Background
Fitting, Melvin Chris was born on January 24, 1942 in Troy, New York, United States. Son of Chris Philip and Helen Gertrude (Van Denburgh) Fitting.
(There are many kinds of books on formal logic. Some have ...)
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.
http://www.amazon.com/gp/product/1461275156/?tag=2022091-20
(There are many kinds of books on formal logic. Some have ...)
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.
http://www.amazon.com/gp/product/0387945938/?tag=2022091-20
("Necessity is the mother of invention. " Part I: What is ...)
"Necessity is the mother of invention. " Part I: What is in this book - details. There are several different types of formal proof procedures that logicians have invented. The ones we consider are: 1) tableau systems, 2) Gentzen sequent calculi, 3) natural deduction systems, and 4) axiom systems. We present proof procedures of each of these types for the most common normal modal logics: S5, S4, B, T, D, K, K4, D4, KB, DB, and also G, the logic that has become important in applications of modal logic to the proof theory of Peano arithmetic. Further, we present a similar variety of proof procedures for an even larger number of regular, non-normal modal logics (many introduced by Lemmon). We also consider some quasi-regular logics, including S2 and S3. Virtually all of these proof procedures are studied in both propositional and first-order versions (generally with and without the Barcan formula). Finally, we present the full variety of proof methods for Intuitionistic logic (and of course Classical logic too). We actually give two quite different kinds of tableau systems for the logics we consider, two kinds of Gentzen sequent calculi, and two kinds of natural deduction systems. Each of the two tableau systems has its own uses; each provides us with different information about the logics involved. They complement each other more than they overlap. Of the two Gentzen systems, one is of the conventional sort, common in the literature.
http://www.amazon.com/gp/product/9027715734/?tag=2022091-20
(Everything you'll need to know if you yearn to escape to ...)
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
http://www.amazon.com/gp/product/0679505113/?tag=2022091-20
(Russell's paradox arises when we consider those sets that...)
Russell's paradox arises when we consider those sets that do not belong to themselves. The collection of such sets cannot constitute a set. Step back a bit. Logical formulas define sets (in a standard model). Formulas, being mathematical objects, can be thought of as sets themselves-mathematics reduces to set theory. Consider those formulas that do not belong to the set they define. The collection of such formulas is not definable by a formula, by the same argument that Russell used. This quickly gives Tarski's result on the undefinability of truth. Variations on the same idea yield the famous results of Gödel, Church, Rosser, and Post. This book gives a full presentation of the basic incompleteness and undecidability theorems of mathematical logic in the framework of set theory. Corresponding results for arithmetic follow easily, and are also given. Gödel numbering is generally avoided, except when an explicit connection is made between set theory and arithmetic. The book assumes little technical background from the reader. One needs mathematical ability, a general familiarity with formal logic, and an understanding of the completeness theorem, though not its proof. All else is developed and formally proved, from Tarski's Theorem to Gödel's Second Incompleteness Theorem. Exercises are scattered throughout.
http://www.amazon.com/gp/product/1904987346/?tag=2022091-20
(This book describes computability theory and provides an ...)
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.
http://www.amazon.com/gp/product/0195036913/?tag=2022091-20
(This monograph on classical logic presents fundamental co...)
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.
http://www.amazon.com/gp/product/1468403591/?tag=2022091-20
Fitting, Melvin Chris was born on January 24, 1942 in Troy, New York, United States. Son of Chris Philip and Helen Gertrude (Van Denburgh) Fitting.
Bachelor of Science, Rensselaer Polytechnic Institute, 1963. Master of Arts, Yeshiva University, 1968. Doctor of Philosophy, Yeshiva University, 1968.
Professor computer science, philosophy, mathematics City University of New York, Bronx, since 1969.
(This book describes computability theory and provides an ...)
(This monograph on classical logic presents fundamental co...)
(Everything you'll need to know if you yearn to escape to ...)
(Russell's paradox arises when we consider those sets that...)
(There are many kinds of books on formal logic. Some have ...)
(There are many kinds of books on formal logic. Some have ...)
("Necessity is the mother of invention. " Part I: What is ...)
(Hardbound.)
Married Greer Aladar Russell, January 17, 1971 (divorced July 1983). Children: Miriam Amy, Rebecca Jo. Married Roma Simon, January 11, 1992.