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.

Computability Theory, Semantics, and Logic Programming (Oxford Logic Guides)

Computers & Technology

Fitting, Melvin

Software

Oxford University Press

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.

Set Theory and the Continuum Problem (Oxford Logic Guides)

Science & Math

Smullyan, Raymond M.

Mathematics

There are many kinds of books on formal logic. Some have philosophers as their intended audience, some mathematicians, some computer scien tists. Although there is a common core to all such books, they will be very different in emphasis, methods, and even appearance. This book is intended for computer scientists. But even this is not precise. Within computer science formal logic turns up in a number of areas, from pro gram verification to logic programming to artificial intelligence. This book is intended for computer scientists interested in automated theo rem proving in classical logic. To be more precise yet, it is essentially a theoretical treatment, not a how-to book, although how-to issues are not neglected. This does not mean, of course, that the book will be of no interest to philosophers or mathematicians. It does contain a thorough presentation of formal logic and many proof techniques, and as such it contains all the material one would expect to find in a course in formal logic covering completeness but, not incompleteness issues. The first item to be addressed is, What are we talking about and why are we interested in it? We are primarily talking about truth as used in mathematical discourse, and our interest in it is, or should be, self evident. Truth is a semantic concept, so we begin with models and their properties. These are used to define our subject.

First-Order Logic and Automated Theorem Proving (Texts in Computer Science)

Computer Science

Springer

This graduate-level text presents fundamental concepts and results of classical logic in a rigorous mathematical style. Applications to automated theorem proving are considered and usable Prolog programs provided. It will serve both as a first text in formal logic and an introduction to automation issues for students in computer science or mathematics. The book treats propositional logic, first-order logic, and first-order logic with equality. In each case the initial presentation is semantic, to define the intended subjects independently of the choice of proof mechanism. Then many kinds of proof procedure are introduced. Results such as completeness, compactness, and interpolation are established, and theorem provers are implemented in Prolog. This new edition includes material on AE calculus, Herbrand's Theorem, Gentzen's Theorem, and related topics.

First-Order Logic and Automated Theorem Proving (Texts & Monographs in Computer Science)

Springer-Verlag Telos

A lucid, elegant, and complete survey of set theory, this volume is drawn from the authors' substantial teaching experience. The first of three parts focuses on axiomatic set theory. The second part explores the consistency of the continuum hypothesis, and the final section examines forcing and independence results. Part One's focus on axiomatic set theory features nine chapters that examine problems related to size comparisons between infinite sets, basics of class theory, and natural numbers. Additional topics include author Raymond Smullyan's double induction principle, super induction, ordinal numbers, order isomorphism and transfinite recursion, and the axiom of foundation and cardinals. The six chapters of Part Two address Mostowski-Shepherdson mappings, reflection principles, constructible sets and constructibility, and the continuum hypothesis. The text concludes with a seven-chapter exploration of forcing and independence results. This treatment is noteworthy for its clear explanations of highly technical proofs and its discussions of countability, uncountability, and mathematical induction, which are simultaneously charming for experts and understandable to graduate students of mathematics.

Set Theory and the Continuum Problem (Dover Books on Mathematics)

Dover Publications

Everything you'll need to know if you yearn to escape to your own place in the country. Two young city people who bought an old house and acreage- and grow nearly all their own food- share with you what they've learned about every aspect of "homesteading".- Renovating a "handyman's Special" house - replacing siding, taking out the old foundation and putting a new one in. - Chickens - how to buy, house, and feed them - and prepare them for the table.- Gardening - a book in itself: how to grow all kinds of vegetables, spelled out clearly for beginners.- "Putting up" what you've grown- complete directions for making jams and jellies, and canning, freezing, and storing fruits and vegetables.- Winemaking, form simple to fancy- step-by-step details, with essential charts and formulas- Imaginative recipes throught for dishes based on the produce from your land.- All necessary tools, supplies, and equipment described, with resources and approximate costs. With illustrations

In praise of simple things

Fitting, Greer

McKay

Classical logic is concerned, loosely, with the behaviour of truths. Epistemic logic similarly is about the behaviour of known or believed truths. Justification logic is a theory of reasoning that enables the tracking of evidence for statements and therefore provides a logical framework for the reliability of assertions. This book, the first in the area, is a systematic account of the subject, progressing from modal logic through to the establishment of an arithmetic interpretation of intuitionistic logic. The presentation is mathematically rigorous but in a style that will appeal to readers from a wide variety of areas to which the theory applies. These include mathematical logic, artificial intelligence, computer science, philosophical logic and epistemology, linguistics, and game theory.

