### Infinite probability computation by cyclic explanation graphs

Taisuke Sato, Tokyo Institute of Technology

Philipp Meyer, Technical Univeristy Munich

### Abstract

Tabling in logic programming has been used to eliminate redundant computation and also to stop infinite loop. In this paper we investigate another possibility of tabling, i.e. to compute an infinite sum of probabilities for probabilistic logic programs. Using PRISM, a logic-based probabilistic modeling language with a tabling mechanism, we generalize prefix probability computation for probabilistic context free grammars (PCFGs) to probabilistic logic programs. Given a top-goal, we search for all proofs with tabling and obtain an explanation graph which compresses them and may be cyclic. We then convert the explanation graph 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 general approach to prefix probability computation through tabling not only allows to deal with non-PCFGs such as probabilistic left-corner grammars (PLCGs) but has applications such as plan recognition and probabilistic model checking and makes it possible to compute probability for probabilistic models describing cyclic relations.