Logical Foundations of Proof Complexity

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Author: Stephen Cook,Phuong Nguyen

Publisher: Cambridge University Press

ISBN: 1139486306

Category: Mathematics

Page: N.A

View: 2618

This book treats bounded arithmetic and propositional proof complexity from the point of view of computational complexity. The first seven chapters include the necessary logical background for the material and are suitable for a graduate course. Associated with each of many complexity classes are both a two-sorted predicate calculus theory, with induction restricted to concepts in the class, and a propositional proof system. The complexity classes range from AC0 for the weakest theory up to the polynomial hierarchy. Each bounded theorem in a theory translates into a family of (quantified) propositional tautologies with polynomial size proofs in the corresponding proof system. The theory proves the soundness of the associated proof system. The result is a uniform treatment of many systems in the literature, including Buss's theories for the polynomial hierarchy and many disparate systems for complexity classes such as AC0, AC0(m), TC0, NC1, L, NL, NC, and P.

Logical Foundations of Mathematics and Computational Complexity

A Gentle Introduction

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Author: Pavel Pudlák

Publisher: Springer Science & Business Media

ISBN: 3319001191

Category: Mathematics

Page: 695

View: 4962

The two main themes of this book, logic and complexity, are both essential for understanding the main problems about the foundations of mathematics. Logical Foundations of Mathematics and Computational Complexity covers a broad spectrum of results in logic and set theory that are relevant to the foundations, as well as the results in computational complexity and the interdisciplinary area of proof complexity. The author presents his ideas on how these areas are connected, what are the most fundamental problems and how they should be approached. In particular, he argues that complexity is as important for foundations as are the more traditional concepts of computability and provability. Emphasis is on explaining the essence of concepts and the ideas of proofs, rather than presenting precise formal statements and full proofs. Each section starts with concepts and results easily explained, and gradually proceeds to more difficult ones. The notes after each section present some formal definitions, theorems and proofs. Logical Foundations of Mathematics and Computational Complexity is aimed at graduate students of all fields of mathematics who are interested in logic, complexity and foundations. It will also be of interest for both physicists and philosophers who are curious to learn the basics of logic and complexity theory.

The Incomputable

Journeys Beyond the Turing Barrier

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Author: S. Barry Cooper,Mariya I. Soskova

Publisher: Springer

ISBN: 3319436694

Category: Computers

Page: 292

View: 4915

This book questions the relevance of computation to the physical universe. Our theories deliver computational descriptions, but the gaps and discontinuities in our grasp suggest a need for continued discourse between researchers from different disciplines, and this book is unique in its focus on the mathematical theory of incomputability and its relevance for the real world. The core of the book consists of thirteen chapters in five parts on extended models of computation; the search for natural examples of incomputable objects; mind, matter, and computation; the nature of information, complexity, and randomness; and the mathematics of emergence and morphogenesis. This book will be of interest to researchers in the areas of theoretical computer science, mathematical logic, and philosophy.

Logical Foundations of Computer Science

International Symposium, LFCS 2016, Deerfield Beach, FL, USA, January 4-7, 2016. Proceedings

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Author: Sergei Artemov,Anil Nerode

Publisher: Springer

ISBN: 3319276832

Category: Mathematics

Page: 407

View: 6547

This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2016, held in Deerfield Beach, FL, USA in January 2016. The 27 revised full papers were carefully reviewed and selected from 46 submissions. The scope of the Symposium is broad and includes constructive mathematics and type theory; homotopy type theory; logic, automata, and automatic structures; computability and randomness; logical foundations of programming; logical aspects of computational complexity; parameterized complexity; logic programming and constraints; automated deduction and interactive theorem proving; logical methods in protocol and program verification; logical methods in program specification and extraction; domain theory logics; logical foundations of database theory; equational logic and term rewriting; lambda and combinatory calculi; categorical logic and topological semantics; linear logic; epistemic and temporal logics; intelligent and multiple-agent system logics; logics of proof and justification; non-monotonic reasoning; logic in game theory and social software; logic of hybrid systems; distributed system logics; mathematical fuzzy logic; system design logics; and other logics in computer science.

Johan van Benthem on Logic and Information Dynamics

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Author: Alexandru Baltag,Sonja Smets

