Texts in Computer Science

Deduction Systems

Authors: Socher-Ambrosius, Rolf, Johann, Patricia

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About this Textbook

The idea of mechanizing deductive reasoning can be traced all the way back to Leibniz, who proposed the development of a rational calculus for this purpose. But it was not until the appearance of Frege's 1879 Begriffsschrift-"not only the direct ancestor of contemporary systems of mathematical logic, but also the ancestor of all formal languages, including computer programming languages" ([Dav83])-that the fundamental concepts of modern mathematical logic were developed. Whitehead and Russell showed in their Principia Mathematica that the entirety of classical mathematics can be developed within the framework of a formal calculus, and in 1930, Skolem, Herbrand, and Godel demonstrated that the first-order predicate calculus (which is such a calculus) is complete, i. e. , that every valid formula in the language of the predicate calculus is derivable from its axioms. Skolem, Herbrand, and GOdel further proved that in order to mechanize reasoning within the predicate calculus, it suffices to Herbrand consider only interpretations of formulae over their associated universes. We will see that the upshot of this discovery is that the validity of a formula in the predicate calculus can be deduced from the structure of its constituents, so that a machine might perform the logical inferences required to determine its validity. With the advent of computers in the 1950s there developed an interest in automatic theorem proving.

Table of contents (9 chapters)

  • Introduction

    Socher-Ambrosius, Rolf (et al.)

    Pages 1-7

  • Mathematical Preliminaries

    Socher-Ambrosius, Rolf (et al.)

    Pages 8-23

  • Syntax of First-order Languages

    Socher-Ambrosius, Rolf (et al.)

    Pages 24-35

  • Semantics of First-order Languages

    Socher-Ambrosius, Rolf (et al.)

    Pages 36-45

  • The Gentzen Calculus G

    Socher-Ambrosius, Rolf (et al.)

    Pages 46-64

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-1-4612-2266-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.00
price for USA
  • ISBN 978-1-4612-7479-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Deduction Systems
Authors
Series Title
Texts in Computer Science
Copyright
1997
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York, Inc.
eBook ISBN
978-1-4612-2266-8
DOI
10.1007/978-1-4612-2266-8
Softcover ISBN
978-1-4612-7479-7
Series ISSN
1868-0941
Edition Number
1
Number of Pages
XII, 206
Topics