Computability in Context

Computation and Logic in the Real World

Author: S Barry Cooper,Andrea Sorbi

Publisher: World Scientific

ISBN: 1908978767

Category: Mathematics

Page: 420

View: 4175

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Computability has played a crucial role in mathematics and computer science, leading to the discovery, understanding and classification of decidable/undecidable problems, paving the way for the modern computer era, and affecting deeply our view of the world. Recent new paradigms of computation, based on biological and physical models, address in a radically new way questions of efficiency and challenge assumptions about the so-called Turing barrier. This volume addresses various aspects of the ways computability and theoretical computer science enable scientists and philosophers to deal with mathematical and real-world issues, covering problems related to logic, mathematics, physical processes, real computation and learning theory. At the same time it will focus on different ways in which computability emerges from the real world, and how this affects our way of thinking about everyday computational issues. Contents:Computation, Information, and the Arrow of Time (P Adriaans & P van Emde Boas)The Isomorphism Conjecture for NP (M Agrawal)The Ershov Hierarchy (M M Arslanov)Complexity and Approximation in Reoptimization (G Ausiello et al.)Definability in the Real Universe (S B Cooper)HF-Computability (Y L Drshov et al.)The Mathematics of Computing Between Logic and Physics (G Longo & T Paul)Liquid State Machines: Motivation, Theory, and Applications (W Maass)Experiments on an Internal Approach to Typed Algorithms in Analysis (D Normann)Recursive Functions: An Archeological Look (P Odifreddi)Reverse Mathematics and Well-Ordering Principles (M Rathjen & A Weiermann)Discrete Transfinite Computation Models (P D Welch) Readership: Researchers in computational mathematics, logic, and theoretical computer science. Keywords:Computability;Logic;Real World;Turing Barrier;Real Computation;Learning Theory

Logic Colloquium 2005

Author: Costas Dimitracopoulos

Publisher: Cambridge University Press

ISBN: 052188425X

Category: Computers

Page: 272

View: 9086

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This 2007 volume includes surveys, tutorials, and selected research papers on advances in logic.

Fundamentals of Mathematical Logic

Author: Peter G. Hinman

Publisher: CRC Press

ISBN: 1439864276

Category: Mathematics

Page: 894

View: 5817

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This introductory graduate text covers modern mathematical logic from propositional, first-order and infinitary logic and Gödel's Incompleteness Theorems to extensive introductions to set theory, model theory and recursion (computability) theory. Based on the author's more than 35 years of teaching experience, the book develops students' intuition by presenting complex ideas in the simplest context for which they make sense. The book is appropriate for use as a classroom text, for self-study, and as a reference on the state of modern logic.

Pillars of Computer Science

Essays Dedicated to Boris (Boaz) Trakhtenbrot on the Occasion of His 85th Birthday

Author: Arnon Avron,Nachum Dershowitz,Alexander Rabinovich

Publisher: Springer

ISBN: 3540781277

Category: Computers

Page: 683

View: 3672

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For over half a century, Boris (Boaz) Trakhtenbrot has made seminal contributions to virtually all of the central areas of theoretical computer science. This festschrift volume readily illustrates the profound influence he has had on the field.

Constructibility

Author: Keith J. Devlin

Publisher: Cambridge University Press

ISBN: 110716835X

Category: Computers

Page: 437

View: 5722

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A comprehensive account of the theory of constructible sets at an advanced level, aimed at graduate mathematicians.

Intermediate set theory

Author: Frank Robert Drake,Dasharath Singh

Publisher: John Wiley & Sons Inc

ISBN: 9780471964940

Category: Mathematics

Page: 234

View: 3628

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The authors cover first order logic and the main topics of set theory in a clear mathematical style with sensible philosophical discussion. The emphasis is on presenting the use of set theory in various areas of mathematics, with particular attention paid to introducing axiomatic set theory, showing how the axioms are needed in mathematical practice and how they arise. Other areas introduced include the axiom of choice, filters and ideals. Exercises are provided which are suitable for both beginning students and degree-level students.

The higher infinite

large cardinals in set theory from their beginnings

Author: Akihiro Kanamori

Publisher: Springer

ISBN: N.A

Category: Mathematics

Page: 536

View: 7218

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Truth in perspective

recent issues in logic, representation and ontology

Author: Concha Martínez,Uxía Rivas,Luis Villegas-Forero

Publisher: Avebury

ISBN: 9781859726983

Category: Philosophy

Page: 417

View: 5150

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This volume has its origin in a meeting that was held in Santiago de Compostela University, Santiago de Compostela (Spain) in January 1996. The meeting was organized by the Department of Logic and Philosophy of Science in cooperation with the Association for Logic, Methodology and Philosophy of Science in Spain.Within analytical philosophy issues such as the definability of truth, its semantic relevance, its role in the distinction between formal and natural languages, the status of truth-bearers or in its case of truth-makers, have become a crossroads in the studies of logic, philosophy of science, philosophy of language, philosophy of mind, epistemology and ontology. Thus, in spite of what the title Truth in Perspective may suggest to the reader at first, the present volume is not only - though it is also - a presentation of different theories or conceptions of truth. Most of the book presents a vision of different groups of philosophical questions in which the issue of truth appears embedded together with other related themes, from different points of view.

Admissible Sets and Structures

Author: Jon Barwise

Publisher: Cambridge University Press

ISBN: 1107168333

Category: Mathematics

Page: 408

View: 7083

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This volume makes the basic facts about admissible sets accessible to logic students and specialists alike.