{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T09:49:14Z","timestamp":1747216154682,"version":"3.40.5"},"reference-count":0,"publisher":"IOS Press","isbn-type":[{"type":"electronic","value":"9781643685489"}],"license":[{"start":{"date-parts":[[2024,10,16]],"date-time":"2024-10-16T00:00:00Z","timestamp":1729036800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,10,16]]},"abstract":"<jats:p>We consider the task of weighted first-order model counting (WFOMC), a fundamental problem of probabilistic inference in statistical relational learning. The goal of WFOMC is to compute the weighted sum of models of a given first-order logic sentence over a finite domain, where each model is assigned a weight by a pair of weighting functions. Past work has shown that WFOMC can be solved in polynomial time in the domain size if the sentence is in the two-variable fragment of first-order logic (FO2). This result is later extended to the case where the sentence is in FO2with the linear order axiom, which requires a binary predicate in the sentence to introduce a linear ordering of the domain elements. However, despite its polynomial theoretical complexity, the existing domain-liftable algorithm for WFOMC with the linear order often suffers from inefficiencies when applied to real-world problems. This paper introduces a novel domain-lifted algorithm for WFOMC with the linear order axiom. Compared to the existing approach, our proposed algorithm exploits the inherent symmetries within first-order logic sentences and weighting functions to minimize redundant computations. Experimental results verify the efficiency of our approach, demonstrating a significant speedup over the existing approach.<\/jats:p>","DOI":"10.3233\/faia240858","type":"book-chapter","created":{"date-parts":[[2024,10,17]],"date-time":"2024-10-17T13:34:13Z","timestamp":1729172053000},"source":"Crossref","is-referenced-by-count":0,"title":["A More Practical Algorithm for Weighted First-Order Model Counting with Linear Order Axiom"],"prefix":"10.3233","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-3413-5421","authenticated-orcid":false,"given":"Qiaolan","family":"Meng","sequence":"first","affiliation":[{"name":"State Key Laboratory of Software Development Environment, Beihang University, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2663-248X","authenticated-orcid":false,"given":"Jan","family":"T\u00f3th","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering, Czech Technical University in Prague, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1801-9634","authenticated-orcid":false,"given":"Yuanhong","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Software Development Environment, Beihang University, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7273-9873","authenticated-orcid":false,"given":"Yuyi","family":"Wang","sequence":"additional","affiliation":[{"name":"CRRC Zhuzhou Insitute, Zhuzhou, China"},{"name":"Tengen Intelligence Institute, Zhuzhou, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6523-9114","authenticated-orcid":false,"given":"Ond\u0159ej","family":"Ku\u017eelka","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering, Czech Technical University in Prague, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"7437","container-title":["Frontiers in Artificial Intelligence and Applications","ECAI 2024"],"original-title":[],"link":[{"URL":"https:\/\/ebooks.iospress.nl\/pdf\/doi\/10.3233\/FAIA240858","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,17]],"date-time":"2024-10-17T13:34:14Z","timestamp":1729172054000},"score":1,"resource":{"primary":{"URL":"https:\/\/ebooks.iospress.nl\/doi\/10.3233\/FAIA240858"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,16]]},"ISBN":["9781643685489"],"references-count":0,"URL":"https:\/\/doi.org\/10.3233\/faia240858","relation":{},"ISSN":["0922-6389","1879-8314"],"issn-type":[{"type":"print","value":"0922-6389"},{"type":"electronic","value":"1879-8314"}],"subject":[],"published":{"date-parts":[[2024,10,16]]}}}