Computational logic and set theory
Subtitle: applying formalized logic to analysis
By: Jacob T. Schwartz, Domenico Cantone, Eugenio G. Omodeo
Contributors: Cantone, Domenico; Omodeo, Eugenio
Publisher: Springer
Published: 2011
Place of publication: London; New York
Language: eng
Number of pages: 416
ISBN-13: 9780857298072; 9780857298089
Subjects: Set theory
Other titles: Applying formalized logic to analysis
Description: As computer software becomes more complex, the question of how its correctness can be assured grows ever more critical. Formal logic embodied in computer programs is an important part of the answer to this problem. This must-read text presents the pioneering work of the late Professor Jacob (Jack) T. Schwartz on computational logic and set theory and its application to proof verification techniques, culminating in the ÆtnaNova system, a prototype computer program designed to verify the correctness of mathematical proofs presented in the language of set theory. Taking a systematic approach, the book begins with a survey of traditional branches of logic before describing in detail the underlying design of the ÆtnaNova system. Major classical results on undecidability and unsolvability are then recast for this system. Readers do not require great knowledge of formal logic in order to follow the text, but a good understanding of standard programming techniques, and a familiarity with mathematical definitions and proofs reflecting the usual levels of rigor is assumed.
Notes: Includes bibliographical references and index.
Table of contents: title: Introduction; title: Propositional- and predicate-calculus preliminaries; title: A survey of inference mechanisms; title: More on the structure of the verifier system; title: A closer examination of the sequence of definitions and theorems presented in this book; title: Undecidability and unsolvability; title: A self-contained beginning for Ref's main proof scenario.