0573509 20240402214138.420230712235959.9 85165538154 001048425800001 10.1016/j.ijar.2023.108976 15 s. P cav_un_epca*02567740888-613X160Elsevier Dempster-Shafer theory of belief functions Conditional belief functions Smets' conditional embedding Belief-function directed graphical models cav_un_auth*0101118 Jiroušek Radim UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0216188 Kratochvíl Václav UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory CZ Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0275452 Shenoy P. P. US http://library.utia.cas.cz/separaty/2023/MTR/jirousek-0573509.pdf https://www.sciencedirect.com/science/article/pii/S0888613X2300107X?via%3Dihub GA21-07494S GA ČR CZ cav_un_auth*0430801 The primary goal is to define conditional belief functions in the Dempster-Shafer theory. We do so similarly to probability theory's notion of conditional probability tables. Conditional belief functions are necessary for constructing directed graphical belief function models in the same sense as conditional probability tables are necessary for constructing Bayesian networks. We provide examples of conditional belief functions, including those obtained by Smets' conditional embedding. Besides defining conditional belief functions, we state and prove a few basic properties of conditionals. In the belief-function literature, conditionals are defined starting from a joint belief function. Conditionals are then defined using the removal operator, an inverse of Dempster's combination operator. When such conditionals are well-defined belief functions, we show that our definition is equivalent to these definitions. WOS BA 10000 10100 10102 2024 3 RVO:67985556 https://hdl.handle.net/11104/0344419 S 108976 Article Computer Science Artificial Intelligence A COMPUTERSCIENCE.ARTIFICIALINTELLIGENCE 3.2 0.7 6.3 0.00458 0.75 5066 116 0.877 47.31 3.74 1655 Q1 2.600 155 Q2 57.6 Q3 Q2 1.02 Q2 57.6 2023 85165538154 SCOPUS PUBMED 001048425800001 WOS cav_un_epca*0256774 International Journal of Approximate Reasoning 160 1 2023 0888-613X 1873-4731 Elsevier