{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T08:21:44Z","timestamp":1760170904652},"reference-count":23,"publisher":"Cambridge University Press (CUP)","issue":"4-5","license":[{"start":{"date-parts":[[2014,7,21]],"date-time":"2014-07-21T00:00:00Z","timestamp":1405900800000},"content-version":"unspecified","delay-in-days":20,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Theory and Practice of Logic Programming"],"published-print":{"date-parts":[[2014,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Lifted inference has been proposed for various probabilistic logical frameworks in order to compute the probability of queries in a time that depends on the size of the domains of the random variables rather than the number of instances. Even if various authors have underlined its importance for probabilistic logic programming (PLP), lifted inference has been applied up to now only to relational languages outside of logic programming. In this paper we adapt Generalized Counting First Order Variable Elimination (GC-FOVE) to the problem of computing the probability of queries to probabilistic logic programs under the distribution semantics. In particular, we extend the Prolog Factor Language (PFL) to include two new types of factors that are needed for representing ProbLog programs. These factors take into account the existing causal independence relationships among random variables and are managed by the extension to variable elimination proposed by Zhang and Poole for dealing with convergent variables and heterogeneous factors. Two new operators are added to GC-FOVE for treating heterogeneous factors. The resulting algorithm, called LP<jats:sup>2<\/jats:sup>for Lifted Probabilistic Logic Programming, has been implemented by modifying the PFL implementation of GC-FOVE and tested on three benchmarks for lifted inference. A comparison with PITA and ProbLog2 shows the potential of the approach.<\/jats:p>","DOI":"10.1017\/s1471068414000283","type":"journal-article","created":{"date-parts":[[2014,7,21]],"date-time":"2014-07-21T11:52:50Z","timestamp":1405943570000},"page":"681-695","source":"Crossref","is-referenced-by-count":11,"title":["Lifted Variable Elimination for Probabilistic Logic Programming"],"prefix":"10.1017","volume":"14","author":[{"given":"ELENA","family":"BELLODI","sequence":"first","affiliation":[]},{"given":"EVELINA","family":"LAMMA","sequence":"additional","affiliation":[]},{"given":"FABRIZIO","family":"RIGUZZI","sequence":"additional","affiliation":[]},{"given":"VITOR SANTOS","family":"COSTA","sequence":"additional","affiliation":[]},{"given":"RICCARDO","family":"ZESE","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,7,21]]},"reference":[{"key":"S1471068414000283_ref3","first-page":"1319","volume-title":"19th International Joint Conference on Artificial Intelligence","author":"de Salvo Braz","year":"2005"},{"key":"S1471068414000283_ref22","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-27775-0_14"},{"key":"S1471068414000283_ref10","first-page":"131","article-title":"Learning ground CP-Logic theories by leveraging Bayesian network learning techniques.","volume":"89","author":"Meert","year":"2008","journal-title":"Fundamenta Informaticae"},{"key":"S1471068414000283_ref20","unstructured":"Van den Broeck G. , Meert W. , and Darwiche A. 2014. Skolemization for weighted first-order model counting. ArXiv e-prints 1312.5378v2. To appear in the 14th International Conference on Principles of Knowledge Representation and Reasoning."},{"key":"S1471068414000283_ref14","first-page":"985","volume-title":"18th International Joint Conference on Artificial Intelligence","author":"Poole","year":"2003"},{"key":"S1471068414000283_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/0004-3702(93)90061-F"},{"key":"S1471068414000283_ref15","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-78652-8_8"},{"key":"S1471068414000283_ref7","first-page":"74","volume-title":"22nd International Conference on Inductive Logic Programming","author":"Gomes","year":"2012"},{"key":"S1471068414000283_ref9","unstructured":"Kisynski J. and Poole D. 2009b. Lifted aggregation in directed first-order probabilistic models. In 24th International Joint Conference on Artificial Intelligence, C. Boutilier, Ed. 1922\u20131929."},{"key":"S1471068414000283_ref6","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/7432.001.0001","volume-title":"Introduction to Statistical Relational Learning","author":"Getoor","year":"2007"},{"key":"S1471068414000283_ref13","doi-asserted-by":"publisher","DOI":"10.1016\/S0004-3702(97)00027-1"},{"key":"S1471068414000283_ref17","doi-asserted-by":"crossref","first-page":"715","DOI":"10.7551\/mitpress\/4298.003.0069","volume-title":"12th International Conference on Logic Programming","author":"Sato","year":"1995"},{"key":"S1471068414000283_ref5","doi-asserted-by":"crossref","unstructured":"Fierens D. , Van den Broeck G. , Renkens J. , Shterionov D. , Gutmann B. , Thon I. , Janssens G. , and De Raedt L. 2014. Inference and learning in probabilistic logic programs using weighted boolean formulas. Theory and Practice of Logic Programming FirstView Articles.","DOI":"10.1017\/S1471068414000076"},{"key":"S1471068414000283_ref16","doi-asserted-by":"publisher","DOI":"10.1017\/S147106841100010X"},{"key":"S1471068414000283_ref4","unstructured":"D\u00edez F. J. and Gal\u00e1n S. F. 2003. Efficient computation for the noisy max. International Journal of Intelligent Systems, 165\u2013177."},{"key":"S1471068414000283_ref2","first-page":"2462","volume-title":"20th International Joint Conference on Artificial Intelligence (IJCAI-2007)","author":"De Raedt","year":"2007"},{"key":"S1471068414000283_ref1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-78652-8"},{"key":"S1471068414000283_ref23","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1613\/jair.305","article-title":"Exploiting causal independence in bayesian network inference.","volume":"5","author":"Zhang","year":"1996","journal-title":"Journal of Artificial Intelligence Research"},{"key":"S1471068414000283_ref18","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1613\/jair.3793","article-title":"Lifted variable elimination: Decoupling the operators from the constraint language.","volume":"47","author":"Taghipour","year":"2013","journal-title":"Journal of Artificial Intelligence Research"},{"key":"S1471068414000283_ref11","first-page":"1062","volume-title":"23rd AAAI Conference on Artificial Intelligence","author":"Milch","year":"2008"},{"key":"S1471068414000283_ref19","unstructured":"Takikawa M. and D'Ambrosio B. 1999. Multiplicative factorization of noisy-max. In 15th Conference on Uncertainty in Artificial Intelligence. 622\u2013630."},{"key":"S1471068414000283_ref21","first-page":"2178","volume-title":"21st International Joint Conference on Artificial Intelligence","author":"Van den Broeck","year":"2011"},{"key":"S1471068414000283_ref8","first-page":"293","volume-title":"25th Conference on Uncertainty in Artificial Intelligence","author":"Kisynski","year":"2009"}],"container-title":["Theory and Practice of Logic Programming"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1471068414000283","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,30]],"date-time":"2024-05-30T22:59:03Z","timestamp":1717109943000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1471068414000283\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,7]]},"references-count":23,"journal-issue":{"issue":"4-5","published-print":{"date-parts":[[2014,7]]}},"alternative-id":["S1471068414000283"],"URL":"https:\/\/doi.org\/10.1017\/s1471068414000283","relation":{},"ISSN":["1471-0684","1475-3081"],"issn-type":[{"value":"1471-0684","type":"print"},{"value":"1475-3081","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,7]]}}}