Model checking is commonly recognized as one of the most effective tools for system verification. While it has been systematically investigated in the context of classical, point-based temporal logics, it is still largely unexplored in the interval logic setting. Recently, a non-elementary model checking algorithm for Halpern and Shoham’s modal logic of time intervals HS, interpreted over finite Kripke structures, has been proposed, together with a proof of the EXPSPACE-hardness of the problem. In this paper, we devise an EXPSPACE model checking procedure for two meaningful HS fragments. It exploits a suitable contraction technique that allows one to replace sufficiently long tracks of a Kripke structure by equivalent shorter ones.
