Download or read book Logic Colloquium 02 written by Zoé Chatzidakis and published by Cambridge University Press. This book was released on 2017-03-31 with total page 373 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-seventh publication in the Lecture Notes in Logic series, contains the proceedings of two conferences: the European Summer Meeting of the Association for Symbolic Logic and the Colloquium Logicum, held in Münster, Germany in August, 2002. This compilation of articles from some of the world's preeminent logicians spans all areas of mathematical logic, including philosophical logic and computer science logic. It contains expanded versions of a number of invited plenary talks and tutorials that will be of interest to graduate students and researchers in the field of mathematical logic.
Download or read book Logic Colloquium 02 Lecture Notes in Logic 27 written by Zoe Chatzidakis and published by CRC Press. This book was released on 2006-07-13 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Logic Colloquium '02 includes articles from some of the world's preeminent logicians. The topics span all areas of mathematical logic, but with an emphasis on Computability Theory and Proof Theory. This book will be of interest to graduate students and researchers in the field of mathematical logic.
Download or read book Logic Colloquium 2006 written by S. Barry Cooper and published by Cambridge University Press. This book was released on 2009 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Annual European Meeting of the Association for Symbolic Logic, also known as the Logic Colloquium, is among the most prestigious annual meetings in the field. The current volume, with contributions from plenary speakers and selected special session speakers, contains both expository and research papers by some of the best logicians in the world. The most topical areas of current research are covered: valued fields, Hrushovski constructions (from model theory), algorithmic randomness, relative computability (from computability theory), strong forcing axioms and cardinal arithmetic, large cardinals and determinacy (from set theory), as well as foundational topics such as algebraic set theory, reverse mathematics, and unprovability. This volume will be invaluable for experts as well as those interested in an overview of central contemporary themes in mathematical logic.
Download or read book Around and Beyond the Square of Opposition written by Jean-Yves Béziau and published by Springer Science & Business Media. This book was released on 2012-05-10 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of oppositions based on Aristotelian foundations of logic has been pictured in a striking square diagram which can be understood and applied in many different ways having repercussions in various fields: epistemology, linguistics, mathematics, sociology, physics. The square can also be generalized in other two-dimensional or multi-dimensional objects extending in breadth and depth the original Aristotelian theory. The square of opposition from its origin in antiquity to the present day continues to exert a profound impact on the development of deductive logic. Since 10 years there is a new growing interest for the square due to recent discoveries and challenging interpretations. This book presents a collection of previously unpublished papers by high level specialists on the square from all over the world.
Download or read book Philosophy of Information written by and published by Elsevier. This book was released on 2008-11-10 with total page 823 pages. Available in PDF, EPUB and Kindle. Book excerpt: Information is a recognized fundamental notion across the sciences and humanities, which is crucial to understanding physical computation, communication, and human cognition. The Philosophy of Information brings together the most important perspectives on information. It includes major technical approaches, while also setting out the historical backgrounds of information as well as its contemporary role in many academic fields. Also, special unifying topics are high-lighted that play across many fields, while we also aim at identifying relevant themes for philosophical reflection. There is no established area yet of Philosophy of Information, and this Handbook can help shape one, making sure it is well grounded in scientific expertise. As a side benefit, a book like this can facilitate contacts and collaboration among diverse academic milieus sharing a common interest in information.• First overview of the formal and technical issues involved in the philosophy of information• Integrated presentation of major mathematical approaches to information, form computer science, information theory, and logic• Interdisciplinary themes across the traditional boundaries of natural sciences, social sciences, and humanities.
