{"paper":{"title":"Locality Theorems in Semiring Semantics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Clotilde Bizi\\`ere, Erich Gr\\\"adel, Matthias Naaf","submitted_at":"2023-03-22T15:09:12Z","abstract_excerpt":"Semiring semantics of first-order logic generalises classical Boolean semantics by permitting truth values from a commutative semiring, which can model information such as costs or access restrictions. This raises the question to what extent classical model theoretic properties still apply, and how this depends on the algebraic properties of the semiring.\n  In this paper, we study this question for the classical locality theorems due to Hanf and Gaifman. We prove that Hanf's Locality Theorem generalises to all semirings with idempotent operations, but fails for many non-idempotent semirings. W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.12627","kind":"arxiv","version":4},"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/2303.12627/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"}