  The multimodal Lambek calculus is an extension of the Lambek calculus that
includes several product operations (some of them being commutative or/and
associative), unary modalities, and corresponding residual implications. In
this work, we relate this calculus to the hypergraph Lambek calculus HL. The
latter is a general pure logic of residuation defined in a sequent form;
antecedents of its sequents are hypergraphs, and the rules of HL involve
hypergraph transformation. Our main result is the embedding of the multimodal
Lambek calculus (with at most one associative product) in HL. It justifies that
HL is a very general Lambek-style logic and also provides a novel syntactic
interface for the multimodal Lambek calculus: antecedents of sequents of the
multimodal Lambek calculus are represented as tree-like hypergraphs in HL, and
they are derived from each other by means of hyperedge replacement. The
advantage of this embedding is that commutativity and associativity are
incorporated in the sequent structure rather than added as separate rules.
Besides, modalities of the multimodal Lambek calculus are represented in HL
using the product and the division of HL, which explicitizes their residual
nature.
