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: 7193

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.

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: 1123

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: 5228

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

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Author: Qing Wang

Publisher: Logos Verlag Berlin GmbH

ISBN: 3832525637

Category: Computers

Page: 252

View: 1860

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.

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: 9699

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: 8721

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/)

Theory and Experiment

Recent Insights and New Perspectives on Their Relation

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Author: Diderik Batens,Jean-Paul van Bendegem

Publisher: Springer Science & Business Media

ISBN: 9400928750

Category: Science

Page: 296

View: 9428

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.

Knowledge in Action

Logical Foundations for Specifying and Implementing Dynamical Systems

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Author: Raymond Reiter

Publisher: MIT Press

ISBN: 9780262264310

Category: Computers

Page: 448

View: 9940

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.

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: 1919

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.

Nots

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Author: Mark C. Taylor

Publisher: University of Chicago Press

ISBN: 9780226791319

Category: Philosophy

Page: 275

View: 1281

Nots is a virtuoso exploration of negation and negativity in theology, philosophy, art, architecture, postmodern culture, and medicine. In nine essays that range from nihility in Buddhism to the embodiment of negativity in disease, Mark C. Taylor looks at the surprising ways in which contrasting concepts of negativity intersect. In the first section of this book, Taylor discusses the question of the "not" in the religious thought of Anselm, Hegel, Derrida, and Nishitani. In the second part, he analyzes artistic efforts "to figure not" in the work of artists Arakawa and Madeline Gins, architect Daniel Libeskind, pop artist David Sallee, and pop icon Madonna. The final section consists of a deeply personal and scientifically informed chapter that discusses the workings of negativity in immunology and illness. Taylor's essays work toward a sense of the not as unnameable as it is irrepressible—an "unthinkable third" that falls between being and nonbeing. Bringing together concerns that span Taylor's early investigations of Hegel and Kierkegaard and recent studies of art and architecture, Nots is an important contribution by one of the most original and distinctive voices now writing on the American scene. Religion and Postmodernism series

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: 2560

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“

Wie man Freunde gewinnt

Die Kunst, beliebt und einflussreich zu werden

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Author: Dale Carnegie

Publisher: S. Fischer Verlag

ISBN: 3104031479

Category: Self-Help

Page: 304

View: 8914

Dieses Buch zeigt Ihnen: - wie man Freunde gewinnt - wie man auf neuen Wegen zu neuen Zielen gelangt - wie man beliebt wird - wie man seine Umwelt beeinflußt - wie man mehr Ansehen erlangt - wie man im Beruf erfolgreicher wird - wie man Streit vermeidet - wie man ein guter Redner und brillanter Gesellschafter wird - wie man den Charakter seiner Mitmenschen erkennt - wie man seine Mitarbeiter anspornt und vieles mehr...

Internal Logic

Foundations of Mathematics from Kronecker to Hilbert

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Author: Y. Gauthier

Publisher: Springer Science & Business Media

ISBN: 9401700834

Category: Mathematics

Page: 251

View: 9133

Internal logic is the logic of content. The content is here arithmetic and the emphasis is on a constructive logic of arithmetic (arithmetical logic). Kronecker's general arithmetic of forms (polynomials) together with Fermat's infinite descent is put to use in an internal consistency proof. The view is developed in the context of a radical arithmetization of mathematics and logic and covers the many-faceted heritage of Kronecker's work, which includes not only Hilbert, but also Frege, Cantor, Dedekind, Husserl and Brouwer. The book will be of primary interest to logicians, philosophers and mathematicians interested in the foundations of mathematics and the philosophical implications of constructivist mathematics. It may also be of interest to historians, since it covers a fifty-year period, from 1880 to 1930, which has been crucial in the foundational debates and their repercussions on the contemporary scene.

Logic and Metaphysics

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Author: N.A

Publisher: Manchester University Press

ISBN: N.A

Category: Logic

Page: 806

View: 3566

Two volumes of philosophy lecture notes, citing classical authors, the Bible, and early modern philosophers such as René Descartes and John Locke, probably copied from a printed source in 1793. The first, completed 19 June 1793, has the caption title Logic Vol. 3d and contains lectures 71-121, and although the contents do refer to logic, they focus more on moral philosophy. The second, begun 19 June 1793, has the running title Metaphysics over its first five lectures and contains lectures 1-56.

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: 1534

Logical Analysis of Hybrid Systems

Proving Theorems for Complex Dynamics

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Author: André Platzer

Publisher: Springer Science & Business Media

ISBN: 9783642145094

Category: Mathematics

Page: 426

View: 6090

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.