{"paper":{"title":"Positive Instantial Neighbourhood logic","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Anupam Khanra, Litan Kumar Das, Sujit Kumar Sardar","submitted_at":"2026-06-06T10:06:19Z","abstract_excerpt":"Instantial neighbourhood logic is a modal language for neighbourhood frames in which formulas can express information about the kinds of worlds occurring inside a neighbourhood of a given world. In this paper, we study a positive, negation-free version of instantial neighbourhood logic with two primitive instantial modalities, one of box-type and one of diamond-type. Since classical negation is not available, the two modalities are treated independently. We introduce the language and proof system of positive instantial neighbourhood logic (PINL) and interpret it over persistent two-sided neigh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08083","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/2606.08083/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"}