  The development of compositional distributional models of semantics
reconciling the empirical aspects of distributional semantics with the
compositional aspects of formal semantics is a popular topic in the
contemporary literature. This paper seeks to bring this reconciliation one step
further by showing how the mathematical constructs commonly used in
compositional distributional models, such as tensors and matrices, can be used
to simulate different aspects of predicate logic.
  This paper discusses how the canonical isomorphism between tensors and
multilinear maps can be exploited to simulate a full-blown quantifier-free
predicate calculus using tensors. It provides tensor interpretations of the set
of logical connectives required to model propositional calculi. It suggests a
variant of these tensor calculi capable of modelling quantifiers, using few
non-linear operations. It finally discusses the relation between these
variants, and how this relation should constitute the subject of future work.
