Title: Models for the Displacement Calculus,
Abstract: The displacement calculus $\mathbf{D}$ is a conservative extension of the
Lambek calculus $\mathbf{L1}$ (with empty antecedents allowed in sequents).
$\mathbf{L1}$ can be said to be the logic of concatenation, while $\mathbf{D}$
can be said to be the logic of concatenation and intercalation. In many senses,
it can be claimed that $\mathbf{D}$ mimics $\mathbf{L1}$ in that the proof
theory, generative capacity and complexity of the former calculus are natural
extensions of the latter calculus. In this paper, we strengthen this claim. We
present the appropriate classes of models for $\mathbf{D}$ and prove some
completeness results; strikingly, we see that these results and proofs are
natural extensions of the corresponding ones for $\mathbf{L1}$.