Product Description
Introductory text in fuzzy logic, for those who have no previous experience with the topic. Aims to demonstrate to the reader how one can apply fuzzy theory to real problems, explaining the basics of the theory itself, and fundamental applications of the theory in modern life. Softcover, hardcover not yet available. ... Read more

Customer Reviews (5)

huge disapointment
I am an engineer and have read a lot of books on science, math and
of course engineering.But I have never read a book this bad in
English. Apparently, translator's mother tongue is not English.
I am inclined to blame the publisher who publishes a book without
checking the credential of the translator. My recommendation is:
do not waist your money on this book.

This book says nothing!
I agree with Mr. Lentini. If you want to learn something about fuzzy logic - look for some other book. This is actually a booklet that only characterizes Fuzzy Logic in a very childish manner. The translator is an utter ignorant: Leibnitz is called "Ripunitz" and Aristole is "Alistoter" or something like that (probably following the Japanese transcription...). Even 1 cent is a waste for it.

Its for beginners, it says so in the title.
While I would agree that the text of the book is a poor translation from the original Japanese (my guess is they waved it in the general direction of an editor while he was distracted) and there is not much in the way of technical depth to the book, it seems to me to very nicely and concisely capture the spirit of the "Fuzzy" movement.

All in all I think its a great introduction if you are wondering what all this fuzzy nonsense is about anyway, but don't plan on reading it twice.

Don't Waste Your Time
I had hoped to get a concise introduction to fuzzy logic from this book. But the author only discusses fuzzy logic at the highest level, not much more deeply than most newspaper and magazine articles. The original text was clearly written in Japanese, and the translation is among the worst I've dealt with in the science and mathematical subjects.

In short, apply the money you would spend for this book to one that is more expensive but actually useful. Just accept that getting to know fuzzy will not be cheap!

Fuzzy Translation for Logic Beginners
I found this text to be a satisfactory introduction to the principles of Fuzzy Logic. I don't think that the book presents the relevant information to developing a fuzzy system, but rather tries to excite the viewer with useless examples of fuzzy systems.

It did answer and explain in detail fuzzy logic and the history behind the controversial mathematical concept. To predict the characteristic of something based on a table of measured values is something whose problem lies in the implementation of such a process. It would take a good amount of testing to find how much torque is needed to counteract the steering in commuter trains. The previous sentence was one of the examples used in the text. ... Read more

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Customer Reviews (1)

Outdated but has value as time capsule
I bought this because it has brief treatments of combinatory logic and the lambda calculus. I was dissapointed, however, because of the rather idiosyncratic notation; I had to go back and start nearly from the beginning to see how he was developing his formal systems. I've had logic, so I felt that it was inconvenient to have to read chapters just to get a handle on his notation and outlook. When I did finally arive at the sections on combinators and lambda, the treatment was too superficial to be a benefit. Should've just bought Hindley.

The problems stated, I found the author's discussion of early research informative and interesting. This book was written before an interpretation was formally defined in Tarski (1956), so the different research directions to escape this problem I thought were neat. There is much discussion about purely syntactical systems vs. systems where semantics are defined. ... Read more

Product Description
In mathematics we are interested in why a particular formula is true. Intuition and statistical evidence are insufficient, so we need to construct a formal logical proof. The purpose of this book is to describe why such proofs are important, what they are made of, how to recognize valid ones, how to distinguish different kinds, and how to construct them. This book is written for 1st year students with no previous experience of formulating proofs. Dave Johnson has drawn from his considerable experience to provide a text that concentrates on the most important elements of the subject using clear, simple explanations that require no background knowledge of logic. It gives many useful examples and problems, many with fully-worked solutions at the end of the book. In addition to a comprehensive index, there is also a useful `Dramatis Personae` an index to the many symbols introduced in the text, most of which will be new to students and which will be used throughout their degree programme. ... Read more

Customer Reviews (1)

The Best Introduction To Logic and Set Theory
This is the clearest and most thorough introduction to the subject matter I've read.The beginner interested in logic, sets, relations, maps and cardinal numbers cannot do better than to read this text.

