{"paper":{"title":"Constructive S4 modal logics with the finite birelational frame property","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Brett McLean, David Fern\\'andez-Duque, Mart\\'in Di\\'eguez, Philippe Balbiani","submitted_at":"2024-03-01T00:21:46Z","abstract_excerpt":"The logics $\\mathsf{CS4}$ and $\\mathsf{IS4}$ are the two leading intuitionistic variants of the modal logic $\\mathsf{S4}$. Whether the finite model property holds for each of these logics have been long-standing open problems. It was recently shown that $\\mathsf{IS4}$ has the finite frame property and thus the finite model property. In this paper, we prove that $\\mathsf{CS4}$ also enjoys the finite frame property.\n  Additionally, we investigate the following three logics closely related to $\\mathsf{IS4}$. The logic $\\mathsf{GS4}$ is obtained by adding the G\\\"odel--Dummett axiom to $\\mathsf{IS4"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.00201","kind":"arxiv","version":3},"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/2403.00201/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"}