When data dependencies over SQL tables meet the logics of paradox and S-3

We study functional and multivalued dependencies over SQL tables with NOT NULL constraints. Under a no-information interpretation of null values we develop tools for reasoning. We further show that in the absence of NOT NULL constraints the associated implication problem is equivalent to that in propositional fragments of Priest's paraconsistent Logic of Paradox. Subsequently, we extend the equivalence to Boolean dependencies and to the presence of NOT NULL constraints using Schaerf and Cadoli's S-3 logics where S corresponds to the set of attributes declared NOT NULL. The findings also apply to Codd's interpretation "value at present unknown" utilizing a weak possible world semantics. Our results establish NOT NULL constraints as an effective mechanism to balance the expressiveness and tractability of consequence relations, and to control the degree by which the existing classical theory of data dependencies can be soundly approximated in practice.