{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T07:39:50Z","timestamp":1723016390529},"publisher-location":"California","reference-count":0,"publisher":"International Joint Conferences on Artificial Intelligence Organization","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,9]]},"abstract":"<jats:p>We consider the problem of weighted first-order model counting (WFOMC): given a first-order sentence \u03d5 and domain size n \u2208 \u2115, determine the weighted sum of models of \u03d5 over the domain {1, ..., n}. Past work has shown that any sentence using at most two logical variables admits an algorithm for WFOMC that runs in time polynomial in the given domain size (Van den Broeck 2011; Van den Broeck, Meert, and Darwiche 2014). In this paper, we extend this result to any two-variable sentence \u03d5 with the addition of a tree axiom, stating that some distinguished binary relation in \u03d5 forms a tree in the graph-theoretic sense.<\/jats:p>","DOI":"10.24963\/kr.2021\/57","type":"proceedings-article","created":{"date-parts":[[2021,10,11]],"date-time":"2021-10-11T16:45:56Z","timestamp":1633970756000},"page":"599-608","source":"Crossref","is-referenced-by-count":1,"title":["Lifted Inference with Tree Axioms"],"prefix":"10.24963","author":[{"given":"Timothy","family":"van Bremen","sequence":"first","affiliation":[{"name":"KU Leuven"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ond\u0159ej","family":"Ku\u017eelka","sequence":"additional","affiliation":[{"name":"Czech Technical University in Prague"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"10584","event":{"number":"18","sponsor":["Artificial Intelligence Journal","Principles of Knowledge Representation and Reasoning Inc.","Sea AI Lab","Potassco Solutions","European Association for Artificial Intelligence"],"acronym":"KR-2021","name":"18th International Conference on Principles of Knowledge Representation and Reasoning {KR-2021}","start":{"date-parts":[[2020,11,12]]},"theme":"Artificial Intelligence","location":"Hanoii, Vietnam","end":{"date-parts":[[2021,11,18]]}},"container-title":["Proceedings of the Eighteenth International Conference on Principles of Knowledge Representation and Reasoning"],"original-title":[],"deposited":{"date-parts":[[2021,10,11]],"date-time":"2021-10-11T16:46:26Z","timestamp":1633970786000},"score":1,"resource":{"primary":{"URL":"https:\/\/proceedings.kr.org\/2021\/57"}},"subtitle":[],"proceedings-subject":"Artificial Intelligence Research Articles","short-title":[],"issued":{"date-parts":[[2021,9]]},"references-count":0,"URL":"https:\/\/doi.org\/10.24963\/kr.2021\/57","relation":{},"subject":[],"published":{"date-parts":[[2021,9]]}}}