Computability Theory

Author: S. Barry Cooper
Publisher: CRC Press
ISBN: 9781351991964
Release Date: 2017-09-06
Genre: Mathematics

Computability theory originated with the seminal work of Gödel, Church, Turing, Kleene and Post in the 1930s. This theory includes a wide spectrum of topics, such as the theory of reducibilities and their degree structures, computably enumerable sets and their automorphisms, and subrecursive hierarchy classifications. Recent work in computability theory has focused on Turing definability and promises to have far-reaching mathematical, scientific, and philosophical consequences. Written by a leading researcher, Computability Theory provides a concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results. The basic concepts and techniques of computability theory are placed in their historical, philosophical and logical context. This presentation is characterized by an unusual breadth of coverage and the inclusion of advanced topics not to be found elsewhere in the literature at this level. The book includes both the standard material for a first course in computability and more advanced looks at degree structures, forcing, priority methods, and determinacy. The final chapter explores a variety of computability applications to mathematics and science. Computability Theory is an invaluable text, reference, and guide to the direction of current research in the field. Nowhere else will you find the techniques and results of this beautiful and basic subject brought alive in such an approachable and lively way.

Quantifiers and Cognition Logical and Computational Perspectives

Author: Jakub Szymanik
Publisher: Springer
ISBN: 9783319287492
Release Date: 2016-02-19
Genre: Language Arts & Disciplines

This volume on the semantic complexity of natural language explores the question why some sentences are more difficult than others. While doing so, it lays the groundwork for extending semantic theory with computational and cognitive aspects by combining linguistics and logic with computations and cognition. Quantifier expressions occur whenever we describe the world and communicate about it. Generalized quantifier theory is therefore one of the basic tools of linguistics today, studying the possible meanings and the inferential power of quantifier expressions by logical means. The classic version was developed in the 1980s, at the interface of linguistics, mathematics and philosophy. Before this volume, advances in "classic" generalized quantifier theory mainly focused on logical questions and their applications to linguistics, this volume adds a computational component, the third pillar of language use and logical activity. This book is essential reading for researchers in linguistics, philosophy, cognitive science, logic, AI, and computer science.

Theory and Applications of Models of Computation

Author: Manindra Agrawal
Publisher: Springer Science & Business Media
ISBN: 9783540792277
Release Date: 2008-04-08
Genre: Computers

This book constitutes the refereed proceedings of the 5th International Conference on Theory and Applications of Models of Computation, TAMC 2008, held in Xi'an, China in April 2008. The 48 revised full papers presented together with 2 invited talks and 1 plenary lecture were carefully reviewed and selected from 192 submissions. The papers address current issues of all major areas in computer science, mathematics (especially logic) and the physical sciences - computation, algorithms, complexity and computability theory in particular. With this crossdisciplinary character the conference is given a special flavor and distinction.

Cylindric like Algebras and Algebraic Logic

Author: Hajnal Andréka
Publisher: Springer Science & Business Media
ISBN: 9783642350252
Release Date: 2014-01-27
Genre: Mathematics

Algebraic logic is a subject in the interface between logic, algebra and geometry, it has strong connections with category theory and combinatorics. Tarski’s quest for finding structure in logic leads to cylindric-like algebras as studied in this book, they are among the main players in Tarskian algebraic logic. Cylindric algebra theory can be viewed in many ways: as an algebraic form of definability theory, as a study of higher-dimensional relations, as an enrichment of Boolean Algebra theory, or, as logic in geometric form (“cylindric” in the name refers to geometric aspects). Cylindric-like algebras have a wide range of applications, in, e.g., natural language theory, data-base theory, stochastics, and even in relativity theory. The present volume, consisting of 18 survey papers, intends to give an overview of the main achievements and new research directions in the past 30 years, since the publication of the Henkin-Monk-Tarski monographs. It is dedicated to the memory of Leon Henkin.​

Computability Theory Second Edition

Author: S. Barry Cooper
Publisher: Chapman and Hall/CRC
ISBN: 1439838437
Release Date: 2015-12-15
Genre: Mathematics

Designed for advanced undergraduate or beginning graduate students, this book provides a complete introduction to computability theory. This second edition includes new material on hyperarithmetical and Borel sets as well as more material on computability of structures, Pi-0-1 classes, and computability in science. It features an expanded treatment of complexity of computations and updated future directions in computability. In addition, the section on randomness is now a separate chapter. The author also discusses advanced topics in greater depth, including Post’s problem, forcing and category, applications of determinacy, and the computability of theories.

Der Turing Omnibus

Author: A.K. Dewdney
Publisher: Springer-Verlag
ISBN: 9783642788727
Release Date: 2013-03-12
Genre: Computers

Der Turing Omnibus macht in 66 exzellent geschriebenen Beiträgen Station bei den interessantesten Themen aus der Informatik, der Computertechnologie und ihren Anwendungen.

