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Computer Science

Parallel ABox Reasoning of ${\mathcal{EL}}$ Ontologies

Profile image of Kevin leeKevin lee

2012, Lecture Notes in Computer Science

https://doi.org/10.1007/978-3-642-29923-0_2
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16 pages

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Abstract

In order to support the vision of the Semantic Web, ontology reasoning needs to be highly scalable and efficient. A natural way to achieve scalability and efficiency is to develop parallel ABox reasoning algorithms for tractable OWL 2 profiles to distribute the load between different computation units within a reasoning system. So far there have been some work on parallel ABox reasoning algorithms for the pD* fragment of OWL 2 RL. However, there is still no work on parallel ABox reasoning algorithm for OWL 2 EL, which is the language for many influential ontologies (such as the SNOMED CT ontology). In this paper, we extend a parallel TBox reasoning algorithm [5] for ELHR+ to parallel ABox reasoning algorithms for ELH ⊥,R+ , which also supports the bottom concept so as to model disjointness and inconsistency. In design of algorithms, we exploit the characteristic of ABox reasonings to improve parallelisation and reduce unnecessary resource cost. Our evaluation shows that a naive implementation of our approach can compute all ABox entailments of a Not-Galen − ontology with about 1 million individuals and 9 million axioms in about 3 minutes.

Key takeaways
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AI

  1. This paper presents a parallel ABox reasoning algorithm for OWL 2 EL ontologies, enhancing scalability.
  2. The evaluation shows a naive implementation computes entailments for 1 million individuals in approximately 3 minutes.
  3. Parallelisation reduces the reasoning time, achieving up to 9 times speedup compared to sequential reasoners.
  4. The algorithms separate TBox and ABox reasoning to optimize efficiency and memory usage.
  5. Optimizing memory access is crucial, as performance gains diminish beyond 4 parallel workers.
Figures (5)
Table 1. ELH 1 z+ Syntax and Semantics
Table 1. ELH 1 z+ Syntax and Semantics
Algorithm 1: saturate(input): saturation of axioms under inference rules In the saturation (Algorithm 1), the activeContexts queue is initialised with an empty set (line 1), and then all input axioms are added into an axiomQueue (line 2). After that, two main loops (lines 3-8 and lines 9-17) are sequentially parallelised. In the first main loop, multiple workers independently retrieve axioms from the ax- iomQueue (line 4), then get the contexts of the axioms (line 6), add the axioms into corresponding scheduled queues (line 7) and activate the contexts.
Algorithm 1: saturate(input): saturation of axioms under inference rules In the saturation (Algorithm 1), the activeContexts queue is initialised with an empty set (line 1), and then all input axioms are added into an axiomQueue (line 2). After that, two main loops (lines 3-8 and lines 9-17) are sequentially parallelised. In the first main loop, multiple workers independently retrieve axioms from the ax- iomQueue (line 4), then get the contexts of the axioms (line 6), add the axioms into corresponding scheduled queues (line 7) and activate the contexts.
Table 2. Ontologies and Results of Sequential Reasoners (in sec)
Table 2. Ontologies and Results of Sequential Reasoners (in sec)
Table 3. Results of PEL (in sec) From the comparison between Table 2 and 3 we can see that PEL is in general faster than sequential reasoners, especially when more workers are used. PEL is also good when dealing with combination of complex TBox and large ABox. For example, in the relatively simpler VICODI ontology, PEL is about 2 times faster than TTOWL, which is also highly optimised for €£ reasoning. While in the more complex NotGalen™ on- tologies with a large ABox, PEL is up to 6 times faster than TrOWL with one worker, and up to about 8-9 times faster with multiple workers.
Table 3. Results of PEL (in sec) From the comparison between Table 2 and 3 we can see that PEL is in general faster than sequential reasoners, especially when more workers are used. PEL is also good when dealing with combination of complex TBox and large ABox. For example, in the relatively simpler VICODI ontology, PEL is about 2 times faster than TTOWL, which is also highly optimised for €£ reasoning. While in the more complex NotGalen™ on- tologies with a large ABox, PEL is up to 6 times faster than TrOWL with one worker, and up to about 8-9 times faster with multiple workers.
Table 4. Results of PEL (in sec) for Scalability Tests viduals. In general, the improvement is most profound from | worker to 2 workers, and start to decrease when more workers are involved. With more than 4 workers, the per- formance may even decrease. We believe one of the the CPU cores can work in parallel, the RAM still sequential. In relatively “light-weight” A for RAM access. This makes memory I/O a potentia potential reasons is that although bandwidth is limited and RAM access is Box reasoning with large ABox, the RAM access will be enormous and very often so that multi ple workers will have to compete bottleneck of parallelisation and wastes CPU cycles. In our algorithm, especially the cascading processing, we have al- ready tried to reduce unnecessary memory I/O. A better management of memory will be an important direction of our future work.
Table 4. Results of PEL (in sec) for Scalability Tests viduals. In general, the improvement is most profound from | worker to 2 workers, and start to decrease when more workers are involved. With more than 4 workers, the per- formance may even decrease. We believe one of the the CPU cores can work in parallel, the RAM still sequential. In relatively “light-weight” A for RAM access. This makes memory I/O a potentia potential reasons is that although bandwidth is limited and RAM access is Box reasoning with large ABox, the RAM access will be enormous and very often so that multi ple workers will have to compete bottleneck of parallelisation and wastes CPU cycles. In our algorithm, especially the cascading processing, we have al- ready tried to reduce unnecessary memory I/O. A better management of memory will be an important direction of our future work.

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