Overview
- Authors:
-
-
Rolf Socher-Ambrosius
-
FB Elektrotechnik und Informatik, Fachhochschule Ostfriesland, Emden, Germany
-
Patricia Johann
-
Pacific Software Research Center, Oregon Graduate Institute, Beaverton, USA
Access this book
Other ways to access
Table of contents (9 chapters)
-
-
- Rolf Socher-Ambrosius, Patricia Johann
Pages 1-7
-
- Rolf Socher-Ambrosius, Patricia Johann
Pages 8-23
-
- Rolf Socher-Ambrosius, Patricia Johann
Pages 24-35
-
- Rolf Socher-Ambrosius, Patricia Johann
Pages 36-45
-
- Rolf Socher-Ambrosius, Patricia Johann
Pages 46-64
-
- Rolf Socher-Ambrosius, Patricia Johann
Pages 65-90
-
- Rolf Socher-Ambrosius, Patricia Johann
Pages 91-131
-
- Rolf Socher-Ambrosius, Patricia Johann
Pages 132-164
-
- Rolf Socher-Ambrosius, Patricia Johann
Pages 165-198
-
Back Matter
Pages 199-206
About this book
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.
Authors and Affiliations
-
FB Elektrotechnik und Informatik, Fachhochschule Ostfriesland, Emden, Germany
Rolf Socher-Ambrosius
-
Pacific Software Research Center, Oregon Graduate Institute, Beaverton, USA
Patricia Johann
