  Lambek calculus with a relevant modality $!\mathbf{L^*}$ of arXiv:1601.06303
syntactically resolves parasitic gaps in natural language. It resembles the
Lambek calculus with anaphora $\mathbf{LA}$ of (J\"ager, 1998) and the Lambek
calculus with controlled contraction, $\mathbf{L}_{\Diamond}$, of
arXiv:1905.01647v1 which deal with anaphora and ellipsis. What all these
calculi add to Lambek calculus is a copying and moving behaviour.
Distributional semantics is a subfield of Natural Language Processing that uses
vector space semantics for words via co-occurrence statistics in large corpora
of data. Compositional vector space semantics for Lambek Calculi are obtained
via the DisCoCat models arXiv:1003.4394v1. $\mathbf{LA}$ does not have a vector
space semantics and the semantics of $\mathbf{L}_{\Diamond}$ is not
compositional. Previously, we developed a DisCoCat semantics for
$!\mathbf{L^*}$ and focused on the parasitic gap applications. In this paper,
we use the vector space instance of that general semantics and show how one can
also interpret anaphora, ellipsis, and for the first time derive the sloppy vs
strict vector readings of ambiguous anaphora with ellipsis cases. The base of
our semantics is tensor algebras and their finite dimensional variants: the
Fermionic Fock spaces of Quantum Mechanics. We implement our model and
experiment with the ellipsis disambiguation task of arXiv:1905.01647.
