Approximate Inference in Probabilistic Answer Set Programming for Statistical Probabilities

Type 1 statements were introduced by Halpern in 1990 with the goal to represent statistical information about a domain of interest. These are of the form ''x of the elements share the same property''. The recently proposed language PASTA (Probabilistic Answer set programming for STAtistical probabilities) extends Probabilistic Logic Programs under the Distribution Semantics and allows the definition of this type of statements. To perform exact inference, PASTA programs are converted into probabilistic answer set programs under the Credal Semantics. However, this algorithm is infeasible for scenarios when more than a few random variables are involved. Here, we propose several algorithms to perform both conditional and unconditional approximate inference in PASTA programs and test them on different benchmarks. The results show that approximate algorithms scale to hundreds of variables and thus can manage real world domains.