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Implication Problems over Positive Semirings
Minna Hirvonen
https://arxiv.org/abs/2510.08112 https://arxiv.org/pdf/2510.08112

Implication Problems over Positive Semirings
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 fo…