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Foundations of Logic and Theory of Computation by A. Sernadas (2008, Trade Paperback)

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About this product

Product Identifiers

PublisherCollege Publications

ISBN-101904987885

ISBN-139781904987888

eBay Product ID (ePID)66603320

Product Key Features

Number of Pages352 Pages

Publication NameFoundations of Logic and Theory of Computation

LanguageEnglish

SubjectIntelligence (Ai) & Semantics, Computer Science, Logic

Publication Year2008

TypeTextbook

AuthorA. Sernadas

Subject AreaMathematics, Computers

FormatTrade Paperback

Dimensions

Item Height0.7 in

Item Weight17.5 Oz

Item Length9.2 in

Item Width6.1 in

Additional Product Features

Dewey Edition22

IllustratedYes

Dewey Decimal511.3

SynopsisThe book provides a self-contained introduction to mathematical logic and computability theory for students of mathematics or computer science. It is organized around the failures and successes of Hilbert's programme for the formalization of Mathematics. It is widely known that the programme failed with G del's incompleteness theorems and related negative results about arithmetic. Unfortunately, the positive outcomes of the programme are less well known, even among mathematicians. The book covers key successes, like G del's proof of the completeness of first-order logic, Gentzen's proof of its consistency by purely symbolic means, and the decidability of a couple of useful theories. The book also tries to convey the message that Hilbert's programme made a significant contribution to the advent of the computer as it is nowadays understood and, thus, to the latest industrial revolution. Part I of the book addresses Hilbert's programme and computability. Part II presents first-order logic, including G del's completeness theorem and Gentzen's consistency theorem. Part III is focused on arithmetic, representability of computable maps, G del's incompleteness theorems and decidability of Presburger arithmetic. Part IV provides detailed answers to selected exercises. The book can be used at late undergraduate level or early graduate level. An undergraduate course would concentrate on Parts I and II, leaving out the Gentzen calculus, and sketching the way to the 1st incompleteness theorem. A more advanced course might skip early material already known to the students and concentrate on the positive and negative results of Hilbert's programme, thus covering Gentzen's proof of consistency and Part III in full.