The Complexity of the Constructive Master Modality

Abstract

We introduce the semantically-defined constructive master-modality logics $\sf CK^*$ and $\sf WK^*$, extending the basic constructive modal logic $\sf CK$ and the Wijesekera-style logic $\sf WK$ obtained by impossing infallibility. Using translations between our logics and fragments of $\sf PDL$, we show that both $\sf CK^*$ and $\sf WK^*$ are EXPTIME-complete and admit an exponential-size finite model property. In particular, for their diamond-free fragment, also studied by Afshari et al. and Celoni, we establish EXPTIME-completeness, thereby settling the conjecture of Afshari et al. As an application, we embed $\sf CS4$ and $\sf WS4$ into the master-modality logics, showing that their validity problems are in EXPTIME.