Tabling for infinite probability computation

Abstract

Tabling in logic programming has been used to eliminate redundant computation and also to stop infinite loop. In this paper we add  the third usage of tabling, i.e. to make infinite computation possible  for probabilistic logic programs. Using PRISM, a logic-based probabilistic modeling language with a tabling mechanism,  we generalize prefix probability computation for PCFGs to probabilistic logic programs. Given a top-goal, we search for all SLD proofs
by tabled  search regardless of whether  they contain loop or not. We then convert them to a set of linear probability equations and solve them by matrix operation. The solution gives us the probability of the top-goal, which, in nature, is an infinite sum of probabilities. Our generalized approach to prefix probability computation through tabling opens a way to logic-based probabilistic modeling of cyclic dependencies.