| 书目名称 | Deduction Systems | | 编辑 | Rolf Socher-Ambrosius,Patricia Johann | | 视频video | | | 丛书名称 | Texts in Computer Science | | 图书封面 |  | | 描述 | 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 | | 出版日期 | Textbook 1997 | | 关键词 | Syntax; automated deduction; calculus; complexity; logic; proving; semantics | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4612-2266-8 | | isbn_softcover | 978-1-4612-7479-7 | | isbn_ebook | 978-1-4612-2266-8Series ISSN 1868-0941 Series E-ISSN 1868-095X | | issn_series | 1868-0941 | | copyright | Springer-Verlag New York, Inc. 1997 |
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发表于 2025-3-21 17:11:09
