  We provide a lower complexity bound for the satisfiability problem of a
multi-agent justification logic, establishing that the general NEXP upper bound
from our previous work is tight. We then use a simple modification of the
corresponding reduction to prove that satisfiability for all multi-agent
justification logics from there is hard for the Sigma 2 p class of the second
level of the polynomial hierarchy - given certain reasonable conditions. Our
methods improve on these required conditions for the same lower bound for the
single-agent justification logics, proven by Buss and Kuznets in 2009, thus
answering one of their open questions.
