Computability Theory, Semantics, and Logic Programming

Author: Melvin Fitting

Publisher: Oxford University Press, USA

ISBN: N.A

Category: Mathematics

Page: 198

View: 9178

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This book describes computability theory and provides an extensive treatment of data structures and program correctness. It makes accessible some of the author's work on generalized recursion theory, particularly the material on the logic programming language PROLOG, which is currently of great interest. Fitting considers the relation of PROLOG logic programming to the LISP type of language.

Handbook of Philosophical Logic

Author: Dov M. Gabbay,Franz Guenthner

Publisher: Springer Science & Business Media

ISBN: 9780792370185

Category: Philosophy

Page: 385

View: 9532

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It is with great pleasure that we are presenting to the community the second edition of this extraordinary handbook. It has been over 15 years since the publication of the first edition and there have been great changes in the landscape of philosophical logic since then. The first edition has proved invaluable to generations of students and researchers in formal philosophy and language, as well as to consumers of logic in many applied areas. The main logic article in the Encyclopaedia Britannica 1999 has described the first edition as 'the best starting point for exploring any of the topics in logic'. We are confident that the second edition will prove to be just as good. ! The first edition was the second handbook published for the logic commu nity. It followed the North Holland one volume Handbook of Mathematical Logic, published in 1977, edited by the late Jon Barwise, The four volume Handbook of Philosophical Logic, published 1983-1989 came at a fortunate temporal junction at the evolution of logic. This was the time when logic was gaining ground in computer science and artificial intelligence circles. These areas were under increasing commercial pressure to provide devices which help and/or replace the human in his daily activity. This pressure required the use of logic in the modelling of human activity and organisa tion on the one hand and to provide the theoretical basis for the computer program constructs on the other.

Reductive Logic and Proof-search

Proof Theory, Semantics, and Control

Author: David J. Pym,Eike Ritter

Publisher: Oxford University Press on Demand

ISBN: 0198526334

Category: Mathematics

Page: 208

View: 8243

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This book is a specialized monograph on the development of the mathematical and computational metatheory of reductive logic and proof-search, areas of logic that are becoming important in computer science. A systematic foundational text on these emerging topics, it includes proof-theoretic, semantic/model-theoretic and algorithmic aspects. The scope ranges from the conceptual background to reductive logic, through its mathematical metatheory, to its modern applications in the computational sciences. Suitable for researchers and graduate students in mathematical, computational and philosophical logic, and in theoretical computer science and artificial intelligence, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism (2nd Edition), Dov M. Gabbay, Mark A. Reynolds, and Marcelo Finger's Temporal Logic Mathematical Foundations and Computational Aspects , J. M. Dunn and G. Hardegree's Algebraic Methods in Philosophical Logic, H. Rott's Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning , and P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2 .

Logic for Applications

Author: Anil Nerode,Richard A. Shore

Publisher: Springer Science & Business Media

ISBN: 1468402110

Category: Computers

Page: 365

View: 6997

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In writing this book, our goal was to produce a text suitable for a first course in mathematical logic more attuned than the traditional textbooks to the recent dramatic growth in the applications of logic to computer science. Thus our choice of topics has been heavily influenced by such applications. Of course, we cover the basic traditional topics - syntax, semantics, soundness, completeness and compactness - as well as a few more advanced results such as the theorems of Skolem-Lowenheim and Herbrand. Much of our book, however, deals with other less traditional topics. Resolution theorem proving plays a major role in our treatment of logic, especially in its application to Logic Programming and PROLOG. We deal extensively with the mathematical foundations of all three of these subjects. In addition, we include two chapters on nonclassical logic- modal and intuitionistic - that are becoming increasingly important in computer science. We develop the basic material on the syntax and se mantics (via Kripke frames) for each of these logics. In both cases, our approach to formal proofs, soundness and completeness uses modifications of the same tableau method introduced for classical logic. We indicate how it can easily be adapted to various other special types of modal log ics. A number of more advanced topics (including nonmonotonic logic) are also briefly introduced both in the nonclassical logic chapters and in the material on Logic Programming and PROLOG.

