{"paper":{"title":"Domain size asymptotics for Markov logic networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO","math.LO"],"primary_cat":"cs.AI","authors_text":"Vera Koponen","submitted_at":"2025-09-04T13:15:02Z","abstract_excerpt":"A Markov logic network (MLN) $\\mathbb{M}$ determines a probability distribution $\\mathbb{P}_n^\\mathbb{M}$ on the set $\\mathbf{W}_n$ of structures, or ``possible worlds'', with domain $\\{1, \\ldots, n\\}$. We study the properties of such distributions as $n$ tends to infinity.\n  We show that with mild assumptions on an MLN $\\mathbb{M}$ with one soft constraint with an arbitrary positive weight the distribution $\\mathbb{P}_n^\\mathbb{M}$ will behave quite differently from the uniform distribution $\\mathbb{P}_n^{uni}$ on $\\mathbf{W}_n$ for all sufficiently large $n$.\n  For a language with only one r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.04192","kind":"arxiv","version":2},"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/2509.04192/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"}