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{KimmigJAL16,
  author = {Kimmig, Angelika and Van den Broeck, Guy and De Raedt, Luc},
  title = {Algebraic Model Counting},
  journal = {International Journal of Applied Logic},
  month = Nov,
  year = {2016},
  url = "http://starai.cs.ucla.edu/papers/KimmigJAL16.pdf",
  doi = "10.1016/j.jal.2016.11.031",
  keywords   = {journal}
}