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 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.
