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Classical and New Paradigms of Computation and their Complexity Hierarchies
The notion of complexity is an important contribution of logic to theoretical computer science and mathematics. This volume attempts to approach complexity in a holistic way, investigating mathematical properties of complexity hierarchies at the same time as discussing algorithms and computational properties. A main focus of the volume is on some of the new paradigms of computation, among them Quantum Computing and Infinitary Computation. The papers in the volume are tied together by an introductory article describing abstract properties of complexity hierarchies. This volume will be of great interest to both mathematical logicians and theoretical computer scientists, providing them with new insights into the various views of complexity and thus shedding new light on their own research.
Foundations of the Formal Sciences II
"Foundations of the Formal Sciences" (FotFS) is a series of interdisciplinary conferences in mathematics, philosophy, computer science and linguistics. The main goal is to reestablish the traditionally strong links between these areas of research that have been lost in the past decades. The second conference in the series had the subtitle "Applications of Mathematical Logic in Philosophy and Linguistics" and brought speakers from all parts of the Formal Sciences together to give a holistic view of how mathematical methods can improve our philosophical and technical understanding of language and scientific discourse, ranging from the theoretical level up to applications in language recognition software. Audience: This volume is of interest to all formal philosophers and theoretical linguists. In addition to that, logicians interested in the applications of their field and logic students in mathematics, computer science, philosophy and linguistics can use the volume to broaden their knowledge of applications of logic.
Interactive Logic
Traditionally, logic has dealt with notions of truth and reasoning. In the past several decades, however, research focus in logic has shifted to the vast field of interactive logic—the domain of logics for both communication and interaction. The main applications of this move are logical approaches to games and social software; the wealth of these applications was the focus of the seventh Augustus de Morgan Workshop in November 2005. This collection of papers from the workshop serves as the initial volume in the new series Texts in Logics and Games—touching on research in logic, mathematics, computer science, and game theory. “A wonderful demonstration of contemporary topics in logic.”—Wiebe van der Hoek, University of Liverpool
New Computational Paradigms
This superb exposition of a complex subject examines new developments in the theory and practice of computation from a mathematical perspective, with topics ranging from classical computability to complexity, from biocomputing to quantum computing. This book is suitable for researchers and graduate students in mathematics, philosophy, and computer science with a special interest in logic and foundational issues. Most useful to graduate students are the survey papers on computable analysis and biological computing. Logicians and theoretical physicists will also benefit from this book.
Games, Scales and Suslin Cardinals
Presents seminal papers from the Caltech-UCLA 'Cabal Seminar', unpublished material, and related new papers.
Large Cardinals, Determinacy and Other Topics: Volume 4
The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Large Cardinals, Determinacy and Other Topics is the final volume in a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes. This final volume contains Parts VII and VIII of the series. Part VII focuses on 'Extensions of AD, models with choice', while Part VIII ('Other topics') collects material important to the Cabal that does not fit neatly into one of its main themes. These four volumes will be a necessary part of the book collection of every set theorist.
Logic and Theory of Algorithms
CiE 2008: Logic and Theory of Algorithms Athens, Greece, June 15–20, 2008 Computability in Europe (CiE) is an informal network of European scientists working on computability theory, including its foundations, technical devel- ment, and applications. Among the aims of the network is to advance our t- oretical understanding of what can and cannot be computed, by any means of computation. Its scienti?c vision is broad: computations may be performed with discrete or continuous data by all kinds of algorithms, programs, and - chines. Computations may be made by experimenting with any sort of physical system obeying the laws of a physical theory such as Newtonian mechanics, quantum theory, or r...
Large Cardinals, Determinacy and Other Topics
The final volume in a series of four books presenting the seminal papers from the Caltech-UCLA 'Cabal Seminar'.
Mathematical Theory and Computational Practice
This book constitutes the proceedings of the 5th Conference on Computability in Europe, CiE 2009, held in Heidelberg, Germany, during July 19-24, 2009. The 34 papers presented together with 17 invited lectures were carefully reviewed and selected from 100 submissions. The aims of the conference is to advance our theoretical understanding of what can and cannot be computed, by any means of computation. It is the largest international meeting focused on computability theoretic issues.
