Probabilistic reasoning with terms

Many problems in artificial intelligence can be naturally approached by generating and manipulating probability distributions over structured objects. First-order terms such as lists, trees and tuples and nestings thereof can represent individuals with complex structure in the underlying domain, such as sequences or molecules. Higher-order terms such as sets and multisets provide additional representational flexibility. In this paper we present two Bayesian approaches that employ such probability distributions over structured objects: the first is an upgrade of the well-known naive Bayesian classifier to deal with first-order and higher-order terms, and the second is an upgrade of propositional Bayesian net- works to deal with nested tuples.