  In this paper hypergraph Lambek calculus ($\mathrm{HL}$) is presented. This
formalism aims to generalize the Lambek calculus ($\mathrm{L}$) to hypergraphs
as hyperedge replacement grammars extend context-free grammars. In contrast to
the Lambek calculus, $\mathrm{HL}$ deals with hypergraph types and sequents;
its axioms and rules naturally generalize those of $\mathrm{L}$. Consequently,
certain properties (e.g. the cut elimination) can be lifted from $\mathrm{L}$
to $\mathrm{HL}$. It is shown that $\mathrm{L}$ can be naturally embedded in
$\mathrm{HL}$; moreover, a number of its variants ($\mathrm{LP}$,
$\mathrm{NL}$, $\mathrm{NLP}$, $\mathrm{L}$ with modalities,
$\mathrm{L}^\ast(\mathbf{1})$, $\mathrm{L}^{\mathrm{R}}$) can also be embedded
in $\mathrm{HL}$ via different graph constructions. We also establish a
connection between $\mathrm{HL}$ and Datalog with embedded implications. It is
proved that the parsing problem for $\mathrm{HL}$ is NP-complete.
