Similarity and bisimilarity notions appropriate for characterizing   indistinguishability in fragments of the calculus of relations
  Motivated by applications in databases, this paper considers various fragments of the calculus of binary relations. The fragments are obtained by leaving out, or keeping in, some of the standard operators, along with some derived operators such as set difference, projection, coprojection, and residuation. For each considered fragment, a characterization is obtained for when two given binary relational structures are indistinguishable by expressions in that fragment. The characterizations are based on appropriately adapted notions of simulation and bisimulation. 
George H. L. Fletcher, Marc Gyssens, Dirk Leinders, Jan Van den   Bussche, Dirk Van Gucht, Stijn Vansummeren
cs.LO cs.DB