Extensions of First-Order Logic

by Maria Manzano

Overview

Classical logic has proved inadequate in various areas of computer science, artificial intelligence, mathematics, philosopy and linguistics. This is an introduction to extensions of first-order logic, based on the principle that many-sorted logic (MSL) provides a unifying framework in which to place, for example, second-order logic, type theory, modal and dynamic logics and MSL itself. The aim is two fold: only one theorem-prover is needed; proofs of the metaproperties of the different existing calculi can be avoided by borrowing them from MSL. To make the book accessible to readers from different disciplines, whilst maintaining precision, the author has supplied detailed step-by-step proofs, avoiding difficult arguments, and continually motivating the material with examples. Consequently this can be used as a reference, for self-teaching or for first-year graduate courses.

Product Details

ISBN-13:	9780521019026
Publisher:	Cambridge University Press
Publication date:	08/22/2005
Series:	Cambridge Tracts in Theoretical Computer Science , #19
Edition description:	Revised ed.
Pages:	412
Product dimensions:	6.69(w) x 9.61(h) x 0.83(d)

Table of Contents

1. Standard second order logic; 2. Deductive calculi; 3. Categoricity of second order peano arithmetic; 4. Frames and general structures; 5. Type theory; 6. Many-sorted logic; 7. Applying MSL.

Editorial Reviews

A textbook for an introductory graduate or senior course, assuming at least a modest knowledge of first-order logic and set theory. Also suitable for computer scientists, philosophers, and linguists who have or are willing to acquire the prerequisite background. Details many useful logical systems, contending that most can be naturally translated into many-sorted first-order logic. The treatment is unified and intended to be read entirely and in order. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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