B and D Are Enough to Make the Halpern–Shoham Logic Undecidable

Abstract

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 (among other results), that the BD fragment (where only the operators begins and during are allowed) is undecidable over discrete structures.