It also has solutions to most exercises, a very good index and a guide to all of the symbols and notation that appear. ... Read more

Product Description
Designed to make logic interesting and accessible—without sacrificing content or rigor—this classic introduction to contemporary propositional logic explains the symbolization of English sentences and develops formal-proof, truth-table, and truth-tree techniques for evaluating arguments. An accompanying computer tutorial program, PropLogic, is available on CD-ROM in two versions: one version can be installed and run off a hard drive; one (identical) “portable” version can be run off the CD-ROM itself (allowing students/instructors flexibility on when/where they use the program). An appendix in the text describes program details.Tutors readers on formula construction, symbolization, formal proofs, full and brief truth tables, and truth trees. Also provides additional practice exercises. Content organized around natural-deduction formal-proof procedures, truth tables, and truth trees. Gradual presentation of logical statement connectives. Shows students how to symbolize sentences containing the connective and how to use proof rules involving that connective before introducing additional connectives. Examples of actual arguments similar to those readers encounter, and to which they can readily relate. Draws examples and exercises from newspapers, magazines, television, books, textbooks, term papers, posters, comic strips, television programs, films, records, and conversations. Increases students' awareness of the arguments they read and hear every day. Extensive exercise sets throughout provide solutions to about one-quarter of the exercises (in an appendix). Provides ample opportunities for assignments and practice. ... Read more

Customer Reviews (2)

OK for a Logic Book
Up until maybe Chapter 4 or 5 everything's fairly well-explained, but after that, when you get into the longer proofs, it gets a bit muddied and our Prof had to side-step from the book a bit to keep everyone on-track. It has comic cells that help to illustrate the ideas, which was nice.

The most user-friendly book for Propositional Logic
This is a easy to use text for learning the basics of Propositional Logic. The rule set is simple and symmetrical, easy to use. The CD gives important feedback to the student and contains the answers to almost every exercise in the book plus additional practice exercises. I would recommend this textbook to any professor wishing to teach Propositional Logic. ... Read more

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"There is a principle in things, about which we cannot be deceived, but must always, on the contrary, recognize the truth - viz. that the same thing cannot at one and the same time be and not be": with these words of the Metaphysics, Aristotle introduced the Law of Non-Contradiction, which was to become the most authoritative principle in the history of Western thought. However, things have recently changed, and nowadays various philosophers, called dialetheists, claim that this Law does not hold unrestrictedly - that in peculiar circumstances the same thing may at the same time be and not be, and contradictions may obtain in the world.This book opens with an examination of the famous logical paradoxes that appear to speak on behalf of contradictions (e.g., the Liar paradox, the set-theoretic paradoxes such as Cantor's and Russell's), and of the reasons for the failure of the standard attempts to solve them. It provides, then, an introduction to paraconsistent logics - non-classical logics in which the admission of contradictions does not lead to logical chaos -, and their astonishing applications, going from inconsistent data base management to contradictory arithmetics capable of circumventing Gödel's celebrated Incompleteness Theorem. The final part of the book discusses the philosophical motivations and difficulties of dialetheism, and shows how to extract from Aristotle's ancient words a possible reply to the dialetheic challenge.How to Sell a Contradiction will appeal to anyone interested in non-classical logics, analytic metaphysics, and philosophy of mathematics, and especially to those who consider challenging our most entrenched beliefs the main duty of philosophical inquiry. Francesco Berto is Lecturer in Logic and Metaphysics at the University of Venice, Italy. He has published articles in American Philosophical Quarterly, The Australasian Journal of Philosophy, Dialectica, Logique et Analyse, The European Journal of Philosophy, and the books La dialettica della struttura originaria [The Dialectics of the Basic Structure, Padua 2003], Che cos'è la dialettica hegeliana [What is Hegel's Dialectics?, Padua 2005], Teorie dell'assurdo [Theories of the Absurd, Rome 2006] and Logica da zero a Gödel [Logic, from Zero to Gödel, Rome 2007]. ... Read more

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This clearly written book makes logic interesting and easier to learn without sacrificing content or rigor. It covers symbolization, proofs, counterexamples, and truth trees. These topics are presented in graded steps, beginning with the symbolization of categorical propositions and concluding with the properties of relations. Logic is applied to materials with which readers will be familiar; both examples and exercises are drawn from newspapers, television, and other popular sources. For individuals intrigued by the formal study of logic.

Customer Reviews (1)

predicate logic
the book predicate logic was a very useful book, especially at the beginning of the semester when the class became stressful but i was say the book will help you understand everything. ... Read more

Product Description
Proof and Consequence An Introduction to Classical Logic with SIMON and SIMON SAYS By Ray Jennings & Nicole A. Friedrich

Forthcoming April 2006

Proof and Consequence, SIMON, and SIMON SAYS form an integrated logic teaching package, including textbook, student exercise software, and grading program.