Publisher: Springer

ISBN: 3319060252

Category: Philosophy

Page: 1027

View: 6992

This book illustrates the program of Logical-Informational Dynamics. Rational agents exploit the information available in the world in delicate ways, adopt a wide range of epistemic attitudes, and in that process, constantly change the world itself. Logical-Informational Dynamics is about logical systems putting such activities at center stage, focusing on the events by which we acquire information and change attitudes. Its contributions show many current logics of information and change at work, often in multi-agent settings where social behavior is essential, and often stressing Johan van Benthem's pioneering work in establishing this program. However, this is not a Festschrift, but a rich tapestry for a field with a wealth of strands of its own. The reader will see the state of the art in such topics as information update, belief change, preference, learning over time, and strategic interaction in games. Moreover, no tight boundary has been enforced, and some chapters add more general mathematical or philosophical foundations or links to current trends in computer science. The theme of this book lies at the interface of many disciplines. Logic is the main methodology, but the various chapters cross easily between mathematics, computer science, philosophy, linguistics, cognitive and social sciences, while also ranging from pure theory to empirical work. Accordingly, the authors of this book represent a wide variety of original thinkers from different research communities. And their interconnected themes challenge at the same time how we think of logic, philosophy and computation. Thus, very much in line with van Benthem's work over many decades, the volume shows how all these disciplines form a natural unity in the perspective of dynamic logicians (broadly conceived) exploring their new themes today. And at the same time, in doing so, it offers a broader conception of logic with a certain grandeur, moving its horizons beyond the traditional study of consequence relations.

Semantic Web

Grundlagen

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Author: Pascal Hitzler,Markus Krötzsch,Sebastian Rudolph,York Sure

Publisher: Springer-Verlag

ISBN: 3540339949

Category: Computers

Page: 277

View: 7994

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 ..." (http://www.literaturnetz.com/content/view/8742/44/)

The Design of Everyday Things

Psychologie und Design der alltäglichen Dinge

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Author: Norman Don

Publisher: Vahlen

ISBN: 3800648105

Category: Business & Economics

Page: 320

View: 8738

Apple, Audi, Braun oder Samsung machen es vor: Gutes Design ist heute eine kritische Voraussetzung für erfolgreiche Produkte. Dieser Klassiker beschreibt die fundamentalen Prinzipien, um Dinge des täglichen Gebrauchs umzuwandeln in unterhaltsame und zufriedenstellende Produkte. Don Norman fordert ein Zusammenspiel von Mensch und Technologie mit dem Ziel, dass Designer und Produktentwickler die Bedürfnisse, Fähigkeiten und Handlungsweisen der Nutzer in den Vordergrund stellen und Designs an diesen angepasst werden. The Design of Everyday Things ist eine informative und spannende Einführung für Designer, Marketer, Produktentwickler und für alle an gutem Design interessierten Menschen. Zum Autor Don Norman ist emeritierter Professor für Kognitionswissenschaften. Er lehrte an der University of California in San Diego und der Northwest University in Illinois. Mitte der Neunzigerjahre leitete Don Norman die Advanced Technology Group bei Apple. Dort prägte er den Begriff der User Experience, um über die reine Benutzbarkeit hinaus eine ganzheitliche Erfahrung der Anwender im Umgang mit Technik in den Vordergrund zu stellen. Norman ist Mitbegründer der Beratungsfirma Nielsen Norman Group und hat unter anderem Autohersteller von BMW bis Toyota beraten. „Keiner kommt an Don Norman vorbei, wenn es um Fragen zu einem Design geht, das sich am Menschen orientiert.“ Brand Eins 7/2013 „Design ist einer der wichtigsten Wettbewerbsvorteile. Dieses Buch macht Spaß zu lesen und ist von größter Bedeutung.” Tom Peters, Co-Autor von „Auf der Suche nach Spitzenleistungen“

Mathematical Intuitionism and Intersubjectivity

A Critical Exposition of Arguments for Intuitionism

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Author: Tomasz Placek

Publisher: Springer Science & Business Media

ISBN: 9401593159

Category: Science

Page: 220

View: 3032

In 1907 Luitzen Egbertus Jan Brouwer defended his doctoral dissertation on the foundations of mathematics and with this event the modem version of mathematical intuitionism came into being. Brouwer attacked the main currents of the philosophy of mathematics: the formalists and the Platonists. In tum, both these schools began viewing intuitionism as the most harmful party among all known philosophies of mathematics. That was the origin of the now-90-year-old debate over intuitionism. As both sides have appealed in their arguments to philosophical propositions, the discussions have attracted the attention of philosophers as well. One might ask here what role a philosopher can play in controversies over mathematical intuitionism. Can he reasonably enter into disputes among mathematicians? I believe that these disputes call for intervention by a philo sopher. The three best-known arguments for intuitionism, those of Brouwer, Heyting and Dummett, are based on ontological and epistemological claims, or appeal to theses that properly belong to a theory of meaning. Those lines of argument should be investigated in order to find what their assumptions are, whether intuitionistic consequences really follow from those assumptions, and finally, whether the premises are sound and not absurd. The intention of this book is thus to consider seriously the arguments of mathematicians, even if philosophy was not their main field of interest. There is little sense in disputing whether what mathematicians said about the objectivity and reality of mathematical facts belongs to philosophy, or not.

Principia Mathematica.

