On database query languages for K-relations

The 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 RA(K)(+), 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 RA(K)(+) 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 RA(K)(+) 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 RA(K)(+) and extensions thereof in the sense of Bancilhon and Paredaens (C) 2009 Elsevier B V All rights reserved