Download or read book A Hierarchy of Turing Degrees written by Rod Downey and published by Princeton University Press. This book was released on 2020-06-16 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computability theory is a branch of mathematical logic and computer science that has become increasingly relevant in recent years. The field has developed growing connections in diverse areas of mathematics, with applications in topology, group theory, and other subfields. In A Hierarchy of Turing Degrees, Rod Downey and Noam Greenberg introduce a new hierarchy that allows them to classify the combinatorics of constructions from many areas of computability theory, including algorithmic randomness, Turing degrees, effectively closed sets, and effective structure theory. This unifying hierarchy gives rise to new natural definability results for Turing degree classes, demonstrating how dynamic constructions become reflected in definability. Downey and Greenberg present numerous construction techniques involving high-level nonuniform arguments, and their self-contained work is appropriate for graduate students and researchers. Blending traditional and modern research results in computability theory, A Hierarchy of Turing Degrees establishes novel directions in the field.
Download or read book Logic Colloquium 02 Lecture Notes in Logic 27 written by Zoé Chatzidakis and published by A K Peters/CRC Press. This book was released on 2006-07-13 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Logic Colloquium '02 includes articles from some of the world's preeminent logicians. The topics span all areas of mathematical logic, but with an emphasis on Computability Theory and Proof Theory. This book will be of interest to graduate students and researchers in the field of mathematical logic.
Download or read book G del s Disjunction written by Leon Horsten and published by Oxford University Press. This book was released on 2016-09-08 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: The logician Kurt Gödel in 1951 established a disjunctive thesis about the scope and limits of mathematical knowledge: either the mathematical mind is not equivalent to a Turing machine (i.e., a computer), or there are absolutely undecidable mathematical problems. In the second half of the twentieth century, attempts have been made to arrive at a stronger conclusion. In particular, arguments have been produced by the philosopher J.R. Lucas and by the physicist and mathematician Roger Penrose that intend to show that the mathematical mind is more powerful than any computer. These arguments, and counterarguments to them, have not convinced the logical and philosophical community. The reason for this is an insufficiency if rigour in the debate. The contributions in this volume move the debate forward by formulating rigorous frameworks and formally spelling out and evaluating arguments that bear on Gödel's disjunction in these frameworks. The contributions in this volume have been written by world leading experts in the field.
Download or read book Computability and Randomness written by André Nies and published by OUP Oxford. This book was released on 2012-03-29 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interplay between computability and randomness has been an active area of research in recent years, reflected by ample funding in the USA, numerous workshops, and publications on the subject. The complexity and the randomness aspect of a set of natural numbers are closely related. Traditionally, computability theory is concerned with the complexity aspect. However, computability theoretic tools can also be used to introduce mathematical counterparts for the intuitive notion of randomness of a set. Recent research shows that, conversely, concepts and methods originating from randomness enrich computability theory. The book covers topics such as lowness and highness properties, Kolmogorov complexity, betting strategies and higher computability. Both the basics and recent research results are desribed, providing a very readable introduction to the exciting interface of computability and randomness for graduates and researchers in computability theory, theoretical computer science, and measure theory.
Download or read book Reverse Mathematics written by Damir D. Dzhafarov and published by Springer Nature. This book was released on 2022-07-25 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reverse mathematics studies the complexity of proving mathematical theorems and solving mathematical problems. Typical questions include: Can we prove this result without first proving that one? Can a computer solve this problem? A highly active part of mathematical logic and computability theory, the subject offers beautiful results as well as significant foundational insights. This text provides a modern treatment of reverse mathematics that combines computability theoretic reductions and proofs in formal arithmetic to measure the complexity of theorems and problems from all areas of mathematics. It includes detailed introductions to techniques from computable mathematics, Weihrauch style analysis, and other parts of computability that have become integral to research in the field. Topics and features: Provides a complete introduction to reverse mathematics, including necessary background from computability theory, second order arithmetic, forcing, induction, and model construction Offers a comprehensive treatment of the reverse mathematics of combinatorics, including Ramsey's theorem, Hindman's theorem, and many other results Provides central results and methods from the past two decades, appearing in book form for the first time and including preservation techniques and applications of probabilistic arguments Includes a large number of exercises of varying levels of difficulty, supplementing each chapter The text will be accessible to students with a standard first year course in mathematical logic. It will also be a useful reference for researchers in reverse mathematics, computability theory, proof theory, and related areas. Damir D. Dzhafarov is an Associate Professor of Mathematics at the University of Connecticut, CT, USA. Carl Mummert is a Professor of Computer and Information Technology at Marshall University, WV, USA.
