  Statistical relational AI and probabilistic logic programming have so far
mostly focused on discrete probabilistic models. The reasons for this is that
one needs to provide constructs to succinctly model the independencies in such
models, and also provide efficient inference.
  Three types of independencies are important to represent and exploit for
scalable inference in hybrid models: conditional independencies elegantly
modeled in Bayesian networks, context-specific independencies naturally
represented by logical rules, and independencies amongst attributes of related
objects in relational models succinctly expressed by combining rules.
  This paper introduces a hybrid probabilistic logic programming language, DC#,
which integrates distributional clauses' syntax and semantics principles of
Bayesian logic programs. It represents the three types of independencies
qualitatively. More importantly, we also introduce the scalable inference
algorithm FO-CS-LW for DC#. FO-CS-LW is a first-order extension of the
context-specific likelihood weighting algorithm (CS-LW), a novel sampling
method that exploits conditional independencies and context-specific
independencies in ground models. The FO-CS-LW algorithm upgrades CS-LW with
unification and combining rules to the first-order case.
