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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Armstrong's axioms ： ウィキペディア英語版 Armstrong's axioms Armstrong's axioms are a set of axioms (or, more precisely, inference rules) used to infer all the functional dependencies on a relational database. They were developed by William W. Armstrong on his 1974 paper.〔William Ward Armstrong: ''Dependency Structures of Data Base Relationships'', page 580-583. IFIP Congress, 1974.〕 The axioms are sound in generating only functional dependencies in the closure of a set of functional dependencies (denoted as $F^$) when applied to that set (denoted as $F$). They are also complete in that repeated application of these rules will generate all functional dependencies in the closure $F^+$. More formally, let $\backslash langle\; R(U),\; F\; \backslash rangle$ denote a relational scheme over the set of attributes $U$ with a set of functional dependencies $F$. We say that a functional dependency $f$ is logically implied by $F$,and denote it with $F\; \backslash models\; f$ if and only if for every instance $r$ of $R$ that satisfies the functional dependencies in $F$, r also satisfies $f$. We denote by $F^$ the set of all functional dependencies that are logically implied by $F$. Furthermore, with respect to a set of inference rules $A$, we say that a functional dependency $f$ is derivable from the functional dependencies in $F$ by the set of inference rules $A$, and we denote it by $F\; \backslash vdash\; \_\; f$ if and only if $f$ is obtainable by means of repeatedly applying the inference rules in $A$ to functional dependencies in $F$. We denote by $F^\_$ the set of all functional dependencies that are derivable from $F$ by inference rules in $A$. Then, a set of inference rules $A$ is sound if and only if the following holds: $$ F^_ \subseteq F^ that is to say, we cannot derive by means of $A$ functional dependencies that are not logically implied by $F$. The set of inference rules $A$ is said to be complete if the following holds: $$ F^ \subseteq F^_ more simply put, we are able to derive by $A$ all the functional dependencies that are logically implied by $F$. ==Axioms== Let $R(U)$ be a relation scheme over the set of attributes $U$. Henceforth we will denote by letters $X$, $Y$, $Z$ any subset of $U$ and, for short, the union of two sets of attributes $X$ and $Y$ by $XY$ instead of the usual $X\; \backslash cup\; Y$; this notation is rather standard in database theory when dealing with sets of attributes. 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「Armstrong's axioms」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.