{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T16:35:45Z","timestamp":1762101345417},"reference-count":33,"publisher":"Cambridge University Press (CUP)","issue":"4-5","license":[{"start":{"date-parts":[[2012,9,5]],"date-time":"2012-09-05T00:00:00Z","timestamp":1346803200000},"content-version":"unspecified","delay-in-days":66,"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":[[2012,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Probabilistic Logic Programming (PLP), exemplified by Sato and Kameya's PRISM, Poole's ICL, Raedt <jats:italic>et al<\/jats:italic>.'s ProbLog and Vennekens <jats:italic>et al<\/jats:italic>.'s LPAD, is aimed at combining statistical and logical knowledge representation and inference. However, the inference techniques used in these works rely on enumerating sets of explanations for a query answer. Consequently, these languages permit very limited use of random variables with continuous distributions. In this paper, we present a <jats:italic>symbolic<\/jats:italic> inference procedure that uses constraints and represents sets of explanations without enumeration. This permits us to reason over PLPs with Gaussian or Gamma-distributed random variables (in addition to discrete-valued random variables) and linear equality constraints over reals. We develop the inference procedure in the context of PRISM; however the procedure's core ideas can be easily applied to other PLP languages as well. An interesting aspect of our inference procedure is that PRISM's query evaluation process becomes a special case in the absence of any continuous random variables in the program. The symbolic inference procedure enables us to reason over complex probabilistic models such as Kalman filters and a large subclass of Hybrid Bayesian networks that were hitherto not possible in PLP frameworks.<\/jats:p>","DOI":"10.1017\/s1471068412000154","type":"journal-article","created":{"date-parts":[[2012,9,5]],"date-time":"2012-09-05T07:28:45Z","timestamp":1346830125000},"page":"505-523","source":"Crossref","is-referenced-by-count":13,"title":["Inference in probabilistic logic programs with continuous random variables"],"prefix":"10.1017","volume":"12","author":[{"given":"MUHAMMAD ASIFUL","family":"ISLAM","sequence":"first","affiliation":[]},{"given":"C. R.","family":"RAMAKRISHNAN","sequence":"additional","affiliation":[]},{"given":"I. V.","family":"RAMAKRISHNAN","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2012,9,5]]},"reference":[{"key":"S1471068412000154_ref33","unstructured":"Wang J. and Domingos P. 2008. 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PRISM: A symbolic-statistical modeling language. In IJCAI."},{"key":"S1471068412000154_ref27","unstructured":"Sato T. and Kameya Y. 1999. Parameter learning of logic programs for symbolic-statistical modeling. Journal of Artificial Intelligence Research, 391\u2013454."},{"key":"S1471068412000154_ref29","unstructured":"Swift T. , Warren D. S. . 2012. The XSB Logic Programming System, Version 3.3. Technical rep., Computer Science, SUNY, Stony Brook. http:\/\/xsb.sourceforge.net."},{"key":"S1471068412000154_ref15","doi-asserted-by":"crossref","unstructured":"Kersting K. and Raedt L. D. 2001. Adaptive Bayesian logic programs. In ILP.","DOI":"10.1007\/3-540-44797-0_9"},{"key":"S1471068412000154_ref23","doi-asserted-by":"crossref","unstructured":"Richardson M. and Domingos P. 2006. Markov logic networks. 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