On database query languages for K-relations

AbstractThe relational model has recently been extended to so-called K-relations in which tuples are assigned a unique value in a semiring K. A query language, denoted by RAK+, similar to the classical positive relational algebra, allows for the querying of K-relations. In this paper, we define more expressive query languages for K-relations that extend RAK+ with the difference and constant annotations operations on annotated tuples. The latter are natural extensions of the duplicate elimination operator of the relational algebra on bags. We investigate conditions on semirings under which these operations can be added to RAK+ in a natural way, and establish basic properties of the resulting query languages. Moreover, we show how the provenance semiring of Green et al. can be extended to record provenance of data in the presence of difference and constant annotations. Finally, we investigate the completeness of RAK+ and extensions thereof in the sense of Bancilhon and Paredaens