2026/03/05 by Sofía Santiago-Fernández, David Fernández-Duque, Joost J. Joosten
#cs.LO #math.LO
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.