Proof and Consequence is a friendly introduction to a difficult but rewarding subject. The text, intended for intermediate-level logic learners, briefly reviews the basics and quickly moves on to propositional and quantificational logic, and the connectives of natural language.

Accompanying the text is the software package, SIMON, which allows students to work on the 800 exercises printed in the text, detecting errors in their work as they go. For extra help, an extensive study guide and additional chatroom software will also be available.

While the text and exercise software are a great aid to students, SIMON SAYS, an innovative remote grading program, is available for instructors. It marks students’ work according to an instructor-created template, keeps all course records, and allows the instructor to create and schedule assignments, as well as to add more exercises if desired. Students are able to register their SIMON documents, submit their assignments, and view their own course records with SIMON SAYS. A complete set of PowerPoint slides is also available for lecture material or as a study resource. ... Read more

Product Description
Modal logics, originally conceived in philosophy, have recently found many applications in computer science, artificial intelligence, the foundations of mathematics, linguistics and other disciplines. Celebrated for their good computational behaviour, modal logics are used as effective formalisms for talking about time, space, knowledge, beliefs, actions, obligations, provability, etc. However, the nice computational properties can drastically change if we combine some of these formalisms into a many-dimensional system, say, to reason about knowledge bases developing in time or moving objects.

To study the computational behaviour of many-dimensional modal logics is the main aim of this book. On the one hand, it is concerned with providing a solid mathematical foundation for this discipline, while on the other hand, it shows that many seemingly different applied many-dimensional systems (e.g., multi-agent systems, description logics with epistemic, temporal and dynamic operators, spatio-temporal logics, etc.) fit in perfectly with this theoretical framework, and so their computational behaviour can be analyzed using the developed machinery.

We start with concrete examples of applied one- and many-dimensional modal logics such as temporal, epistemic, dynamic, description, spatial logics, and various combinations of these. Then we develop a mathematical theory for handling a spectrum of 'abstract' combinations of modal logics - fusions and products of modal logics, fragments of first-order modal and temporal logics - focusing on three major problems: decidability, axiomatizability, and computational complexity. Besides the standard methods of modal logic, the technical toolkit includes the method of quasimodels, mosaics, tilings, reductions to monadic second-order logic, algebraic logic techniques. Finally, we apply the developed machinery and obtained results to three case studies from the field of knowledge representation and reasoning: temporal epistemic logics for reasoning about multi-agent systems, modalized description logics for dynamic ontologies, and spatio-temporal logics.

The genre of the book can be defined as a research monograph. It brings the reader to the front line of current research in the field by showing both recent achievements and directions of future investigations (in particular, multiple open problems). On the other hand, well-known results from modal and first-order logic are formulated without proofs and supplied with references to accessible sources.

The intended audience of this book is logicians as well as those researchers who use logic in computer science and artificial intelligence. More specific application areas are, e.g., knowledge representation and reasoning, in particular, terminological, temporal and spatial reasoning, or reasoning about agents.And we also believe that researchers from certain other disciplines, say, temporal and spatial databases or geographical information systems, will benefit from this book as well.

Key Features:

• Integrated approach to modern modal and temporal logics and their applications in artificial intelligence and computer science

• Written by internationally leading researchers in the field of pure and applied logic

• Combines mathematical theory of modal logic and applications in artificial intelligence and computer science

• Numerous open problems for further research

• Well illustrated with pictures and tables
... Read more

Customer Reviews (2)

Do not buy it here
It's really an good book but too expensive.
You can buy it in www.aslonline.org.
It just be $40 and there is a discount for ASL member.

