[Paper Review] Optimizing the computation of overriding

Piero A. Bonatti, Iliana M. Petrova+1 more|arXiv (Cornell University)|Jul 16, 2015

Logic, Reasoning, and Knowledge27 references6 citations

TL;DR

This paper presents two optimization techniques—module extraction and optimistic reasoning—for accelerating query answering in nonmonotonic description logic $π\mathcal{DL}^N$, significantly improving performance on large knowledge bases. The methods reduce response times by over an order of magnitude, enabling real-time reasoning on KBs with more than 30,000 axioms.

ABSTRACT

We introduce optimization techniques for reasoning in DLN---a recently introduced family of nonmonotonic description logics whose characterizing features appear well-suited to model the applicative examples naturally arising in biomedical domains and semantic web access control policies. Such optimizations are validated experimentally on large KBs with more than 30K axioms. Speedups exceed 1 order of magnitude. For the first time, response times compatible with real-time reasoning are obtained with nonmonotonic KBs of this size.

Motivation & Objective

• To address the performance bottleneck in $π\mathcal{DL}^N$ reasoning when scaling to large knowledge bases with over 30,000 axioms.
• To reduce query response times in nonmonotonic reasoning, which currently hinder real-time deployment despite $π\mathcal{DL}^N$'s tractability and applicability to biomedical and access control domains.
• To develop sound and complete optimization techniques that preserve the logical properties of $π\mathcal{DL}^N$, such as no inheritance blocking and prototype consistency.
• To validate the effectiveness of these optimizations on large, realistic KBs, including synthetic and real-world ontologies.
• To enable practical deployment of nonmonotonic reasoning by achieving response times compatible with real-time systems.

Proposed method

• The paper introduces a module extraction technique based on dependency analysis to restrict reasoning to only the axioms relevant to a given query, reducing computational overhead.
• It proposes an optimistic reasoning algorithm that minimizes costly axiom deletions by reusing previous reasoning results, leveraging incremental reasoning capabilities.
• The method combines module extraction with optimistic reasoning to further reduce response times, particularly effective in N-free knowledge bases.
• The approach is formally proven sound and complete for $π\mathcal{DL}^N$, ensuring correctness while improving efficiency.
• The optimizations are evaluated using synthetic and real-world KBs, including those derived from the Gene Ontology, with varying ratios of defeasible inclusions and normality concepts.
• The implementation uses the OWLAPI and is publicly available, enabling reproducibility and further benchmarking.

Experimental results

Research questions

• RQ1 Can module extraction be soundly applied to nonmonotonic description logics like $π\mathcal{DL}^N$, despite known unsoundness in other nonmonotonic logics?
• RQ2 How can incremental reasoning be optimized in $π\mathcal{DL}^N$ to reduce the cost of axiom deletions during query processing?
• RQ3 To what extent can the combination of module extraction and optimistic reasoning improve response times in large-scale $π\mathcal{DL}^N$ KBs?
• RQ4 What performance gains are achievable on real-world and synthetic KBs with more than 20,000 concept names and 30,000 axioms?
• RQ5 Can the optimizations achieve real-time response times for nonmonotonic reasoning at scale, particularly in biomedical and access control applications?

Key findings

• The combined optimization of module extraction and optimistic reasoning achieved speedups exceeding one order of magnitude, with some cases reaching up to 780 times faster response times.
• For KBs with 15% defeasible inclusions, the optimized method reduced average response time from over 90 seconds (naive) to under 0.32 seconds, even with 30% DIs.
• In N-free KBs, the module-based method alone reduced response times from over 30 minutes (naive) to under 40 seconds, even with 250 normality concepts.
• The optimistic reasoning method was particularly effective in reducing the number of axiom deletions, improving performance on dynamic KBs.
• Even with complex role range restrictions involving normality concepts, most queries completed in under 2 seconds, with only a few cases exceeding 40 seconds.
• The results demonstrate, for the first time, that real-time reasoning is feasible with nonmonotonic KBs of this scale, enabling practical deployment in biomedical and semantic web applications.