The parabolic intersection conjecture for Artin groups

Let $A$ be an Artin group, and let parabolic subgroups mean the parabolic subgroups of $A$. The parabolic intersection conjecture. The intersection of any two parabolic subgroups is again a parabolic subgroup. This concerns the closure of the class of parabolic subgroups under intersections, a basic structural question in the study of Artin groups. The supplied text does not specify whether the assertion is known in full generality.