Justification Logic: Reasoning with Reasons (Cambridge Tracts in Mathematics, Series Number 216)

Artemov, Sergei

Cambridge University Press

This monograph on classical logic presents fundamental concepts and results in a rigorous mathematical style. Applications to automated theorem proving are considered and usable programs in Prolog are provided. This material can be used both as a first text in formal logic and as an introduction to automation issues, and is intended for those interested in computer science and mathematics at the beginning graduate level. The book begins with propositional logic, then treats first-order logic, and finally, first-order logic with equality. In each case the initial presentation is semantic: Boolean valuations for propositional logic, models for first-order logic, and normal models when equality is added. This defines the intended subjects independently of a particular choice of proof mechanism. Then many kinds of proof procedures are introduced: tableau, resolution, natural deduction, Gentzen sequent and axiom systems. Completeness issues are centered in a model existence theorem, which permits the coverage of a variety of proof procedures without repetition of detail. In addition, results such as compactness, interpolation, and the Beth definability theorem are easily established. Implementations of tableau theorem provers are given in Prolog, and resolution is left as a project for the student.

First-Order Logic and Automated Theorem Proving (Monographs in Computer Science)

The various number systems are usually taken for granted by most people, and rightly so. But at least once in the career of every person seriously interested in mathematics, they should be looked at with a critical eye. Why were they created, and why are their properties what they are? Numbers is intended to be a readable but rigorous book that addresses these points. Edmund Landau's 1930 book Grundlagen der Analysis (Foundations of Analysis) is still in print, showing the continuing desire for such a book, but it is extraordinarily terse, and is famous for it. It is a long string of definitions and theorems with no informal material at all. We have tried to find a good mix of informality and formal development. We spend much time on motivation, giving informal reasons why a formal development can proceed as it does. Then and only then do we present the formal material. Thus the reader learns not only the mechanism of the number systems, but also how formal mathematics gets created and thought about at a pre-formal level. The role of set theory and its relationship to the number systems is important, but in a book concentrating on numbers it is rather diversionary. Some set theory is necessary, of course, but the principles needed are simple and straightforward. We assume they are part of the reader's logical machinery and go on from there. A few foundational issues are mentioned, but this is not a book on set theory. Common pencil-and-paper algorithms for arithmetical computation are discussed along the way. They are, after all, among the great human creations and should be seen as such. The system of real numbers is often presented using Dedekind cuts or Cauchy sequences. We have chosen an approach whose intuition is more familiar to most: infinite decimals. We develop them in a simple, yet rigorous, way that builds naturally on what people have already had exposure to. Exercises are included. Some are computational and some are of the supply-a-proof type. If successfully done, the reader will not only have come to know something, but will have come to know that he or she has come to know it.

Numbers

College Publications

See the best price to sell, buy, or rent books by Fitting, Melvin. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Fitting, Melvin

See the best price to sell, buy, or rent books by Fitting, Melvin. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Computability Theory, Semantics, and Logic Programming (Oxford Logic Guides)

Set Theory and the Continuum Problem (Oxford Logic Guides)

First-Order Logic and Automated Theorem Proving (Texts in Computer Science)

First-Order Logic and Automated Theorem Proving (Texts & Monographs in Computer Science)

Set Theory and the Continuum Problem (Dover Books on Mathematics)

In praise of simple things

Justification Logic: Reasoning with Reasons (Cambridge Tracts in Mathematics, Series Number 216)

First-Order Logic and Automated Theorem Proving (Texts in Computer Science)

First-Order Logic and Automated Theorem Proving (Monographs in Computer Science)

Numbers