Abstract : We prove, by introducing a new kind of sequent calculus, that the decision problem for the non-associative Lambek calculus with \mbox{product} belongs to PTIME. This solves an open problem.
Philippe de Groote. The Non-associative Lambek calculus with product in polynomial time. Automatic Reasoning with Analytic Tableaux and Related Methods, Jun 1999, Saratoga Springs, NY USA, pp.128-139. ⟨inria-00108070⟩