The proof theory portion presents classical propositional logic and first-order logic using a computer-oriented (resolution) formal system. Linear resolution and its connection to the programming language Prolog are also treated. The computability component offers a machine model and mathematical model for computation, proves the equivalence of the two approaches, and includes famous decision problems unsolvable by an algorithm. The section on nonclassical logic discusses the shortcomings of classical logic in its treatment of implication and an alternate approach that improves upon it: Anderson and Belnap's relevance logic. Applications are included in each section. The material on a four-valued semantics for relevance logic is presented in textbook form for the first time.
Aimed at upper-level undergraduates of moderate analytical background, Three Views of Logic will be useful in a variety of classroom settings.
Boizumault introduces the specific problems posed by the implementation of Prolog, studies and compares different solutions--notably those of the schools of Marseilles and Edinburgh--and concludes with three examples of implementation. Major points of interest include identifying the important differences in implementing unification and resolution; presenting three features of Prolog II--infinite trees, dif, and freeze--that introduce constraints; thoroughly describing Warren's Abstract Machine (WAM); and detailing a Lisp imple-mentation of Prolog.
Originally published in 1993.
The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Thus the book attacks the problem of existence and classification (up to isotopy) of differential structures compatible with a given combinatorial structure on a manifold. The problem is completely "solved" in the sense that it is reduced to standard problems of algebraic topology.
The first part of the book is purely geometrical; it proves that every smoothing of the product of a manifold M and an interval is derived from an essentially unique smoothing of M. In the second part this result is used to translate the classification of smoothings into the problem of putting a linear structure on the tangent microbundle of M. This in turn is converted to the homotopy problem of classifying maps from M into a certain space PL/O. The set of equivalence classes of smoothings on M is given a natural abelian group structure.
This book helps to improve your calculation skill and provide magical techniques that makes easier your mathematical problems and solve in just few moments. The book of Short Tricks of Math covers large number of example with short technique solutions for the purpose of quick practice for basics of Math.
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Logically Fallacious is one of the most comprehensive collections of logical fallacies with all original examples and easy to understand descriptions, perfect for educators, debaters, or anyone who wants to improve his or her reasoning skills.
"Expose an irrational belief, keep a person rational for a day. Expose irrational thinking, keep a person rational for a lifetime." - Bo Bennett
The antidote to fuzzy thinking, with furry animals!
Have you read (or stumbled into) one too many irrational online debates? Ali Almossawi certainly had, so he wrote An Illustrated Book of Bad Arguments! This handy guide is here to bring the internet age a much-needed dose of old-school logic (really old-school, a la Aristotle).
Here are cogent explanations of the straw man fallacy, the slippery slope argument, the ad hominem attack, and other common attempts at reasoning that actually fall short—plus a beautifully drawn menagerie of animals who (adorably) commit every logical faux pas. Rabbit thinks a strange light in the sky must be a UFO because no one can prove otherwise (the appeal to ignorance). And Lion doesn’t believe that gas emissions harm the planet because, if that were true, he wouldn’t like the result (the argument from consequences).
Once you learn to recognize these abuses of reason, they start to crop up everywhere from congressional debate to YouTube comments—which makes this geek-chic book a must for anyone in the habit of holding opinions.