{"paper":{"title":"Weighted First-Order Model Counting over Ordered Domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Jan T\\'oth, Kuncheng Zou, Ond\\v{r}ej Ku\\v{z}elka, Qipeng Kuang, V\\'aclav K\\r{u}la, Yuanhong Wang, Yuyi Wang","submitted_at":"2026-08-11T12:54:21Z","abstract_excerpt":"The Weighted First-Order Model Counting Problem (WFOMC) asks for the weighted sum of models of a first-order logical sentence over a domain. It is a fundamental problem in statistical relational learning, with applications extending to enumerative combinatorics and graph polynomials. Computing WFOMC for the three-variable fragment is $\\mathsf{\\#P}_1$-hard, whereas polynomial-time algorithms exist for the two-variable fragment and its extensions by cardinality constraints and counting quantifiers. In this work, we explore computing WFOMC in polynomial time over linearly ordered domains, enablin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.10877","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/2608.10877/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"}