The best in the area
It's not easy to write a good textbook in Math. Only few people are gifted in that ability. K. Devlin is one of them.
The subject is not easy, but the auther leads you step by step to a full understanding of the constructible universe and the results related to it.
You will find very clear proofs in it, a reasonable ordering of the material, and all the other things that you look for in a good Math book.
Despite the high price, I reccomend buying it. ... Read more

Customer Reviews (1)

Great book, but hard to find
Just FYI for anyone looking for this, it is now available for free online at Project Euclid.You can download each chapter as a PDF.Wish I had noticed that before buying it! ... Read more

Product Description
The aim of this work is to develop the tool of logical deduction schemata and use it to establish upper and lower bounds on the complexity of proofs and their transformations in axiomatized theories. The main results are establishment of upper bounds on the elongation of deductions in cut eliminations; a proof that the length of a direct deduction of an existence theorem in the predicate calculus cannot be bounded above by an elementary function of the length of an indirect deduction of the same theorem; a complexity version of the existence property of the constructive predicate calculus; and, for certain formal systems of arithmetic, restrictions on the complexity of deductions that guarantee that the deducibility of a formula for all natural numbers in some finite set implies the deducibility of the same formula with a universal quantifier over all sufficiently large numbers. ... Read more

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Product Description

University studies in computing require the ability to pass from a concrete problem to an abstract representation, reason with the abstract structure, and return with useful solutions to the specific situation.

The tools for developing these skills are in part qualitative – concepts such as set, relation, function, and structures such as trees and well-founded orders. They are also in part quantitative – notably elementary combinatorics and finite probability. Recurring in all of these are instruments of proof, both purely logical ones (such as proof by contradiction) and mathematical (the various forms of induction).

Features:

• Explains the basic mathematical tools required by students as they set out in their studies of Computer or Information Science

• Explores the interplay between qualitative thinking and calculation

• Teaches the material as a language for thinking, as much as knowledge to be acquired

• Uses an intuitive approach with a focus on examples for all general concepts

• Provides numerous exercises, solutions and proofs to deepen and test the reader’s understanding

• Includes highlight boxes that raise common queries and clear away confusions

• Tandems with additional electronic resources including slides on author's website

http://david.c.makinson.googlepages.com

This easy-to-follow text allows readers to carry out their computing studies with a clear understanding of the basic finite mathematics and logic that they will need. Written explicitly for undergraduates, it requires only a minimal mathematical background and is ideal for self-study as well as classroom use.

Customer Reviews (1)

Great introductory maths textbook for CS students
This is a great maths book for first year Computer Science undergraduates. It assembles in a single text most of the basic mathematical tools required in the study of Computer Science, ranging from sets and relations, to combinatorics and probabilities, to trees and logic.

Most importantly, the book is easy to follow even for someone who is not a great fan of mathematics; in fact, these are the people that will probably benefit most from this book. Concepts are presented very clearly, in a lively prose, with extra care in providing an intuitive grasp of formal notions, and attention in clarifying subtle details. This is further assisted by an on-going dialog spread throughout the book between two fictional characters, Alice and Mad Hatter (borrowed from Lewis Carroll's classical novel), discussing subtleties in the text. Carefully selected exercises in each chapter help to reinforce students understanding of the text.

Overall, a great introductory textbook. I strongly recommend it to anyone starting studies in Computer Science.
... Read more

Product Description
Now in its fourth edition, this book has become a classic because of its accessibility to students without a mathematical background, and because it covers not only the staple topics of an intermediate logic course such as Godel's Incompleteness Theorems, but also a large number of optional topics from Turing's theory of computability to Ramsey's theorem.John Burgess has enhanced the book by adding a selection of problems at the end of each chapter. ... Read more

Customer Reviews (22)

Without doubt the one to go for
This is a classic and an absolute must for anyone required (or wanting) to gain insight into intermediate logic. A more accessible (and yet more comprehensive) introduction is simply not available. The first part introduces basic concepts of computation, the second goes through the standard stock of important first-order result (culminating, of course, in the incompleteness theorems) whereas the third part goes through various further topics, including the Interpolation theorem (obviously), nonstandard models and provability (especially Loeb's theorem).

And the style? The philosophical lexicon contains the following entry: [boo, n. The length of a mathematical or logical proof; hence, booloss, n., the process of shortening such a proof. "Only after significant booloss could the compactness theorem be explained in fifteen minutes."]. That one is pretty apt. With the Berry paradox, Boolos is able to prove the first incompleteness theorem in approximately half a page (a more standard approach is of course included as well). He has elsewhere explained the second incompleteness theorem using only one-syllable words. Point is: these authors (and, one suspects, Boolos in particular) has (had) an almost scary ability to make difficult things simple and easily comprehensible.

