The Complexity of the Constructive Master Modality

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Main Authors: Santiago-Fernández, Sofía, Fernández-Duque, David, Joosten, Joost J.
Format: Preprint
Published: 2026
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author Santiago-Fernández, Sofía
Fernández-Duque, David
Joosten, Joost J.
author_facet Santiago-Fernández, Sofía
Fernández-Duque, David
Joosten, Joost J.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2603_05131
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle The Complexity of the Constructive Master Modality
Santiago-Fernández, Sofía
Fernández-Duque, David
Joosten, Joost J.
Logic in Computer Science
Logic
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.
title The Complexity of the Constructive Master Modality
topic Logic in Computer Science
Logic
url https://arxiv.org/abs/2603.05131