**Author**: Melvin Fitting

**Publisher:**Oxford University Press, USA

**ISBN:**N.A

**Category:**Mathematics

**Page:**198

**View:**9266

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# Search Results for: computability-theory-semantics-and-logic-programming-oxford-logic-guides

**Author**: Melvin Fitting

**Publisher:** Oxford University Press, USA

**ISBN:** N.A

**Category:** Mathematics

**Page:** 198

**View:** 9266

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.

**Author**: Dov M. Gabbay,Franz Guenthner

**Publisher:** Springer Science & Business Media

**ISBN:** 9780792370185

**Category:** Philosophy

**Page:** 385

**View:** 8322

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.

**Author**: Anil Nerode,Richard A. Shore

**Publisher:** Springer Science & Business Media

**ISBN:** 1468402110

**Category:** Computers

**Page:** 365

**View:** 8975

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.

**Author**: Bowker Editorial Staff

**Publisher:** N.A

**ISBN:** 9780835225557

**Category:**

**Page:** 4665

**View:** 4154

*Proof Theory, Semantics, and Control*

**Author**: David J. Pym,Eike Ritter

**Publisher:** Oxford University Press on Demand

**ISBN:** 0198526334

**Category:** Mathematics

**Page:** 208

**View:** 3272

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 .

**Author**: S. Barry Cooper,Andrew Hodges

**Publisher:** Cambridge University Press

**ISBN:** 1107010837

**Category:** Computers

**Page:** 395

**View:** 1244

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

**Author**: N.A

**Publisher:** N.A

**ISBN:** N.A

**Category:** American literature

**Page:** N.A

**View:** 4227

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.
*An Index to the Publishers' Trade List Annual*

**Author**: N.A

**Publisher:** N.A

**ISBN:** N.A

**Category:** American literature

**Page:** N.A

**View:** 6923

**Author**: Raymond M. Smullyan

**Publisher:** Oxford University Press

**ISBN:** 9780195344813

**Category:** Mathematics

**Page:** 184

**View:** 9558

This work is a sequel to the author's G?del's Incompleteness Theorems, though it can be read independently by anyone familiar with G?del's incompleteness theorem for Peano arithmetic. The book deals mainly with those aspects of recursion theory that have applications to the metamathematics of incompleteness, undecidability, and related topics. It is both an introduction to the theory and a presentation of new results in the field.
*Interactive Proof with Cambridge LCF*

**Author**: Lawrence C. Paulson

**Publisher:** Cambridge University Press

**ISBN:** 9780521395601

**Category:** Computers

**Page:** 320

**View:** 7346

Logic and Computation is concerned with techniques for formal theorem-proving, with particular reference to Cambridge LCF (Logic for Computable Functions). Cambridge LCF is a computer program for reasoning about computation. It combines methods of mathematical logic with domain theory, the basis of the denotational approach to specifying the meaning of statements in a programming language. This book consists of two parts. Part I outlines the mathematical preliminaries: elementary logic and domain theory. They are explained at an intuitive level, giving references to more advanced reading. Part II provides enough detail to serve as a reference manual for Cambridge LCF. It will also be a useful guide for implementors of other programs based on the LCF approach.
*A Case for Second-Order Logic*

**Author**: Stewart Shapiro

**Publisher:** Clarendon Press

**ISBN:** 9780191524011

**Category:** Mathematics

**Page:** 300

**View:** 1967

The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed development of higher-order logic, including a comprehensive discussion of its semantics. Professor Shapiro demonstrates the prevalence of second-order notions in mathematics is practised, and also the extent to which mathematical concepts can be formulated in second-order languages . He shows how first-order languages are insufficient to codify many concepts in contemporary mathematics, and thus that higher-order logic is needed to fully reflect current mathematics. Throughout, the emphasis is on discussing the philosophical and historical issues associated with this subject, and the implications that they have for foundational studies. For the most part, the author assumes little more than a familiarity with logic as might be gained from a beginning graduate course which includes the incompleteness of arithmetic and the Lowenheim-Skolem theorems. All those concerned with the foundations of mathematics will find this a thought-provoking discussion of some of the central issues in this subject.

**Author**: Raymond M. Smullyan,Melvin Fitting

**Publisher:** Oxford University Press, USA

**ISBN:** N.A

**Category:** Mathematics

**Page:** 288

**View:** 7434

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.
*exploring an untyped universe*

**Author**: T. E. Forster

**Publisher:** Oxford University Press, USA

**ISBN:** N.A

**Category:** Mathematics

**Page:** 152

**View:** 3238

Set theory is concerned with the foundations of mathematics. In the original formulations, there were paradoxes concerning the idea of the "set of all sets." Current standard theory (Zermelo-Fraenkel) avoids these paradoxes by restricting the way sets may be formed by other sets specifically to disallow the possibility of forming the set of all sets. In the 1930s, Quine proposed a different form of set theory in which the set of all sets-- the universal set-- is allowed, but other restrictions are placed on these axioms. Since then, the steady interest expressed in these non-standard set theories has been boosted by their relevance to computer science. This text concentrates heavily on Quine's New Foundations, reflecting the author's belief that it provides the richest and most mysterious of the various systems dealing with set theories with a universal set. The result is a work that provides a useful introduction for those new to this topic, and a valuable reference for those already involved in the area.
*a logical approach*

**Author**: Jonathan Chapman,Frederick Rowbottom

**Publisher:** Oxford University Press, USA

**ISBN:** N.A

**Category:** Mathematics

**Page:** 263

**View:** 2060

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.

**Author**: American Mathematical Society

**Publisher:** N.A

**ISBN:** N.A

**Category:** Mathematics

**Page:** N.A

**View:** 4329

*Papers from 1923 to 1938*

**Author**: Alfred Tarski

**Publisher:** Hackett Publishing

**ISBN:** 9780915144761

**Category:** Philosophy

**Page:** 506

**View:** 2105

**Author**: Richard Kaye

**Publisher:** Oxford University Press, USA

**ISBN:** N.A

**Category:** Literary Criticism

**Page:** 292

**View:** 8553

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.
*A Guide for Computer Scientists*

**Author**: Chris Hankin

**Publisher:** Oxford University Press, USA

**ISBN:** 9780198538417

**Category:** Mathematics

**Page:** 162

**View:** 7101

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.

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