翻訳と辞書 Words near each other ・ Boole (tree) ・ Boole polynomials ・ Boole's expansion theorem ・ Boole's inequality ・ Boole's rule ・ Boole's syllogistic ・ Boolean ・ Boolean algebra ・ Boolean algebra (structure) ・ Boolean algebras canonically defined ・ Boolean analysis ・ Boolean circuit ・ Boolean conjunctive query ・ Boolean data type ・ Boolean delay equation ・ Boolean domain ・ Boolean expression ・ Boolean function ・ Boolean grammar ・ Boolean hierarchy ・ Boolean model (probability theory) ・ Boolean network ・ Boolean operation ・ Boolean operations on polygons ・ Boolean prime ideal theorem ・ Boolean ring ・ Boolean satisfiability problem ・ Boolean-valued ・ Boolean-valued function ・ Boolean-valued model 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 Boolean domain ： ウィキペディア英語版 Boolean domain In mathematics and abstract algebra, a Boolean domain is a set consisting of exactly two elements whose interpretations include ''false'' and ''true''. In logic, mathematics and theoretical computer science, a Boolean domain is usually written as ,〔Dirk van Dalen, ''Logic and Structure''. Springer (2004), page 15.〕〔David Makinson, ''Sets, Logic and Maths for Computing''. Springer (2008), page 13.〕〔George S. Boolos and Richard C. Jeffrey, ''Computability and Logic''. Cambridge University Press (1980), page 99.〕 , ,〔Elliott Mendelson, ''Introduction to Mathematical Logic (4th. ed.)''. Chapman & Hall/CRC (1997), page 11.〕 $\backslash left\; \backslash$〔Eric C. R. Hehner, ''A Practical Theory of Programming''. Springer (1993, 2010), page 3.〕 or $\backslash mathbb.$ The algebraic structure that naturally builds on a Boolean domain is the Boolean algebra with two elements. The initial object in the category of bounded lattices is a Boolean domain. In computer science, a Boolean variable is a variable that takes values in some Boolean domain. Some programming languages feature reserved words or symbols for the elements of the Boolean domain, for example false and true. However, many programming languages do not have a Boolean datatype in the strict sense. In C or BASIC, for example, falsity is represented by the number 0 and truth is represented by the number 1 or −1 respectively, and all variables that can take these values can also take any other numerical values. == Generalizations == The Boolean domain can be replaced by the unit interval , in which case rather than only taking values 0 or 1, any value between and including 0 and 1 can be assumed. Algebraically, negation (NOT) is replaced with $1-x,$ conjunction (AND) is replaced with multiplication ($xy$), and disjunction (OR) is defined via De Morgan's law to be $1-(1-x)(1-y)$. Interpreting these values as logical truth values yields a multi-valued logic, which forms the basis for fuzzy logic and probabilistic logic. In these interpretations, a value is interpreted as the "degree" of truth – to what extent a proposition is true, or the probability that the proposition is true. 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「Boolean domain」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.