## Logical Foundations of Proof Complexity

Author: Stephen Cook,Phuong Nguyen

Publisher: Cambridge University Press

ISBN: 1139486306

Category: Mathematics

Page: N.A

View: 8233

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

Author: Pavel Pudlák

Publisher: Springer Science & Business Media

ISBN: 3319001191

Category: Mathematics

Page: 695

View: 712

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

Author: S. Barry Cooper,Mariya I. Soskova

Publisher: Springer

ISBN: 3319436694

Category: Computers

Page: 292

View: 4643

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.

## Principia Mathematica.

Publisher: N.A

ISBN: N.A

Category: Logic, Symbolic and mathematical

Page: 167

View: 579

## Logical Foundations of Computer Science

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

Author: Sergei Artemov,Anil Nerode

Publisher: Springer

ISBN: 3319276832

Category: Mathematics

Page: 407

View: 8241

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.

## Logical Foundations of Database Transformations for Complex-Value Databases

Author: Qing Wang

Publisher: Logos Verlag Berlin GmbH

ISBN: 3832525637

Category: Computers

Page: 252

View: 5061

Database transformations consist of queries and updates which are two fundamental types of computations in any databases - the first provides the capability to retrieve data and the second is used to maintain databases in light of ever-changing application domains. This dissertation aims to lay down the foundations for establishing a theoretical framework of database transformations in the context of complex-value databases. The previous findings reveal that it is very difficult to characterise common features of database queries and updates in a way which is meaningful for further investigations. Nevertheless, the advent of the sequential Abstract State Machine (ASM) thesis capturing sequential algorithms sheds light on the study of database transformations. Observing that the class of computations described by database transformations may be formalised as algorithms respecting database principles, we propose the database ASM thesis for a complete characterisation of database transformations. It turns out that every database transformation characterised by five postulates can be behaviourally simulated by a database Abstract State Machine (DB-ASM) with the same signature and background, and vice versa. Furthermore, a logic for DB-ASMs is defined. In spite of bounded non-determinism permitted by DB-ASMs, the logic is proven to be sound and complete.

## The Design of Everyday Things

Psychologie und Design der alltäglichen Dinge

Author: Norman Don

Publisher: Vahlen

ISBN: 3800648105

Page: 320

View: 6126

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“

## Logical Analysis of Hybrid Systems

Proving Theorems for Complex Dynamics

Author: André Platzer

Publisher: Springer Science & Business Media

ISBN: 9783642145094

Category: Mathematics

Page: 426

View: 4784

Hybrid systems are models for complex physical systems and have become a widely used concept for understanding their behavior. Many applications are safety-critical, including car, railway, and air traffic control, robotics, physical–chemical process control, and biomedical devices. Hybrid systems analysis studies how we can build computerized controllers for physical systems which are guaranteed to meet their design goals. The author gives a unique, logic-based perspective on hybrid systems analysis. It is the first book that leverages the power of logic for hybrid systems. The author develops a coherent logical approach for systematic hybrid systems analysis, covering its theory, practice, and applications. It is further shown how the developed verification techniques can be used to study air traffic and railway control systems. This book is intended for researchers, postgraduates, and professionals who are interested in hybrid systems analysis, cyberphysical or embedded systems design, logic and theorem proving, or transportation and automation.

## Theory and Experiment

Recent Insights and New Perspectives on Their Relation

Author: Diderik Batens,Jean-Paul van Bendegem

Publisher: Springer Science & Business Media

ISBN: 9400928750

Category: Science

Page: 296

View: 8569

This is not "another collection of contributions on a traditional subject." Even more than we dared to expect during the preparatory stages, the papers in this volume prove that our thinking about science has taken a new turn and has reached a new stage. The progressive destruction of the received view has been a fascinating and healthy experience. At present, the period of destruction is over. A richer and more equilibrated analysis of a number of problems is possible and is being cru'ried out. In this sense, this book comes right on time. We owe a lot to the scholars of the Kuhnian period. They not only did away with obstacles, but in several respects instigated a shift in attention that changed history and philosophy of science in a irreversible way. A c1earcut example - we borrow it from the paper by Risto Hilpinen - concerns the study of science as a process, Rnd not only as a result. Moreover, they apparently reached several lasting results, e.g., concerning the tremendous impact of theoretical conceptions on empirical data. Apart from baffling people for several decades, this insight rules out an other return to simple-minded empiricism in the future.

## Logik für Informatiker

Author: Uwe Schöning

ISBN: 9783827410054

Category: Computers

Page: 200

View: 5641

Das Buch macht den Leser mit den wesentlichen Teilgebieten der formalen Logik vertraut, die Bestandteil der Ausbildung in Theoretischer Informatik sind. Die Darstellung orientiert sich an den Bedürfnissen von Informatikstudierenden. Insbesondere werden viele mehr auf das Prinzipielle ausgerichtete Resultate der formalen Logik unter einem algorithmischen Gesichtspunkt behandelt. Diese Vorgehensweise erleichtert entscheidend den Zugang zu dem abstrakten Themengebiet. Prof. Schöning gelingt eine kompakte und verständliche Darstellung der Aussagen- und Prädikatenlogik, bei der die benötigten Begriffe präzise eingeführt und durch Beispiele veranschaulicht werden. Darauf beruhend werden Anwendungen der Logik in der Informatik, wie z. B. Resolution, Automatisches Beweisen und Logik-Programmierung behandelt. Zahlreiche Übungsaufgaben mit ausführlichen Lösungshinweisen erleichtern die Vertiefung des Lernstoffes.

## Mathematical Intuitionism and Intersubjectivity

A Critical Exposition of Arguments for Intuitionism

Author: Tomasz Placek

Publisher: Springer Science & Business Media

ISBN: 9401593159

Category: Science

Page: 220

View: 1811

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.

