We propose a technique that combine an OWL 2 EL reasoner with an OWL 2 reasoner to classify expressive ontologies. We exploit the information implied by the ontology structure to identify a small non-EL ontology that contains necessary axioms to ensure the completeness. In the process of ontology classification, the bulk of workload is delegated to an e cient OWL 2 EL reasoner and the small part of workload is handled by a less e cient OWL 2 reasoner. Experimental results show that our approach leads to a reasonable task assignment and o ers a substantial speedup in ontology classification.
EL to a large degree, e.g., of the 226038 axioms in the version V14.03e of NCI ontology,
only 67 are outside the OWL 2 EL fragment. The tableau-based OWL 2 reasoners are
able to reasoning such ontologies, but they are not e cient due to the high complexity
of tableau algorithms for expressive ontologies. The profile-specific OWL 2 EL
reasoners are e cient, but they become incomplete if the ontologies contain axioms that
are outside the OWL 2 EL fragment. Recently, new approaches have been proposed
to improve the reasoning performance for expressive ontologies by combining di
erent reasoners [
captures all the knowledge about a specified signature . The ?-module is one basic
type of locality-based modules (LBMs) and enjoys the following property that can be
used for optimising classification [
module due to the strong logical interrelation among axioms, such axioms that “cling
together” is formalised by the notion of atom [
of atoms of O is denoted by AD?O. For each atom at 2 AD?O, the module M? is denoted at by Mat and the dependent relation between atoms is induced as follows: e Definition 2. Let at1 and at2 be two atoms in AD?O, at1 is dependent on at2 (written at1 at2) if Mat2 Mat1 .
O
union of all atoms on which a given atom at depends is called principal ideal of at ( denoted by (at] ).
Proposition 2. [
An atom ati is called a top atom if there exists no a distinct atom at j such that ati. Hence an ontology O is the union of several independent modules: O = [ f(tat] j tat is a top atomg (1) 3
AD represents the modular structure of an ontology, the information implied by this structure (especially Proposition 2, Proposition 3, and Equation 1) provide us with two important clues for optimising modular classification: Firstly, for two distinct atoms at1 and at2 with at1 at2, (at2] is enough to completely classify all the classed in the module (at2]. Secondly, if not each top atom contains non-EL axioms, it is possible to identify a small non-El module and delegate it to an OWL 2 reasoner for computing the subsumption relation of the following form: (1) A v B (2) A u B v C (3) A v
AR.classify(MEL) //classifying the non-EL subontology MR.classify(HMEL [ O n MEL)
Output: HO: the classification of O 1: MEL ;, HMEL ;, HO ; 2: for each 2 S na do 3: if < MEL then 4: MEL MEL S M 5: end if 6: end for 7: if MEL = O then 8: HO AR.classify(O) 9: else 10: HMEL 11: HO 12: end if 13: return HO 9R:B (4) 9R:A v B (5) R v S (6) A u 9R:B v C (7) 9R:A u 9S :B v C where A, B, and C are atomic concepts or >, and R; S atomic roles. Obviously, these subsumption relations fall into OWL 2 EL. Hence, the computed subsumption relations together with the remaining EL part can be handled by an OWL 2 EL reasoner to obtain complete classification. Let S na be the set of non-EL axioms in an ontology, Algorithm
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reasoner and OWL 2 EL reasoner are integrated in a black-box manner. We conduct an experiment on eight commonly used ontologies available from the NCBO BioPortal ontology repository 5. Table 1 provides statistics of test ontologies and Table 2 shows the experimental results compared with MORe. In Table 2, MMORe (resp. MEL) represents the non-EL subontology that is delegated to the OWL 2 reasoner in MORe (resp. SGMR), and TMORe (resp. TS GMR) represents the time (in seconds) spent in classifying the whole ontology by MORe (resp. SGMR). In our experiments, ELK 0.4.1 and HermiT 1.3.86 are used as OWL 2 EL reasoner and OWL 2 reasoner, respectively. The experimental results show that SGMR delegates a smaller part of workload to the ine cient
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Ontology MMORe TMORe
SYN 187 (1.2% ) 12.6 CSEO 8,693 (32.8% ) 20.3 Galen 35,976 (95.4% ) 25.4 Dermlex 18,347 (75.0% ) 17.2 Protein 3,972 (8.5% ) 12.6
NCI 33,760 (15.4% ) 104.6 UBERON 14,906 (30.5% ) 76.4
EFO 7,348 (29.2% ) 64.2
MEL TS GMR 27 (0.8%) 5.1 94 (0.4% ) 4.7 2,165 (5.7% ) 3.5 8,219 (33.6% ) 3.7 288 (0.6% ) 1.7 7,151 (3.3% ) 17.2 12,988 (26.6% ) 31.4 897 (3.6% ) 21.3 not need to represent an ontology in the decomposed form. Compared with MORe, our approach delegates a smaller workload to the less e cient OWL 2 reasoner hence o ers a substantial speedup in ontology classification.
search and Development Program of China (2016YFB1000603) and the National Natural Science Foundation of China (NSFC) (61502336, 61373035). Xiaowang Zhang is supported by Tianjin Thousand Young Talents Program.