{"paper":{"title":"Hyper Swap Structures: The Case Study of LFIs and Hyper Boolean Algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Ana C. Golzio, Kaique M. A. Roberto, Marcelo E. Coniglio","submitted_at":"2026-06-27T01:20:15Z","abstract_excerpt":"In a previous paper, we introduced the notion of hyper swap structures, a novel class of hyperalgebras that naturally generalizes swap structures semantics. In this paper we introduce the concept of hyper Boolean algebras based on Morgado hyperlattices, proving some basic properties. From this, we show that several paraconsistent logics in the hierarchy of Logics of Formal Inconsistency (LFIs) can be naturally characterized in terms of hyper swap structures semantics generated by hyper Boolean algebras. Finally, for each of these LFIs we obtain a Kalman-style functor which establishes an equiv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28672","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/2606.28672/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"}