## Knowledge in Action

Logical Foundations for Specifying and Implementing Dynamical Systems

Author: Raymond Reiter

Publisher: MIT Press

ISBN: 9780262264310

Category: Computers

Page: 448

View: 3572

Specifying and implementing dynamical systems with the situation calculus. Modeling and implementing dynamical systems is a central problem in artificial intelligence, robotics, software agents, simulation, decision and control theory, and many other disciplines. In recent years, a new approach to representing such systems, grounded in mathematical logic, has been developed within the AI knowledge-representation community. This book presents a comprehensive treatment of these ideas, basing its theoretical and implementation foundations on the situation calculus, a dialect of first-order logic. Within this framework, it develops many features of dynamical systems modeling, including time, processes, concurrency, exogenous events, reactivity, sensing and knowledge, probabilistic uncertainty, and decision theory. It also describes and implements a new family of high-level programming languages suitable for writing control programs for dynamical systems. Finally, it includes situation calculus specifications for a wide range of examples drawn from cognitive robotics, planning, simulation, databases, and decision theory, together with all the implementation code for these examples. This code is available on the book's Web site.

## Language in Action

Categories, Lambdas and Dynamic Logic

Author: Johan van Benthem

Publisher: MIT Press

ISBN: 9780262720243

Category: Language Arts & Disciplines

Page: 365

View: 9831

This volume demonstrates the viability of mathematical research into the foundations of categorial grammar, a topic at the border between logic and linguistics. A new introduction to this paperback edition updates the open research problems and records relevant results through pointers to the literature.

## Theories of Interval Arithmetic

Mathematical Foundations and Applications

Author: Hend Dawood

ISBN: 3846501549

Category: Mathematics

Page: 128

View: 8200

Scientists are, all the time, in a struggle with uncertainty which is always a threat to a trustworthy scientific knowledge. A very simple and natural idea, to defeat uncertainty, is that of enclosing uncertain measured values in real closed intervals. On the basis of this idea, interval arithmetic is constructed. The idea of calculating with intervals is not completely new in mathematics: the concept has been known since Archimedes, who used guaranteed lower and upper bounds to compute his constant Pi. Interval arithmetic is now a broad field in which rigorous mathematics is associated with scientific computing. This connection makes it possible to solve uncertainty problems that cannot be efficiently solved by floating-point arithmetic. Today, application areas of interval methods include electrical engineering, control theory, remote sensing, experimental and computational physics, chaotic systems, celestial mechanics, signal processing, computer graphics, robotics, and computer-assisted proofs. The purpose of this book is to be a concise but informative introduction to the theories of interval arithmetic as well as to some of their computational and scientific applications. Editorial Reviews "This new book by Hend Dawood is a fresh introduction to some of the basics of interval computation. It stops short of discussing the more complicated subdivision methods for converging to ranges of values, however it provides a bit of perspective about complex interval arithmetic, constraint intervals, and modal intervals, and it does go into the design of hardware operations for interval arithmetic, which is something still to be done by computer manufacturers." - Ramon E. Moore, (The Founder of Interval Computations) Professor Emeritus of Computer and Information Science, Department of Mathematics, The Ohio State University, Columbus, U.S.A. "A popular math-oriented introduction to interval computations and its applications. This short book contains an explanation of the need for interval computations, a brief history of interval computations, and main interval computation techniques. It also provides an impressive list of main practical applications of interval techniques." - Vladik Kreinovich, (International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems) Professor of Computer Science, University of Texas at El Paso, El Paso, Texas, U.S.A. "I am delighted to see one more Egyptian citizen re-entering the field of interval mathematics invented in this very country thousands years ago." - Marek W. Gutowski, Institute of Physics, Polish Academy of Sciences, Warszawa, Poland

## Die Verdammten dieser Erde

Author: Frantz Fanon,Jean-Paul Sartre

Publisher: N.A

ISBN: 9783518371688

Category: Afrika - Entkolonialisierung

Page: 266

View: 9404

## Computer Science Logic

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

Author: Leszek Pacholski,Jerzy Tiuryn

Publisher: Springer

ISBN: N.A

Category: Computer logic

Page: 541

View: 934

## Foundations of Databases

Author: Serge Abiteboul,Richard Hull,Victor Vianu

ISBN: N.A

Category: Computers

Page: 685

View: 7635

This work presents comprehensive coverage of the foundations and theory of database systems. It is a reference to both classical material and advanced topics, bringing together many subjects including up-to-date coverage of object-oriented and logic databases. Numerous exercises are provided at three levels of difficulty. The book is intended for use by database professionals at all levels of experience, and graduate and senior level students in Advanced Theory of Databases.

## Excursions in the History of Mathematics

Author: Israel Kleiner

Publisher: Springer Science & Business Media

ISBN: 0817682686

Category: Mathematics

Page: 347

View: 1516

This book comprises five parts. The first three contain ten historical essays on important topics: number theory, calculus/analysis, and proof, respectively. Part four deals with several historically oriented courses, and Part five provides biographies of five mathematicians who played major roles in the historical events described in the first four parts of the work. Excursions in the History of Mathematics was written with several goals in mind: to arouse mathematics teachers’ interest in the history of their subject; to encourage mathematics teachers with at least some knowledge of the history of mathematics to offer courses with a strong historical component; and to provide an historical perspective on a number of basic topics taught in mathematics courses.

## Semantic Web: Concepts, Technologies and Applications

Author: Karin Breitman,Marco Antonio Casanova,Walt Truszkowski

Publisher: Springer Science & Business Media

ISBN: 184628581X

Category: Computers

Page: 327

View: 5910

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.