That said, I do have a few misgivings. The typos have of course been mentioned (a list of errata is available on http://www.princeton.edu/~jburgess/addenda.htm), but most have been corrected in the second printing (so if you buy the book new, you'll probably get this one) - there are a few left, however. I am also not sure about some of the changes to the fourth edition. In particular, the structure of the proofs of the completeness, compactness and Löwenheim-Skolem theorems is somewhat surprising, proceeding from two lemmas concerning "satisfaction properties" and "closure properties". It is an interesting move, but will (partially because of the presentation, admittedly) surely be somewhat confusing to anyone coming to these for the first time not already being aware of how they fit together.

That said, there is no way I can give this book less than five stars. There is simply no relevant competition comparable in accessibility and comprehensiveness. Urgently recommended.

One step from greatness.
The main virtue of this book, and which sets it apart from most other modern textbooks I have seen, is that it provides clear and usually illuminating explanations of the philosophical importance of the topics covered. These explanations and clarifications are given in a clear and usually crisp prose and emphasise the philosophical importance of whatever metalogical method or result they concern. I regard it as a very suitable companion or reference-work for the philosophically interested student of logic. For rigorous and very detailed proofs and definitions I normally consult a book like Mendelson's Introduction to Mathematical Logic, but usually I read what Boolos, Burgess and Jeffrey say too. The fact that the book (in its fourth edition at least) is divided into many short chapters makes it all the more useful as a companion. The short 'abstracts' that introduce each chapter deserve special mention. An index is the best way of localising information about something one knows one needs. The abstracts often do the reverse; they help one realise what one needs.
As other reviewers have pointed out, the book has WAY TOO MANY typos. Burgess has a list of errata on his web-page, but it is not exhaustive and above all a professionally edited book should not have this many typos. The typos is in my mind the only thing that prevents it from earning five stars.

Math majors avoid
If you are a math major, you don't want this book. Get Cutland.

This book was written by philosophy professors and shows it. When philosophers write math, it is less concise, organized, and complete than when mathematicians do it. This was meant as an intermediate logic text for philosophy and math students, but it would try the patience of a math major. The explanations are wordy, sketchy, and poorly related to each other and to exterior topics.

The contents fall into thirds: Turing machines, aspects of decidability, and a hodge podge of topics from other parts of logic. The 4e is 50 pages (17%) longer than the 3e. The changes were mainly adding exercises and making the chapters more independent. The authors were obviously trying hard to make a readable text, but I hated slogging through all that verbiage. You can see a lot of comment in the other reviews that the 3e was better, but I think even the 3e is poor compared to Cutland.

Absolutely rediculous
WAY TOO MANY TYPOS!!!!!! There were so many typos, it made it extremely difficult to follow this book at times.As a first time student to mathematical logic, I found this to be just too much.People who are veterans with logic and logicians may easily spot typos, but for a first time student of the subject, I was confused as hell at some parts simply because there was a typo.I wasted hours trying to figure out some parts (such as the factorial function in chapter 6) when I finally found out that the reason why I couldn't figure it out was because of a typo. The Errata sheet on the internet IS 35 PAGES LONG!!!! I didn't pay money to correct a horde of typos! God that pisses me off.

Prefer the old edition
I have used the old edition for a class in computability and logic where the students did not have much background in either. Having used the new edition this year, I find I greatly prefer the old one. The new one may be more rigorous, but it is much harder to read and understand for students without the background. The first part is not so bad, but the second half on logic gets too involved in the proofs and the students lose sight of the overall pupose and what these result really mean. ... Read more

Product Description
This book presents an overview of the development of theAxiom of Choice since its introduction by Zermelo at thebeginning of the last century. The book surveys the Axiom ofChoice from three perspectives. The first, or mathematicalperspective, is that of the "working mathematician". Thisperspective brings into view the manifold applications of theAxiom of Choice-usually in the guise of Zorn`s Lemma- in agreat variety of areas of mathematics. The second,foundational, perspective is that of the logician orconstructive mathematician concerned with the foundationalstatus of the Axiom of Choice. The third, topos-theoretical,perspective is that taken by the mathematician or logicianinvestigating the role of the Axiom of Choice in topos theory.Certain topics-for instance mathematical applications of theAxiom, and its relationship with logic-are discussed inconsiderable detail. Others-notably the consistency andindependence of the Axiom of the usual systems of settheory-are given no more than summary treatment, thejustification here being that these topics have been given fullexpositions elsewhere.It is hoped that the book will be of interest to logicians andmathematicians, both professional and prospective. ... Read more