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dc.contributor.authorJiroušek, Radim
dc.contributor.authorShenoy, Prakash P.
dc.date.accessioned2015-12-03T15:55:58Z
dc.date.available2015-12-03T15:55:58Z
dc.date.issued2014-01
dc.identifier.citationJiroušek, Radim, and Prakash P. Shenoy. "Compositional Models in Valuation-based Systems." International Journal of Approximate Reasoning 55.1 (2014): 277-93. http://dx.doi.org/10.1016/j.ijar.2013.02.002en_US
dc.identifier.urihttp://hdl.handle.net/1808/19083
dc.descriptionThis is the author final draft. Copyright 2014 Elsevieren_US
dc.description.abstractCompositional models were initially described for discrete probability theory, and later extended for possibility theory and for belief functions in Dempster–Shafer (D–S) theory of evidence. Valuation-based system (VBS) is an unifying theoretical framework generalizing some of the well known and frequently used uncertainty calculi. This generalization enables us to not only highlight the most important theoretical properties necessary for efficient inference (analogous to Bayesian inference in the framework of Bayesian network), but also to design efficient computational procedures. Some of the specific calculi covered by VBS are probability theory, a version of possibility theory where combination is the product t-norm, Spohn’s epistemic belief theory, and D–S belief function theory. In this paper, we describe compositional models in the general framework of VBS using the semantics of no-double counting, which is central to the VBS framework. Also, we show that conditioning can be expressed using the composition operator. We define a special case of compositional models called decomposable models, again in the VBS framework, and demonstrate that for the class of decomposable compositional models, conditioning can be done using local computation. As all results are obtained for the VBS framework, they hold in all calculi that fit in the VBS framework. For the D–S theory of belief functions, the compositional model defined here differs from the one studied by Jiroušek, Vejnarová, and Daniel. The latter model can also be described in the VBS framework, but with a combination operator that is different from Dempster’s rule of combination. For the version of possibility theory in which combination is the product t-norm, the compositional model defined here reduces to the one studied by Vejnarová.en_US
dc.publisherElsevieren_US
dc.rightsThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectValuation-based systemsen_US
dc.subjectProbability theoryen_US
dc.subjectPossibility theoryen_US
dc.subjectDempster–Shafer belief function theoryen_US
dc.subjectSpohn’s epistemic belief theoryen_US
dc.subjectConditionalsen_US
dc.titleCompositional Models in Valuation-Based Systemsen_US
dc.typeArticle
kusw.kuauthorShenoy, Prakash P.
kusw.kudepartmentBusinessen_US
dc.identifier.doi10.1016/j.ijar.2013.02.002
dc.identifier.orcidhttps://orcid.org/0000-0002-8425-896X
kusw.oaversionScholarly/refereed, author accepted manuscript
kusw.oapolicyThis item meets KU Open Access policy criteria.
dc.rights.accessrightsopenAccess


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