Download or read book Large Cardinals Determinacy and Other Topics written by Alexander S. Kechris and published by Cambridge University Press. This book was released on 2020-11-05 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: The final volume in a series of four books presenting the seminal papers from the Caltech-UCLA 'Cabal Seminar'.
Download or read book Logic Colloquium 01 written by Matthias Baaz and published by Cambridge University Press. This book was released on 2017-03-30 with total page 496 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 twentieth publication in the Lecture Notes in Logic series, contains the proceedings of the 2001 European Summer Meeting of the Association for Symbolic Logic, held at the Vienna University of Technology. Two long articles present accessible expositions on resolution theorem proving and the determinacy of long games. The remaining articles cover separate research topics in many areas of mathematical logic, including applications in computer science, proof theory, set theory, model theory, computability theory, linguistics and aspects of philosophy. This collection will interest not only mathematical logicians but also philosophical logicians, historians of logic, computer scientists, formal linguists and mathematicians working in algebra, abstract analysis and topology.
Download or read book Algorithmic Randomness and Complexity written by Rodney G. Downey and published by Springer Science & Business Media. This book was released on 2010-10-29 with total page 883 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computability and complexity theory are two central areas of research in theoretical computer science. This book provides a systematic, technical development of "algorithmic randomness" and complexity for scientists from diverse fields.
Download or read book Computational Prospects of Infinity Presented talks written by Chi-Tat Chong and published by World Scientific. This book was released on 2008 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of written versions of the talks given at the Workshop on Computational Prospects of Infinity, held at the Institute for Mathematical Sciences from 18 June to 15 August 2005. It consists of contributions from many of the leading experts in recursion theory (computability theory) and set theory. Topics covered include the structure theory of various notions of degrees of unsolvability, algorithmic randomness, reverse mathematics, forcing, large cardinals and inner model theory, and many others.
Download or read book Computational Prospects Of Infinity Part Ii Presented Talks written by Chi Tat Chong and published by World Scientific. This book was released on 2008-06-02 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of written versions of the talks given at the Workshop on Computational Prospects of Infinity, held at the Institute for Mathematical Sciences from 18 June to 15 August 2005. It consists of contributions from many of the leading experts in recursion theory (computability theory) and set theory. Topics covered include the structure theory of various notions of degrees of unsolvability, algorithmic randomness, reverse mathematics, forcing, large cardinals and inner model theory, and many others.
Download or read book Logic Language Information and Computation written by Juliette Kennedy and published by Springer. This book was released on 2017-07-10 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: Edited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the 24th Workshop on Logic, Language, Information and Communication, WoLLIC 2017, held in London, UK, in August 2017. The 28 contributed papers were carefully reviewed and selected from 61 submissions. They cover interdisciplinary research in pure and applied logic, aiming at interactions between logic and the sciences related to information and computation.
Download or read book Algorithmic Randomness written by Johanna N. Y. Franklin and published by Cambridge University Press. This book was released on 2020-05-07 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last two decades have seen a wave of exciting new developments in the theory of algorithmic randomness and its applications to other areas of mathematics. This volume surveys much of the recent work that has not been included in published volumes until now. It contains a range of articles on algorithmic randomness and its interactions with closely related topics such as computability theory and computational complexity, as well as wider applications in areas of mathematics including analysis, probability, and ergodic theory. In addition to being an indispensable reference for researchers in algorithmic randomness, the unified view of the theory presented here makes this an excellent entry point for graduate students and other newcomers to the field.
