  Applications of the theory and computations of boolean matrices are of
fundamental importance to study a variety of discrete structural models. But
the increasing ability of data collection systems to store huge volumes of
multidimensional data, the boolean matrix representation of data analysis is
not enough to represent all the information content of the multiway data in
different fields. From this perspective, it is appropriate to develop an
infrastructure that supports reasoning about the theory and computations. In
this paper, we discuss the generalized inverses of the Boolean tensors with the
Einstein product. Further, we elaborate on this theory by producing a few
characterizations of different generalized inverses and several equivalence
results on boolean tensors. In addition to these, we define the rank of a
boolean tensor through space decomposition.
