We study various notions of dependency in semiring team semantics. Semiring teams are essentially database relations, where each tuple is annotated with some element from a positive semiring. We consider semiring generalizations of several dependency notions from database theory and probability theory, including functional and inclusion dependencies, marginal identity, and (probabilistic) independence. We examine axiomatizations of implication problems, which are rule-based characterizations for the logical implication and inference of new dependencies from a given set of dependencies. Semiring team semantics provides a general framework, where different implication problems can be studied simultaneously for various semirings. The choice of the semiring leads to a specific semantic interpretation of the dependencies, and hence different semirings offer a way to study different semantics (e.g., relational, bag, and probabilistic semantics) in a unified framework.

翻译：本文研究了半环团队语义中的多种依赖概念。半环团队本质上是数据库关系，其中每个元组都用一个来自正半环的元素进行标注。我们考虑了数据库理论和概率论中若干依赖概念在半环上的推广，包括函数依赖与包含依赖、边际同一性以及（概率）独立性。我们考察了蕴含问题的公理化，即基于规则的刻画，用于描述从给定依赖集合出发，新依赖的逻辑蕴含与推断。半环团队语义提供了一个通用框架，使得针对不同半环的各种蕴含问题能够被同时研究。半环的选择决定了依赖的具体语义解释，因此不同的半环为在统一框架下研究不同语义（例如关系语义、包语义和概率语义）提供了一种途径。