L-relational algebra

Abstract

In this article we focus on the positive K-relation model for annotated relations in which each U-tuple is mapped to an element of a commutative semiring, K. We propose a new operation in K, called negation, which induces a difference operation on K-relations, i.e., the only basic relational operation not interpreted in the positive K-relational algebra. Because we cannot define negation in all semirings, we move from the commutative semirings to the De Morgan frames, a lattice structure with negation. This has another positive consequence – the obtained L-relational algebra satisfies all the classical relational identities, including those that are not satisfied by the positive K-relational algebra.