher-order computability have proved valuable both for elucidating the constructive content of logical systems, and for investigating the expressive power of various higher-order programming languages. In contrast to the well-known situation for first-order functions, it turns out that at higher types there are several different notions of computability competing for our attention, and each of these has given rise to its own strand of research. In this book, the authors offer an integrated treatment that draws together many of these strands within a unifying framework, revealing not only the range of possible computability concepts but the relationships between them. The book will serve as an ideal introduction to the field for beginning graduate students, as well as a reference for advanced researchers
Download or read book Handbook of Philosophical Logic written by Dov M. Gabbay and published by Springer Science & Business Media. This book was released on 2001-06-30 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is with great pleasure that we are presenting to the community the second edition of this extraordinary handbook. It has been over 15 years since the publication of the first edition and there have been great changes in the landscape of philosophical logic since then. The first edition has proved invaluable to generations of students and researchers in formal philosophy and language, as well as to consumers of logic in many applied areas. The main logic article in the Encyclopaedia Britannica 1999 has described the first edition as 'the best starting point for exploring any of the topics in logic'. We are confident that the second edition will prove to be just as good. ! The first edition was the second handbook published for the logic commu nity. It followed the North Holland one volume Handbook of Mathematical Logic, published in 1977, edited by the late Jon Barwise, The four volume Handbook of Philosophical Logic, published 1983-1989 came at a fortunate temporal junction at the evolution of logic. This was the time when logic was gaining ground in computer science and artificial intelligence circles. These areas were under increasing commercial pressure to provide devices which help and/or replace the human in his daily activity. This pressure required the use of logic in the modelling of human activity and organisa tion on the one hand and to provide the theoretical basis for the computer program constructs on the other.
Download or read book Logic from Computer Science written by Yiannis N. Moschovakis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume is the outgrowth of a workshop with the same title held at MSRI in the week of November 13-17, 1989, and for those who did not get it, Logic from Computer Science is the converse of Logic in Computer Science, the full name of the highly successful annual LICS conferences. We meant to have a conference which would bring together the LICS commu nity with some of the more traditional "mathematical logicians" and where the emphasis would be on the flow of ideas from computer science to logic rather than the other way around. In a LICS talk, sometimes, the speaker presents a perfectly good theorem about (say) the A-calculus or finite model theory in terms of its potential applications rather than its (often more ob vious) intrinsic, foundational interest and intricate proof. This is not meant to be a criticism; the LICS meetings are, after all, organized by the IEEE Computer Society. We thought, for once, it would be fun to see what we would get if we asked the speakers to emphasize the relevance of their work for logic rather than computer science and to point out what is involved in the proofs. I think, mostly, it worked. In any case, the group of people represented as broad a selection of logicians as I have seen in recent years, and the quality of the talks was (in my view) exceptionally, unusually high. I learned a lot and (I think) others did too.
Download or read book Logic Colloquium 88 written by R. Ferro and published by Elsevier. This book was released on 1989-08-04 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: The result of the European Summer Meeting of the Association for Symbolic Logic, this volume gives an overview of the latest developments in most of the major fields of logic being actively pursued today.As well as selected papers, the two panel discussions are also included, on ``Trends in Logic'' and ``The Teaching of Logic''.
Download or read book Domains and Processes written by Klaus Keimel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Domain theory is a rich interdisciplinary area at the intersection of logic, computer science, and mathematics. This volume contains selected papers presented at the International Symposium on Domain Theory which took place in Shanghai in October 1999. Topics of papers range from the encounters between topology and domain theory, sober spaces, Lawson topology, real number computability and continuous functionals to fuzzy modelling, logic programming, and pi-calculi. This book is a valuable reference for researchers and students interested in this rapidly developing area of theoretical computer science.
Download or read book Recursion Theory written by Anil Nerode and published by American Mathematical Soc.. This book was released on 1985 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book General Recursion Theory written by Jens E. Fenstad and published by Cambridge University Press. This book was released on 2017-03-02 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the tenth publication in the Perspectives in Logic series, Jens E. Fenstad takes an axiomatic approach to present a unified and coherent account of the many and various parts of general recursion theory. The main core of the book gives an account of the general theory of computations. The author then moves on to show how computation theories connect with and unify other parts of general recursion theory. Some mathematical maturity is required of the reader, who is assumed to have some acquaintance with recursion theory. This book is ideal for a second course in the subject.
