Fast Inference for Probabilistic Answer Set Programs via the Residual Program

TL;DR

This paper tackles the costly grounding step in Probabilistic Answer Set Programming (PASP) by leveraging SLG resolution to extract a residual program that preserves only the parts of the original program essential to a given query. The key idea is to translate PASP into a normal program under Well-founded Semantics, compute the residual via SLG/tabling, and then solve the reduced PASP to obtain the probability bounds, with theoretical guarantees that upper and lower probabilities are preserved. The authors demonstrate that residual-program extraction dramatically reduces grounding size and speeds up inference on graph-structured datasets, with empirical results showing substantial improvements over using the full program. This approach offers a practical path to scalable probabilistic reasoning in PASP and can be integrated with existing ASP solvers to accelerate probabilistic queries in SRL-like domains.

Abstract

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.

Figures (3)

• Figure 1: Programs, call graphs (CD), and dependency graphs (DG) with (Figure \ref{['subfig:olon']}) and without (Figure \ref{['subfig:no_olon']}) OLON. The dependency graph of both programs is the same. They only differ in the call graph: for the left program, the call graph contains an edge labeled with $-$ (negative) while for the right program the same edge is labeled with $+$ (positive).
• Figure 2: Cactus plot for aspmc and $\mathrm{aspmc}^r$ with 100, 300, and 500 seconds of time on the smokersGrid and smokersBA datasets.
• Figure 3: Cactus plot for aspmc and $\mathrm{aspmc}^r$ with 100, 300, and 500 seconds of time limit on the reachGrid and reachBA datasets.

Theorems & Definitions (11)

• Example 1
• Example 2
• Example 3
• Example 4
• Definition 1
• Lemma 1
• proof
• Theorem 1
• proof
• Theorem 2