We study functional dependencies together with two different probabilistic dependency notions: unary marginal identity and unary marginal distribution equivalence. A unary marginal identity states that two variables x and y are identically distributed. A unary marginal distribution equivalence states that the multiset consisting of the marginal probabilities of all the values for variable x is the same as the corresponding multiset for y. We present a sound and complete axiomatization for the class of these dependencies and show that it has Armstrong relations. The axiomatization is infinite, but we show that there can be no finite axiomatization. The implication problem for the subclass that contains only functional dependencies and unary marginal identities can be simulated with functional dependencies and unary inclusion atoms, and therefore the problem is in polynomial-time. This complexity bound also holds in the case of the full class, which we show by constructing a polynomial-time algorithm.

翻译：本文研究函数依赖与两种概率依赖概念：一元边际恒等性和一元边际分布等价性。一元边际恒等性指出两个变量x和y具有相同的分布；一元边际分布等价性则表明变量x所有可能取值的边际概率构成的多重集与变量y对应的多重集相同。我们为该类依赖关系建立了可靠且完备的公理化系统，并证明其具有阿姆斯特朗关系。该公理化系统是无限阶的，但研究表明不存在有限公理化。仅包含函数依赖与一元边际恒等性的子类蕴含问题可通过函数依赖与一元包含子句进行模拟，因此该问题属于多项式时间复杂度。通过构造多项式时间算法，我们证明这一复杂度上界同样适用于完整原类。