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Deduction Systems (Texts in Computer Science), by Rolf Socher-Ambrosius, Patricia Johann
Ebook Download Deduction Systems (Texts in Computer Science), by Rolf Socher-Ambrosius, Patricia Johann
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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.
- Brand: Brand: Springer
- Published on: 1997-01-01
- Original language: English
- Number of items: 1
- Dimensions: 9.61" h x .51" w x 6.69" l, .80 pounds
- Binding: Paperback
- 206 pages
- Used Book in Good Condition
Most helpful customer reviews
0 of 0 people found the following review helpful.
How much??
By Game Cat
I have this book. It is a fine introduction to the mathematical foundations of logic calculi (first-order resolution theorem proving) which one may then proceed to implement in machines - or not. In particular, this book does not have any code, but lots of quantifier symbols, definitions and lemma (which suits me as well). Check the table of contents in the amazon preview. It is meant to be used in a 2-semester course and at 207 pages, fits into the "thin" 1cm category.
As it was published in 1997, it is likely that a couple of chapters on advances could be added now.
This being said, I don't see how a price of USD 80 can be justified. What's up, Springer?
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