The Once and Future Turing

Author: S. Barry Cooper,Andrew Hodges

Publisher: Cambridge University Press

ISBN: 1107010837

Category: Computers

Page: 395

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Original essays by world-leading researchers reveal Alan Turing's lasting contributions to modern research.

Books in Print

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 8753

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Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.

Set theory and the continuum problem

Author: Raymond M. Smullyan,Melvin Fitting

Publisher: Oxford University Press, USA

ISBN: N.A

Category: Mathematics

Page: 288

View: 8000

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Set Theory and the Continuum Problem is a novel introduction to set theory, including axiomatic development, consistency, and independence results. It is self-contained and covers all the set theory that a mathematician should know. Part I introduces set theory, including basic axioms, development of the natural number system, Zorn's Lemma and other maximal principles. Part II proves the consistency of the continuum hypothesis and the axiom of choice, with material on collapsing mappings, model-theoretic results, and constructible sets. Part III presents a version of Cohen's proofs of the independence of the continuum hypothesis and the axiom of choice. It also presents, for the first time in a textbook, the double induction and superinduction principles, and Cowen's theorem. The book will interest students and researchers in logic and set theory.

Models of Peano arithmetic

Author: Richard Kaye

Publisher: Oxford University Press, USA

ISBN: N.A

Category: Literary Criticism

Page: 292

View: 5116

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Non-standard models of arithmetic are of interest to mathematicians through the presence of infinite integers and the various properties they inherit from the finite integers. Since their introduction in the 1930s, they have come to play an important role in model theory, and in combinatorics through independence results such as the Paris-Harrington theorem. This book is an introduction to these developments, and stresses the interplay between the first-order theory, recursion-theoretic aspects, and the structural properties of these models. Prerequisites for an understanding of the text have been kept to a minimum, these being a basic grounding in elementary model theory and a familiarity with the notions of recursive, primitive recursive, and r.e. sets. Consequently, the book is suitable for postgraduate students coming to the subject for the first time, and a number of exercises of varying degrees of difficulty will help to further the reader's understanding.

Relative category theory and geometric morphisms

a logical approach

Author: Jonathan Chapman,Frederick Rowbottom

Publisher: Oxford University Press, USA

ISBN: N.A

Category: Mathematics

Page: 263

View: 2740

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Topos theory provides an important setting and language for much of mathematical logic and set theory. It is well known that a typed language can be given for a topos to be regarded as a category of sets. This enables a fruitful interplay between category theory and set theory. However, one stumbling block to a logical approach to topos theory has been the treatment of geometric morphisms. This book presents a convenient and natural solution to this problem by developing the notion of a frame relative to an elementary topos. The authors show how this technique enables a logical approach to be taken to topics such as category theory relative to a topos and the relative Giraud theorem. The work is self-contained except that the authors presuppose a familiarity with basic category theory and topos theory. Logicians, set and category theorists, and computer scientist working in the field will find this work essential reading.

Lambda Calculi

A Guide for Computer Scientists

Author: Chris Hankin

Publisher: Oxford University Press, USA

ISBN: 9780198538417

Category: Mathematics

Page: 162

View: 2935

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The [lambda]-calculus lies at the very foundations of computer science. Besides its historical role in computability theory it has had significant influence on programming language design and implementation, denotational semantics, and domain theory. The book emphasizes the proof theory for the type-free [lambda]-calculus. The first six chapters concern this calculus and cover the basic theory, reduction, models, computability, and the relationship between the [lambda]-calculus and combinatory logic. Chapter 7 presents a variety of typed calculi; first the simply typed [lambda]-calculus, then Milner-style polymorphism and, finally, the polymorphic [lambda]-calculus. Chapter 8 concerns three variants of the type-free [lambda]-calculus that have recently appeared in the research literature: the lazy [lambda]-calculus, the concurrent [gamma]-calculus and the [lambda][sigma]-calculus. The final chapter contains references and a guide to further reading. There are exercises throughout.

Semantic Web

Grundlagen

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

Publisher: Springer-Verlag

ISBN: 3540339949

Category: Computers

Page: 277

View: 3261

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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/)

Endliche Gruppen

Eine Einführung in die Theorie der endlichen Gruppen

Author: H. Kurzweil

Publisher: Springer-Verlag

ISBN: 3642953131

Category: Mathematics

Page: 190

View: 1160

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