Distributional logic programming for Bayesian knowledge representation

We present a formalism for combining logic programming and its flavour of nondeterminism with probabilistic reasoning. In particular, we focus on representing prior knowledge for Bayesian inference. Distributional logic programming (Dlp), is considered in the context of a class of generative probabilistic languages. A characterisation based on probabilistic paths which can play a central role in clausal probabilistic reasoning is presented. We illustrate how the characterisation can be utilised to clarify derived distributions with regards to mixing the logical and probabilistic constituents of generative languages. We use this operational characterisation to define a class of programs that exhibit probabilistic determinism. We show how Dlp can be used to define generative priors over statistical model spaces. For example, a single program can generate all possible Bayesian networks having N nodes while at the same time it defines a prior that penalises networks with large families. Two classes of statistical models are considered: Bayesian networks and classification and regression trees. Finally we discuss: (1) a Metropolis-Hastings algorithm that can take advantage of the defined priors and the probabilistic choice points in the prior programs and (2) its application to real-world machine learning tasks.