翻訳と辞書 Words near each other ・ Automated reasoning ・ Automated refraction system ・ Automated restaurant ・ Automated retail ・ Automated retailing ・ Automated sales suppression device ・ Automated Similarity Judgment Program ・ Automated species identification ・ Automated storage and retrieval system ・ Automated system recovery ・ Automated tank cleaning machine ・ Automated Targeting System ・ Automated telephone survey ・ Automated teller machine ・ Automated Testing Framework ・ Automated theorem proving ・ Automated tiered storage ・ Automated tissue image analysis ・ Automated trading system ・ Automated Transfer Vehicle ・ Automated Tropical Cyclone Forecasting System ・ Automated truck loading systems ・ Automated Trusted Information Exchange ・ Automated vacuum collection ・ Automated valuation model ・ Automated weather map display ・ Automated Weather Source ・ Automated whitelist ・ Automated whole-breast ultrasound ・ Automated X-ray inspection Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Automated theorem proving ： ウィキペディア英語版 Automated theorem proving Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a major impetus for the development of computer science. == Logical foundations == While the roots of formalised logic go back to Aristotle, the end of the 19th and early 20th centuries saw the development of modern logic and formalised mathematics. Frege's ''Begriffsschrift'' (1879) introduced both a complete propositional calculus and what is essentially modern predicate logic. His ''Foundations of Arithmetic'', published 1884, expressed (parts of) mathematics in formal logic. This approach was continued by Russell and Whitehead in their influential ''Principia Mathematica'', first published 1910–1913, and with a revised second edition in 1927. Russell and Whitehead thought they could derive all mathematical truth using axioms and inference rules of formal logic, in principle opening up the process to automatisation. In 1920, Thoralf Skolem simplified a previous result by Leopold Löwenheim, leading to the Löwenheim–Skolem theorem and, in 1930, to the notion of a Herbrand universe and a Herbrand interpretation that allowed (un)satisfiability of first-order formulas (and hence the validity of a theorem) to be reduced to (potentially infinitely many) propositional satisfiability problems. In 1929, Mojżesz Presburger showed that the theory of natural numbers with addition and equality (now called Presburger arithmetic in his honor) is decidable and gave an algorithm that could determine if a given sentence in the language was true or false.〔)〕 However, shortly after this positive result, Kurt Gödel published ''On Formally Undecidable Propositions of Principia Mathematica and Related Systems'' (1931), showing that in any sufficiently strong axiomatic system there are true statements which cannot be proved in the system. This topic was further developed in the 1930s by Alonzo Church and Alan Turing, who on the one hand gave two independent but equivalent definitions of computability, and on the other gave concrete examples for undecidable questions. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Automated theorem proving」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.