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空值在多重集合关系中的处理

         

摘要

数据库分别采用空值和重复元组模拟现实世界中的不完全信息和重复实体.现有的数据库大多允许返回多重集合作为查询结果,却仍采用传统集合关系基础上拓展的数据模型处理空值,这给数据库带来安全隐患.为了形式化地描述空值在多重集合关系中的行为,基于空值的Unknown解释,本文提出新的逻辑联结词ψ,对Kleene三值逻辑系统进行扩充,在空值环境下重新定义多重集合关系并扩充了标准多重集合关系代数.此外,还证明了代数运算满足的性质,如:结合律、分配律,这对查询优化有着重要意义.扩充后的标准多重集合关系代数可以用来作为处理数据库空值的抽象查询语言.%Databases use Null value and duplicate tuples to simulate incomplete information and duplicate entities in real world respectively. Multi-set is allowed to be query's result in most of existing database, however, these databases still use data models based on traditional set relations to handle Null values, and that would bring hidden danger to database security. In order to for-mally describe Null value' s behavior in multi-set relations, the paper extends Kleene' s three-valued logic system by adding a new logical connective ψ based on Null' s Unknown interpretation, redefines the multi-set relation data model, and extends the standard relational algebra with Null. What' s more, this paper gives the demonstration analysis of the algebra satisfying properties such as associate law and distributive law, and this makes sense to the query optimization. The extended standard multi-set alge-bra can be used to handle Null value in database as an abstract query language.

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