{"paper":{"title":"The Complexity of the Constructive Master Modality","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"cs.LO","authors_text":"David Fern\\'andez-Duque, Joost J. Joosten, Sof\\'ia Santiago-Fern\\'andez","submitted_at":"2026-03-05T12:59:47Z","abstract_excerpt":"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.\n  As an "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.05131","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.05131/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}