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Titlebook: Deduction Systems; Rolf Socher-Ambrosius,Patricia Johann Textbook 1997 Springer-Verlag New York, Inc. 1997 Syntax.automated deduction.calc

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發(fā)表于 2025-3-21 17:11:09 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Deduction Systems
編輯Rolf Socher-Ambrosius,Patricia Johann
視頻videohttp://file.papertrans.cn/265/264511/264511.mp4
叢書名稱Texts in Computer Science
圖書封面Titlebook: Deduction Systems;  Rolf Socher-Ambrosius,Patricia Johann Textbook 1997 Springer-Verlag New York, Inc. 1997 Syntax.automated deduction.calc
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
關(guān)鍵詞Syntax; automated deduction; calculus; complexity; logic; proving; semantics
版次1
doihttps://doi.org/10.1007/978-1-4612-2266-8
isbn_softcover978-1-4612-7479-7
isbn_ebook978-1-4612-2266-8Series ISSN 1868-0941 Series E-ISSN 1868-095X
issn_series 1868-0941
copyrightSpringer-Verlag New York, Inc. 1997
The information of publication is updating

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Astronomie + Physik = AstrophysikIn this section the formal syntax of first-order logic is defined. As for any natural or artificial language, we require on the one hand an alphabet on which the language is based, and on the other a grammar according to which sentences in the language are constructed.
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Syntax of First-order Languages,In this section the formal syntax of first-order logic is defined. As for any natural or artificial language, we require on the one hand an alphabet on which the language is based, and on the other a grammar according to which sentences in the language are constructed.
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Semantics of First-order Languages,Formulae, it must be remembered, are nothing more than words over an alphabet. But logical formulae were originally developed as a means of describing properties of mathematical structures, and so a reasonable semantics of a first-order language would be one which interprets its formulae in a concrete mathematical structure.
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Texts in Computer Sciencehttp://image.papertrans.cn/d/image/264511.jpg
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https://doi.org/10.1007/978-3-662-06529-7as the investigation of the laws of human thought. With a collection of well-chosen axioms of logical deduction as a point of departure, Aristotle erected a theory of reasoning that endured nearly two thousand years before being developed further by such eminent logicians as Gottlob Frege (1848-1925
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Mechanik und Gravitationstheorieamiliar to the reader, and so we do not provide a comprehensive treatment of them. Instead, our intent is to indicate briefly those ideas which will be used in later chapters, and to set the notation and terminology we will use in discussing them. For a more complete treatment of propositional and f
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