In the first part of this book, we introduce a generic algebraic framework that encompasses and unifies a large number of such formalisms. This formalism, called the Plausibility-Feasibility-Utility (PFU) framework, is based on algebraic structures, graphical models, and sequences of quantifications. This work on knowledge representation is completed by a work on algorithms for answering queries formulated in the PFU framework. The algorithms defined are based on variable elimination or tree search, and work on a new generic architecture for local computations called multi-operator cluster DAGs.