The Last Paper on the Halpern-Shoham Interval Temporal Logic

The Halpern-Shoham logic is a modal logic of time intervals. Some effort has been put in last ten years to classify fragments of this beautiful logic with respect to decidability of its satisfiability problem. We contribute to this effort by showing - what we believe is quite an unexpected result - that the logic of subintervals, the fragment of the Halpern-Shoham where only the operator "during", or D, is allowed, is undecidable over discrete structures. This is surprising as this logic is decidable over dense orders and its reflexive variant is known to be decidable over discrete structures.