Infamously, the finite and unrestricted implication problems for the classes of i) functional and inclusion dependencies together, and ii) embedded multivalued dependencies alone are each undecidable. Famously, the restriction of i) to functional and unary inclusion dependencies in combination with the restriction of ii) to multivalued dependencies yield implication problems that are still different in the finite and unrestricted case, but each are finitely axiomatizable and decidable in low-degree polynomial time. An important embedded tractable fragment of embedded multivalued dependencies are independence atoms that stipulate independence between two attribute sets. We establish a series of results for implication problems over subclasses of the combined class of functional and inclusion dependencies as well as independence atoms. One of our main results is that both finite and unrestricted implication problems for the combined class of independence atoms, unary functional and unary inclusion dependencies are axiomatizable and decidable in low-degree polynomial time.

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关于功能性和包含性依赖项与独立原子的相互作用

臭名昭著的是，对于i）函数和包含依赖关系以及ii）仅嵌入的多值依赖关系，这些类的有限和无限制隐含问题都是不确定的。著名的是，i）对函数和一元包含项的约束与ii）对多值依赖项的约束会产生蕴涵问题，在有限和无约束的情况下，隐含问题仍然不同，但是在低阶多项式中，每个问题都是可公理地确定的时间。嵌入多值依赖项的一个重要的嵌入易处理片段是规定两个属性集之间独立性的独立性原子。我们针对功能性和包含性依赖项以及独立性原子的组合类的子类的蕴涵问题建立了一系列结果。