Logic, Computation, Hierarchies

Logic, Computation, Hierarchies PDF

Author: Vasco Brattka

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2014-09-04

Total Pages: 389

ISBN-13: 1614519404

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Published in honor of Victor L. Selivanov, the 17 articles collected in this volume inform on the latest developments in computability theory and its applications in computable analysis; descriptive set theory and topology; and the theory of omega-languages; as well as non-classical logics, such as temporal logic and paraconsistent logic. This volume will be of interest to mathematicians and logicians, as well as theoretical computer scientists.

Recursion-Theoretic Hierarchies

Recursion-Theoretic Hierarchies PDF

Author: Peter G. Hinman

Publisher: Cambridge University Press

Published: 2017-03-02

Total Pages: 494

ISBN-13: 1316739384

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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. The theory set out in this volume, the ninth publication in the Perspectives in Logic series, is the result of the meeting and common development of two currents of mathematical research: descriptive set theory and recursion theory. Both are concerned with notions of definability and with the classification of mathematical objects according to their complexity. These are the common themes which run through the topics discussed here. The author develops a general theory from which the results of both areas can be derived, making these common threads clear.

A Computational Logic

A Computational Logic PDF

Author: Robert S. Boyer

Publisher: Academic Press

Published: 2014-06-25

Total Pages: 414

ISBN-13: 1483277887

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ACM Monograph Series: A Computational Logic focuses on the use of induction in proving theorems, including the use of lemmas and axioms, free variables, equalities, and generalization. The publication first elaborates on a sketch of the theory and two simple examples, a precise definition of the theory, and correctness of a tautology-checker. Topics include mechanical proofs, informal development, formal specification of the problem, well-founded relations, natural numbers, and literal atoms. The book then examines the use of type information to simplify formulas, use of axioms and lemmas as rewrite rules, and the use of definitions. Topics include nonrecursive functions, computing values, free variables in hypothesis, infinite backwards chaining, infinite looping, computing type sets, and type prescriptions. The manuscript takes a look at rewriting terms and simplifying clauses, eliminating destructors and irrelevance, using equalities, and generalization. Concerns include reasons for eliminating isolated hypotheses, precise statement of the generalization heuristic, restricting generalizations, precise use of equalities, and multiple destructors and infinite looping. The publication is a vital source of data for researchers interested in computational logic.

The Cultural Logic of Computation

The Cultural Logic of Computation PDF

Author: David Golumbia

Publisher: Harvard University Press

Published: 2009-04-30

Total Pages: 276

ISBN-13: 9780674032927

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Advocates of computers make sweeping claims for their inherently transformative power: new and different from previous technologies, they are sure to resolve many of our existing social problems, and perhaps even to cause a positive political revolution. In The Cultural Logic of Computation, David Golumbia, who worked as a software designer for more than ten years, confronts this orthodoxy, arguing instead that computers are cultural “all the way down”—that there is no part of the apparent technological transformation that is not shaped by historical and cultural processes, or that escapes existing cultural politics. From the perspective of transnational corporations and governments, computers benefit existing power much more fully than they provide means to distribute or contest it. Despite this, our thinking about computers has developed into a nearly invisible ideology Golumbia dubs “computationalism”—an ideology that informs our thinking not just about computers, but about economic and social trends as sweeping as globalization. Driven by a programmer’s knowledge of computers as well as by a deep engagement with contemporary literary and cultural studies and poststructuralist theory, The Cultural Logic of Computation provides a needed corrective to the uncritical enthusiasm for computers common today in many parts of our culture.

Logic, Language, Information, and Computation

Logic, Language, Information, and Computation PDF

Author: Juliette Kennedy

Publisher: Springer

Published: 2017-07-10

Total Pages: 401

ISBN-13: 3662553864

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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.

Brain Computation as Hierarchical Abstraction

Brain Computation as Hierarchical Abstraction PDF

Author: Dana H. Ballard

Publisher: MIT Press

Published: 2015-02-20

Total Pages: 457

ISBN-13: 0262323826

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An argument that the complexities of brain function can be understood hierarchically, in terms of different levels of abstraction, as silicon computing is. The vast differences between the brain's neural circuitry and a computer's silicon circuitry might suggest that they have nothing in common. In fact, as Dana Ballard argues in this book, computational tools are essential for understanding brain function. Ballard shows that the hierarchical organization of the brain has many parallels with the hierarchical organization of computing; as in silicon computing, the complexities of brain computation can be dramatically simplified when its computation is factored into different levels of abstraction. Drawing on several decades of progress in computational neuroscience, together with recent results in Bayesian and reinforcement learning methodologies, Ballard factors the brain's principal computational issues in terms of their natural place in an overall hierarchy. Each of these factors leads to a fresh perspective. A neural level focuses on the basic forebrain functions and shows how processing demands dictate the extensive use of timing-based circuitry and an overall organization of tabular memories. An embodiment level organization works in reverse, making extensive use of multiplexing and on-demand processing to achieve fast parallel computation. An awareness level focuses on the brain's representations of emotion, attention and consciousness, showing that they can operate with great economy in the context of the neural and embodiment substrates.

Classical and New Paradigms of Computation and their Complexity Hierarchies

Classical and New Paradigms of Computation and their Complexity Hierarchies PDF

Author: Benedikt Löwe

Publisher: Springer Science & Business Media

Published: 2007-11-04

Total Pages: 266

ISBN-13: 1402027761

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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.

Computation Theory and Logic

Computation Theory and Logic PDF

Author: Egon Börger

Publisher: Springer Science & Business Media

Published: 1987-07-29

Total Pages: 456

ISBN-13: 9783540181705

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In Memory of Dieter Rötting. 24.8.1937 - 4.6.1984. On the Occasion of the 50th Anniversary of His Birth

Logical Approaches to Computational Barriers

Logical Approaches to Computational Barriers PDF

Author: Arnold Beckmann

Publisher: Springer Science & Business Media

Published: 2006-06-26

Total Pages: 623

ISBN-13: 3540354662

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This book constitutes the refereed proceedings of the Second International Conference on Computability in Europe, CiE 2006, held in Swansea, UK, June/July 2006. The book presents 31 revised full papers together with 30 invited papers, including papers corresponding to 8 plenary talks and 6 special sessions on proofs and computation, computable analysis, challenges in complexity, foundations of programming, mathematical models of computers and hypercomputers, and Gödel centenary: Gödel's legacy for computability.

Application and Theory of Petri Nets and Concurrency

Application and Theory of Petri Nets and Concurrency PDF

Author: Ryszard Janicki

Publisher: Springer Nature

Published: 2020-06-30

Total Pages: 442

ISBN-13: 3030518310

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This book constitutes the proceedings of the 41st International Conference on Application and Theory of Petri Nets and Concurrency, PETRI NETS 2020, which was supposed to be held in Paris, France, in June 2020. The conference was held virtually due to the COVID-19 pandemic. The 17 regular and 6 tool papers presented together in this volume were carefully reviewed and selected from 56 submissions. The focus of the conference is on following topics: application of concurrency to system design; languages and synthesis; semantics; process mining and applications; extensions and model checking; tools.