When we want to compute the probability of a query from a Probabilistic Answer Set Program, some parts of a program may not influence the probability of a query, but they impact on the size of the grounding. Identifying and removing them is crucial to speed up the computation. Algorithms for SLG resolution offer the possibility of returning the residual program which can be used for computing answer sets for normal programs that do have a total well-founded model. The residual program does not contain the parts of the program that do not influence the probability. In this paper, we propose to exploit the residual program for performing inference. Empirical results on graph datasets show that the approach leads to significantly faster inference. The paper has been accepted at the ICLP2024 conference and under consideration in Theory and Practice of Logic Programming (TPLP).

Model counting is the problem of computing the number of models that satisfy a given propositional theory. It has recently been applied to solving inference tasks in probabilistic logic programming, where the goal is to compute the probability of given queries being true provided a set of mutually independent random variables, a model (a logic program) and some evidence. The core of solving this inference task involves translating the logic program to a propositional theory and using a model counter. In this paper, we show that for some problems that involve inductive definitions like reachability in a graph, the translation of logic programs to SAT can be expensive for the purpose of solving inference tasks. For such problems, direct implementation of stable model semantics allows for more efficient solving. We present two implementation techniques, based on unfounded set detection, that extend a propositional model counter to a stable model counter. Our experiments show that for particular problems, our approach can outperform a state-of-the-art probabilistic logic programming solver by several orders of magnitude in terms of running time and space requirements, and can solve instances of significantly larger sizes on which the current solver runs out of time or memory.