Deciding an Interval Logic with Accumulated Durations

A decidability result and a model-checking procedure for a rich subset of Duration Calculus (DC) [19] is obtained through reductions to first-order logic over the real-closed field and to Multi-Priced Timed Automata (MPTA) [13]. In contrast to other reductions of fragments of DC to reachability problems in timed automata, the reductions do also cover constraints on positive linear combinations of accumulated durations. By being able to handle accumulated durations under chop as well as in arbitrary positive Boolean contexts, the procedures extend the results of Zhou et al. [22] on decidability of linear duration invariants to a much wider fragment of DC.