  We study the computational complexity of the parsing problem of a variant of
Lambek Categorial Grammar that we call {\em semidirectional}. In
semidirectional Lambek calculus $\SDL$ there is an additional non-directional
abstraction rule allowing the formula abstracted over to appear anywhere in the
premise sequent's left-hand side, thus permitting non-peripheral extraction.
$\SDL$ grammars are able to generate each context-free language and more than
that. We show that the parsing problem for semidirectional Lambek Grammar is
NP-complete by a reduction of the 3-Partition problem.
