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Definition
The implication problem is to decide whether or not a given set of constraints logically implies another constraint. With any constraint (dependency) language \(\mathcal{L}\) there are two implication problems associated, which do not coincide in general.
In the traditional logic framework, an instance of a schema R is a logical structure that is either finite or infinite, referred to as an unrestricted instance of R. A set \(\Sigma \) of constraints over R implies without restriction a constraint Ï•, denoted by \(\Sigma \models _{unr}\phi\), if for each unrestricted instance I of R that satisfies \(\Sigma \), I also satisfies Ï•. The unrestricted implication problem for \(\mathcal{L}\) is to determine, given a set \(\Sigma \) of constraints in \(\mathcal{L}\) and another constraint Ï• in \(\mathcal{L}\), whether or not \(\Sigma \models _{unr}\phi\).
In the context of databases, only finite instances are considered, and implication...
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Fan, W. (2017). Implication of Constraints. In: Liu, L., Özsu, M. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4899-7993-3_1238-2
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DOI: https://doi.org/10.1007/978-1-4899-7993-3_1238-2
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