Fundamentals of Mathematical Logic

Author: Peter G. Hinman
Publisher: A K Peters/CRC Press
ISBN: 1568812620
Release Date: 2005-09-09
Genre: Mathematics

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.

Issues In Heterodox Economics

Author: Donald A. R. George
Publisher: Wiley-Blackwell
ISBN: 1405179619
Release Date: 2008-02-11
Genre: Business & Economics

Through contributions from leading authors, Issues in Heterodox Economics provides a critical analysis of the methodology of mainstream economics. Challenges economists to abandon sterile formalism and develop new intellectual rigors to contribute to pressing contemporary issues A series of cutting-edge articles provides a critical analysis of the dependence of mainstream economics on mathematical modelling and other methodologies Topics discussed include sustainable development, worker control of firms, evolutionary growth theory, and more Challenges economists to abandon sterile formalism and develop new intellectual rigors to contribute to pressing contemporary issues

Invariant Descriptive Set Theory

Author: Su Gao
Publisher: CRC Press
ISBN: 158488794X
Release Date: 2008-09-03
Genre: Mathematics

Presents Results from a Very Active Area of Research Exploring an active area of mathematics that studies the complexity of equivalence relations and classification problems, Invariant Descriptive Set Theory presents an introduction to the basic concepts, methods, and results of this theory. It brings together techniques from various areas of mathematics, such as algebra, topology, and logic, which have diverse applications to other fields. After reviewing classical and effective descriptive set theory, the text studies Polish groups and their actions. It then covers Borel reducibility results on Borel, orbit, and general definable equivalence relations. The author also provides proofs for numerous fundamental results, such as the Glimm–Effros dichotomy, the Burgess trichotomy theorem, and the Hjorth turbulence theorem. The next part describes connections with the countable model theory of infinitary logic, along with Scott analysis and the isomorphism relation on natural classes of countable models, such as graphs, trees, and groups. The book concludes with applications to classification problems and many benchmark equivalence relations. By illustrating the relevance of invariant descriptive set theory to other fields of mathematics, this self-contained book encourages readers to further explore this very active area of research.

Algorithms and Theory of Computation Handbook

Author: Mikhail J. Atallah
Publisher: CRC Press
ISBN: 142004950X
Release Date: 1998-11-23
Genre: Computers

Algorithms and Theory of Computation Handbook is a comprehensive collection of algorithms and data structures that also covers many theoretical issues. It offers a balanced perspective that reflects the needs of practitioners, including emphasis on applications within discussions on theoretical issues. Chapters include information on finite precision issues as well as discussion of specific algorithms where algorithmic techniques are of special importance, including graph drawing, robotics, forming a VLSI chip, vision and image processing, data compression, and cryptography. The book also presents some advanced topics in combinatorial optimization and parallel/distributed computing. • applications areas where algorithms and data structuring techniques are of special importance • graph drawing • robot algorithms • VLSI layout • vision and image processing algorithms • scheduling • electronic cash • data compression • dynamic graph algorithms • on-line algorithms • multidimensional data structures • cryptography • advanced topics in combinatorial optimization and parallel/distributed computing

Semantic Web

Author: Pascal Hitzler
Publisher: Springer-Verlag
ISBN: 9783540339946
Release Date: 2007-10-24
Genre: Computers

Das Buch Semantic Web – Grundlagen vermittelt als erstes deutschsprachiges Lehrbuch die Grundlagen des Semantic Web in verständlicher Weise. Es ermöglicht einen einfachen und zügigen Einstieg in Methoden und Technologien des Semantic Web und kann z.B. als solide Grundlage für die Vorbereitung und Durchführung von Vorlesungen genutzt werden. Die Autoren trennen dabei sauber zwischen einer intuitiven Hinführung zur Verwendung semantischer Technologien in der Praxis einerseits, und der Erklärung formaler und theoretischer Hintergründe andererseits. Nur für letzteres werden Grundkenntnisse in Logik vorausgesetzt, die sich bei Bedarf jedoch durch zusätzliche Lektüre und mit Hilfe eines entsprechenden Kapitels im Anhang aneignen lassen. Das Lehrbuch richtet sich primär an Studenten mit Grundkenntnissen in Informatik sowie an interessierte Praktiker welche sich im Bereich Semantic Web fortbilden möchten. Aus den Rezensionen: "... RDF, RDF-S und OWL. Diese Sprachen ... werden von den Autoren dargestellt. Bei der Darstellung ... fallen sie selten zu schwierigen Fachslang, sondern liefern eine gut nachvollziehbare Schilderung mit einfachen Beispielen, auch Übungsaufgaben runden die Kapitel ab. ... Semantic Web ist ein einfach geschriebenes und anschauliches Buch, das In die Grundkonzepte der Semantic-Web-Techniken einführt. Wer sich schnell in RDF, RDF-S und Co. einarbeiten muss und etwas Vorbildung in Logik und Algebra mitbringt, der trifft mit diesem Lehrbuch sicherlich eine gute Wahl ..." (