Inference in Probabilistic Logic Programs with Continuous Random
  Variables
  Probabilistic Logic Programming (PLP), exemplified by Sato and Kameya's
PRISM, Poole's ICL, Raedt et al's ProbLog and Vennekens et al's LPAD, is aimed
at combining statistical and logical knowledge representation and inference. A
key characteristic of PLP frameworks is that they are conservative extensions
to non-probabilistic logic programs which have been widely used for knowledge
representation. PLP frameworks extend traditional logic programming semantics
to a distribution semantics, where the semantics of a probabilistic logic
program is given in terms of a distribution over possible models of the
program. However, the inference techniques used in these works rely on
enumerating sets of explanations for a query answer. Consequently, these
languages permit very limited use of random variables with continuous
distributions. In this paper, we present a symbolic inference procedure that
uses constraints and represents sets of explanations without enumeration. This
permits us to reason over PLPs with Gaussian or Gamma-distributed random
variables (in addition to discrete-valued random variables) and linear equality
constraints over reals. We develop the inference procedure in the context of
PRISM; however the procedure's core ideas can be easily applied to other PLP
languages as well. An interesting aspect of our inference procedure is that
PRISM's query evaluation process becomes a special case in the absence of any
continuous random variables in the program. The symbolic inference procedure
enables us to reason over complex probabilistic models such as Kalman filters
and a large subclass of Hybrid Bayesian networks that were hitherto not
possible in PLP frameworks. (To appear in Theory and Practice of Logic
Programming).
