2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/151303We 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.7 pages, LaTeX source (uses aclap.sty, tree-dvips.{sty,pro})Computation and Languagetext