Orbital Semilattices

Orbital semilattices are introduced as bounded semilattices that are, in addition, equipped with an outer multiplication (a semigroup action) and diagonals (a concept borrowed from cylindric algebra), where each semilattice element has a certain domain. An example of an orbital semilattice is a table algebra, where the domain is the schema, the diagonals are diagonal relations, and outer multiplication encodes renaming, projection and column duplication. It is shown that each orbital semilattice can be represented by a subalgebra of such a table algebra.