  Weighted model counting (WMC) is a well-known inference task on knowledge
bases, used for probabilistic inference in graphical models. We introduce
algebraic model counting (AMC), a generalization of WMC to a semiring
structure. We show that AMC generalizes many well-known tasks in a variety of
domains such as probabilistic inference, soft constraints and network and
database analysis. Furthermore, we investigate AMC from a knowledge compilation
perspective and show that all AMC tasks can be evaluated using sd-DNNF
circuits. We identify further characteristics of AMC instances that allow for
the use of even more succinct circuits.
