Abstract
在本論文中, 我們提出了一個擴充關聯模式, 稱為 Pv-table. 藉由部份值與變數和屬性的連結, 用以表示互斥型離接式資料 ( 也就是說, 一個資料項對應一組可能值, 且其中恰有一個可能值為真 ). 部份值是用以指示一資料項的整組可能值, 而變數則做為其真實值的號誌.此外, 變數也可用於 (1) 保留值在投射運算中的區別性; (2) 保留值在選擇, 卡氏積, 連結運算中的依存資訊; 以及 (3) 保留值在連結運算中的相等關係.各種關連運算被逐一擴充以處理 Pv-table. 我們證明在 Pv-table上以集合論為基礎的查詢運算是正確且完整的. 這些查詢可含擴充式選擇, 聯集, 交集, 卡氏積,和連結等運算. 我們也證明在傳統關聯模式中的有用代數性質都能在我們所提出的模式中保存. 這些性質不僅有助於提供查詢一個更自然的解釋, 也有助於在分散式查詢最佳化處理中的分解查詢. 這些性質在很多其他的擴充模式中並未被保存.在資料庫更新及強制限制令上必須用到減法. 我們進一步的擴充 Pv-table, 使其具有處理減法的能力. 以一套完整的擴充關聯運算子為基礎, 資料庫的查詢, 更新,及限制令強制得以一致的處理. 我們考慮的限制令包含函數依存和連結依存兩類關係. 這兩類限制令的強制是採用擴充的追獵演算法. 我們證明了這些擴充運算子, 更新運算, 及限制令強化的正確性.透過變數集合, 資料列可被連上兩類關係, 分別為離接關係和連結關係. 依據這些關係, 資料列集合可被區分為共存集合, 共有集合, 與共值集合. 依據這些特性, Pv-table 的解釋可以富含語意的公式化. 同時, 多餘和可合併的資料列也可被識別出來. 在刪除和合併這些資料列之後, 可得到一個更精簡的 Pv-table, 使查詢的結果更易於暸解.In this dissertation, we propose an extended relationalmodel, named Pv-table, for representing exclusive disjunctivedata by associating partial values and variables withattributes. While a partial value denotes the set ofpossible values, a variable serves as an identifier for thetrue value of the data item. In addition, variables can beused to preserve distinctness of values, the equi-relationship of values, and dependency information inthe operations. The relational operators are extended tomanipulate Pv-tables. We show that the set-based queryevaluation on Pv-tables is sound and complete forqueries consisting of extended selection, union,intersection, Cartesian product and join. We also showthat useful algebraic properties in conventional relationalmodels are preserved in our model. These properties are notpreserved for many other extended models. Pv-table isfurther generalized for the ability to correctlysupport the difference operator which is mandatory indatabase updates and dependency enforcement. A set ofgeneralized relational operators is defined, so that a unifiedsolution to queries, updates and constraintenforcement can be obtained. The semantic correctnessis established. By variable sets, tuples may be related withcertain relationships, namely disjunctive relationshipand join relationship. Three kinds of tuple sets areclassified according to these relationships; eachpossesses an important property, namely co-exist, co-nonempty and co-instance. Based on these properties,the interpretation of Pv-tables can be formalized in asemantically meaningful way. Also, the redundant andmergeable tuples can be identified. After removing andmerging tuples accordingly, a more concise Pv-table canthus provide a better understanding of the query result.