Fast Inference for Probabilistic Answer Set Programs via the Residual Program

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.

• The paper introduces residual program extraction using SLG resolution to eliminate irrelevant grounding, substantially accelerating PASP inference.
• It leverages well-founded semantics and relevance properties to prune unnecessary computational complexity in probabilistic logic programming.
• Empirical experiments on graph datasets confirm reduced treewidth and faster inference, solving instances that were previously unsolvable within time limits.

Fast Inference for Probabilistic Answer Set Programs via the Residual Program

The paper "Fast Inference for Probabilistic Answer Set Programs via the Residual Program" by Damiano Azzolini and Fabrizio Riguzzi provides a methodological advancement in the field of Statistical Relational Artificial Intelligence. The focus lies on Probabilistic Answer Set Programming (PASP) which marries Answer Set Programming (ASP) with probabilistic reasoning.

Background and Motivation

In many scenarios, the computation of query probabilities from PASPs involves grounding the entire program, a process that is computationally intensive due to the size explosion of grounding. This paper identifies an optimization opportunity: parts of the ASP may not influence the probability of a given query but still contribute to the grounding complexity. Hence, excluding these parts could significantly speed up the inference process.

Contribution: Residual Program Extraction

The paper proposes leveraging the residual program derived via SLG resolution techniques. SLG resolution is used to identify and eliminate parts of the program irrelevant to the probability computation for a specific query. The method hinges on three resolution aspects: the well-founded semantics (WFS), the relevance property of normal programs without odd loops over negation (OLON), and the residual program resulting from SLG resolution with tabling.

1. Well-founded Semantics (WFS): WFS offers a way to deal with incomplete information by providing a three-valued model (true, false, and undefined) that is useful in eliminating irrelevant parts of the program.
2. Relevance Property: ASP without OLON ensures that the truth value of an atom only depends on a relevant sub-graph of the dependency graph. This property justifies excluding parts of the program that are irrelevant to the query.
3. SLG Resolution and Tabling: By using tabling in SLG resolution as implemented in Prolog systems (SWI and XSB), the authors extract the residual program which excludes irrelevant parts.

Empirical Evidence

The empirical validation of the proposed method was conducted using graph datasets in two domains. The results were compelling:

• Fast inference was achieved by querying the residual program, which is often significantly smaller than the original program.
• The extraction time for the residual program was negligible in comparison to the total inference time.
• The overall execution time for computing query probabilities was substantially reduced.

Methodology and Experiments

The experiments were performed on four datasets: reachability and smokers, generated using Barabasi-Albert and grid structures. The paper provided a detailed comparison between direct querying using aspmc and querying after extracting the residual program (aspmc). The following observations were made:

• The extraction of the residual program consistently simplified the problem structure, reducing the average number of decomposition bags and treewidth.
• The approach solved many instances that were otherwise unsolved within the set time limits.

Implications and Future Directions

This work pushes the boundary of efficient probabilistic reasoning in logic programming by reducing the computational overhead associated with grounding. The proposed technique can be integrated into existing ASP solvers and probabilistic programming frameworks to enhance their performance, especially in large and complex domains.

Future developments could explore:

• Extending the technique to other semantics like LPMLN or variants of the stable model semantics.
• Investigating heuristics for faster residual program extraction.
• Applying residual program extraction to dynamic or evolving knowledge bases for continual learning scenarios.

Conclusion

The paper presents a significant technical contribution by optimizing PASP inference through residual program extraction. This method not only shortens computational time but also simplifies the effective management of large programs and complex queries. Thus, the paper offers a valuable enhancement to the toolbox of researchers and practitioners in the domains of artificial intelligence and logic programming.

This research underscores the importance of leveraging advanced resolution techniques and the relevance property of logical programs, demonstrating notable improvements in efficiency and scalability. The results exhibit the practical applicability and theoretical validity of using residual programs, marking a step forward in the field of probabilistic logic programming.