{"paper":{"title":"Definability of Functional Properties in the Basic Modal-Temporal Language over Ordered Frames","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"cs.LO","authors_text":"Alfredo Burrieza","submitted_at":"2026-07-01T16:01:42Z","abstract_excerpt":"We study the expressive power of the simplest modal-temporal language, obtained by adding Prior's temporal operators \\(G\\) and \\(H\\) to the basic modal language with \\(\\Box\\). This language is the standard bimodal combination of modal and tense logic; under its functional interpretation it is denoted \\(L_{T\\times W}\\). To analyse its definability across five order types, we consider two semantic readings of the temporal operators: the standard reading (\\(G,H\\)), which includes the current instant, and the strict reading (\\(G^{\\ast},H^{\\ast}\\)), which always excludes it.\n  We examine nine funct"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01110","kind":"arxiv","version":1},"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/2607.01110/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"}