Tarski代数视角下函数依赖与属性蕴含的关系

The study of relationship between functional dependency and attribute implication based on Tarski algebra view

研究经典函数依赖与属性蕴含之间的关系.首先介绍Tarski量词消除理论,分别研究Tarski量词消除理论下的函数依赖表示方式和属性蕴含表示方式,得出无量词Tarski代数下函数依赖与属性蕴含表示的统一数学模型;然后,进一步从形式概念分析的角度进行深入研究,得出不同转换背景下函数依赖与属性蕴含两者成立的关系,并从函数的观点分析两者的根本语义差别;最后,基于Armstrong公理的满足性讨论函数依赖与属性蕴含所满足的Armstrong公理,基于Duquenne-Guigues基的满足性得出最小依赖集与Duquenne-Guigues基的关系,并对函数依赖与属性蕴含之间的关系进行全面总结.

The relationship between classical functional dependency and attribute implication is investigated emphatically.Firstly,the quantifier elimination theory of Alfred Tarski is introduced.Then,the representation forms of functional dependency and the attribute implication under the quantifier elimination theory of Alfred Tarski are researched respectively,and the unified mathematics model of functional dependency and attribute implication under the Alfred Tarski algebra without quantifier is established.Then,the relationship between existences of functional dependency and attribute implication is discussed under different conversion contexts from the view of formal concept analysis,and the fundamental semantics difference between them is studied from the view of function.Finally,the problem on whether functional dependency and attribute implication can satisfy the Armsrong’s axiom are researched from their satisfaction degrees according to Armsrong’s axiom,the relationship between minimum dependency set and Duquenne-Guigues base is given from their satisfaction degrees according to Duquenne-Guigues base,and the relationship between classical functional dependency and attribute implication is summarized in all directions.