关于传递闭包和函数依赖完备公理系统存在问题研究

ON THE EXISTENCE OF FINITE COMPLETE AXIOMATIZATION FOR TRANSITIVE CLOSURE AND FUNCTIONAL DEPENDENCIES

数据依赖在数据库设计中起着十分重要的作用．自Ｃｏｄｄ提出函数依赖（ＦＤｓ）、Ｆａｇｉｎ引入多值依赖（ＭＶＤｓ）后，近几年来人们又根据设计中的需要引入多种新的依赖，如在工程数据库设计中所引进的传递闭包依赖（ＣＤｓ）等．对这些依赖一般是按其是否具有完备的公理系统而划分为两大类，因为完备性公理系统往往具有有效的判定算法为先决条件．本文对ＣＤｓ和ＦＤｓ的ｋ元完备公理系统存在问题进行了研究，证明了ＣＤｓ和ＦＤｓ不具有共同的ｋ元完备公理系统这一结论．

Closure dependencies, or CDs, are introduced to capture formally transitive closure relationships between attributes of a relational schema. The problem of a finite complete axiomatization for the interaction of CDs with functional dependencies (FDs) is investigated, leading to a negative result for the existence of a k-ary axiomatization for CDs and FDs taken together, in which every rule is k-ary for some fixed k.