A formalization of the Codd algebra operations in logic $\mathcal{SHOIN}(D)$

In this paper the problem of the interpretation of data bases as ontologies is investigated, in particular, a modeling of the Codd algebra operations via object theories. The problem of modeling the DB's closed world within the open world of description logics is solved. It is shown that within object theories the Codd's algebra can be defined. The results of the paper are also practically significant, because they offer a homogeneous and coherent method for manipulations with data bases as ontologies in logical knowledge bases.