Lifted inference for statistical statements in probabilistic answer set programming

In 1990, Halpern proposed the distinction between Type 1 and Type 2 statements: the former express statistical information about a domain of interest while the latter define a degree of belief. An example of Type 1 statement is “30% of the elements of a domain share the same property” while an example of Type 2 statement is “the element x has the property y with probability p”. Recently, Type 1 statements were given an interpretation in terms of probabilistic answer set programs under the credal semantics in the PASTA framework. The algorithm proposed for inference requires the enumeration of all the answer sets of a given program, and so it is impractical for domains of not trivial size. The field of lifted inference aims to identify programs where inference can be computed without grounding the program. In this paper, we identify some classes of PASTA programs for which we apply lifted inference and develop compact formulas to compute the probability bounds of a query without the need to generate all the possible answer sets.