English

1989

ISBN: 0716782014

PDF

pages: 289

Having used this book to teach courses in elementary model theory, I can attest to its utility. It serves this purpose well, and the book is short enough to allow covering most of the material in the span of a semester. After finishing it, readers will be well prepared to tackle more advanced books in mathematical logic and model theory, or move into areas of artificial intelligence or logic programming. The most popular languages in artificial intelligence, namely LISP and PROLOG are based on the concepts in this book. Some of the areas that are not treated but can be accessed after reading the book include nonmonotonic logics, inductive logic programming, formal learning theory, higher-order languages, automated deduction, and the theory of object-oriented languages.

The author discusses four languages in the book, namely propositional logic, predicate calculus, elementary number theory, and lambda calculus. The author's strategy in discussing each of these languages is to first discuss the syntax, and then move on to treat the truth, deduction, and computational aspects of them. As expected, propositional logic is the "cleanest" of the four languages, for its model theory is constructed via the use of truth tables. The computation, ground resolution is used, which gives a decision procedure for the language. The author shows that truth tables can be generated effectivey for a given well-formed formula, and thus the truth of the language is established. Completeness then implies the language is provable. Thus for propositional logic, the notions of truth, deduction, and computation are equivalent.

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