Measure Theoretic Weighted Model Integration
  Weighted model counting (WMC) is a popular framework to perform probabilistic
inference with discrete random variables. Recently, WMC has been extended to
weighted model integration (WMI) in order to additionally handle continuous
variables. At their core, WMI problems consist of computing integrals and sums
over weighted logical formulas. From a theoretical standpoint, WMI has been
formulated by patching the sum over weighted formulas, which is already present
in WMC, with Riemann integration. A more principled approach to integration,
which is rooted in measure theory, is Lebesgue integration. Lebesgue
integration allows one to treat discrete and continuous variables on equal
footing in a principled fashion. We propose a theoretically sound measure
theoretic formulation of weighted model integration, which naturally reduces to
weighted model counting in the absence of continuous variables. Instead of
regarding weighted model integration as an extension of weighted model
counting, WMC emerges as a special case of WMI in our formulation.
