Stable Model Counting and Its Application in Probabilistic Logic Programming

TL;DR

This paper introduces efficient methods for stable model counting in probabilistic logic programming, significantly improving inference performance for problems involving inductive definitions like graph reachability.

Contribution

It presents novel implementation techniques based on unfounded set detection that extend propositional model counters to stable model counters, enabling more efficient inference.

Findings

Outperforms state-of-the-art solvers by several orders of magnitude in speed.

Handles larger problem instances that current solvers cannot solve due to resource limits.

Demonstrates significant improvements in time and space efficiency for specific problem classes.

Abstract

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.