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.

@article{KimmigAMC12,
  author = "Kimmig, Angelika and Van den Broeck, Guy and De Raedt, Luc",
  title     = "Algebraic Model Counting",
  journal   = "CoRR",
  volume    = "abs/1211.4475",
  year      = "2012",
  url       = "http://starai.cs.ucla.edu/papers/KimmigAMC12.pdf",
  keywords   = {techreport}
}