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Author: Alfred North Whitehead,Bertrand Russell

Publisher: N.A

ISBN: N.A

Category: Logic, Symbolic and mathematical

Page: 167

View: 724

Computer Science Logic

8th Workshop, CSL '94, Kazimierz, Poland, September 25-30, 1994 : Selected Papers

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Author: Leszek Pacholski,Jerzy Tiuryn

Publisher: Springer

ISBN: N.A

Category: Computer logic

Page: 541

View: 4927

Gödel '96

logical foundations of mathematics, computer science, and physics--Kurt Gödel's legacy : Bruno [sic], Czech Republic, August 1996, proceedings

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Author: Petr Hájek

Publisher: Springer Verlag

ISBN: 9783540614340

Category: Computers

Page: 322

View: 3816

This is a proceedings volume of the conference celebrating the 90th anniversary of the birth of Kurt Goedel. The conference has been recognized as an ASL sponsored meeting. Invited papers and contributed papers concern mainly mathematical logic but also philosophy of mathematics, computer science and physics and are devoted to topics related to Goedel's work and reflect the present state of knowledge domains deeply influenced by Goedel.

Semantic Web: Concepts, Technologies and Applications

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Author: Karin Breitman,Marco Antonio Casanova,Walt Truszkowski

Publisher: Springer Science & Business Media

ISBN: 184628581X

Category: Computers

Page: 327

View: 7450

The Web is growing at an astounding pace surpassing the 8 billion page mark. However, most pages are still designed for human consumption and cannot be processed by machines. This book provides a well-paced introduction to the Semantic Web. It covers a wide range of topics, from new trends (ontologies, rules) to existing technologies (Web Services and software agents) to more formal aspects (logic and inference). It includes: real-world (and complete) examples of the application of Semantic Web concepts; how the technology presented and discussed throughout the book can be extended to other application areas.

Think Like a Programmer - Deutsche Ausgabe

Typische Programmieraufgaben kreativ lösen am Beispiel von C++

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Author: V. Anton Spraul

Publisher: MITP-Verlags GmbH & Co. KG

ISBN: 3826692780

Category: Computers

Page: 304

View: 7737

Typische Programmieraufgaben kreativ lösen am Beispiel von C++ Von der Aufgabe zur Lösung – so gehen Sie vor Probleme analysieren und schrittweise bearbeiten Systematisches Vorgehen lernen und anwenden Aus dem Inhalt: Strategien zur Problemlösung Eingabeverarbeitung Statusverfolgung Arrays Zeiger und dynamische Speicherverwaltung Klassen Rekursion Wiederverwendung von Code Rekursive und iterative Programmierung Denken wie ein Programmierer Die Herausforderung beim Programmieren besteht nicht im Erlernen der Syntax einer bestimmten Sprache, sondern in der Fähigkeit, auf kreative Art Probleme zu lösen. In diesem einzigartigen Buch widmet sich der Autor V. Anton Spraul genau jenen Fähigkeiten, die in normalen Lehrbüchern eher nicht behandelt werden: die Fähigkeit, wie ein Programmierer zu denken und Aufgaben zu lösen. In den einzelnen Kapiteln behandelt er jeweils verschiedene Programmierkonzepte wie beispielsweise Klassen, Zeiger und Rekursion, und fordert den Leser mit erweiterbaren Übungen zur praktischen Anwendung des Gelernten auf. Sie lernen unter anderem: Probleme in diskrete Einzelteile zerlegen, die sich leichter lösen lassen Funktionen, Klassen und Bibliotheken möglichst effizient nutzen und wiederholt verwenden die perfekte Datenstruktur für eine Aufgabenstellung auswählen anspruchsvollere Programmiertechniken wie Rekursion und dynamischen Speicher einsetzen Ihre Gendanken ordnen und Strategien entwickeln, um bestimmte Problemkategorien in Angriff zu nehmen Die Beispiele im Buch werden mit C++ gelöst, die dargestellten kreativen Problemlösungskonzepte gehen aber weit über die einzelnen Programmiersprachen und oft sogar über den Bereich der Informatik hinaus. Denn wie die fähigsten Programmierer wissen, handelt es sich beim Schreiben herausragender Quelltexte um kreative Kunst und der erste Schritt auf dem Weg zum eigenen Meisterwerk besteht darin, wie ein Programmierer zu denken. Über den Autor: V. Anton Spraul hat über 15 Jahre lang Vorlesungen über die Grundlagen der Programmierung und Informatik gehalten. In diesem Buch fasst er die von ihm dabei perfektionierten Verfahren zusammen. Er ist auch Autor von »Computer Science Made Simple«.

Proof and System-Reliability

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Author: Helmut Schwichtenberg,Ralf Steinbrüggen

Publisher: Springer Science & Business Media

ISBN: 9781402006081

Category: Computers

Page: 415

View: 8506

Proceedings of the NATO Advanced Study Institute, Marktoberdorf, Germany, from 24 July to 5 August 2001