Ontology Refinement System for Improving Consistency of Classification among Brother Concepts Takeshi Masuda, Kouji Kozaki, Kazunori Komatani The Institute of Scientific and Industrial Research, Osaka University Abstract. The consistency of classification is an indicator of ontologies’ quality. In this paper, we focus on the consistency among brother concepts and develop a refinement system that finds inconsistent parts from a target ontology and pro- pose methods to make such parts consistent. To find inconsistent parts and make proposals, the system compares a slot hierarchy and other two hierarchies that have reference relationship to the slot hierarchy. 1 Introduction Nowadays, ontologies are constructed in various fields such as medical information, mechanical design and so on. These ontologies are used as a schema of knowledge models for application systems. Therefore a construction of better quality ontology is a considerable issue. However, both experience of ontology construction and expertise in the target domain are required to build well organized ontologies. Therefore, it is not easy for beginners to construct good ontologies. Because of these backgrounds, there are some systems that correct some formal errors in ontology and these are embedded in ontology editor like Protégé [1, 2, 3]. While in the case of quality improvement, we have to investigate each concept to check whether the concept should be refined or not. Therefore, we aim to develop the Ontology Refinement support system. 2 Ontology Refinement by Comparing Is-a Hierarchies 2.1 Similarity among Is-a Hierarchies In order to develop a refinement method, we focus on an ontology development guideline that “Each subclass of a super class is distinguished by the values of exactly one attribute of the super class. [4]”, and found the interesting characteristic of among is-a hierarchies under the guideline. We found that conceptual structures are similar to other is-a hierarchies in ontologies which follow the guideline. For example, in Fig.1, these 3 hierarchies, “Basic Concept Hierarchy”, “Slot Hierarchy” and “Referred Con- cept Hierarchy”, are following guideline and then their structure are similar. In this paper, our refinement system compare these 3 hierarchies and detect un-similar parts as a refinement candidates and make proposals to add new concepts for each candidates. Basic Concept Hierarchy Basic Concept Hierarchy Vehicle B BM1 B_BR1 Carriage Movement S Space Movement Ground Space Natural Area Area of BM2 BL1 Airplane refinement SL1 Movement candidate reference Space BL2 Reference Air at the previous B_BR2 SL2 method Slot Hierarchy Reference R RM1 RL1 reference Natural Area Ground R_BR1 RL2 Referred Concept Hierarchy R_BR4 R_BR2 Referred Concept Hierarchy Air R_BR3 Fig.1 similarity among is-a hierarchy Fig.2 Comparing Brother Concepts 2.2 Comparing among Brother Concepts In our previous method [5], we compared 3 hierarchies but it is only use super-sub relations whereas in this paper, we also consider comparing among brother concepts’ hierarchies. To compare these 3 hierarchies with brother concepts, we focus on “Slot Hierarchy” as a basis. “Slot Hierarchy” consists of a certain slot “S” and its lower slots “SLm” (m = 1 ~ M, M is a number of lower slots). These lower slots are specialized only once from “S”. In this case, “Basic Concept Hierarchy” consists of concepts that has slots in slot hierarchy (“B”, “BLm”), these brother concepts (“B_BRx”, x = 1~ X, X is a number of brother concepts.) and middle concepts (“BMa”, a = 1~ A, A is a number of middle concepts.) (Fig.2.). “Referred Concept Hierarchy” consists likewise. 2.3 Patterns of Refinement Candidates Comparing 3 hierarchies like Fig.2, if there are no brother concepts (B_BRx, R_BRy) that did not have (or be referred from) “Sm”, these 3 hierarchies are not similar. So we can classify patterns of refinement candidate by existence of B_BRx or R_BRy. To sum up, patterns of refinement candidate are the following four. (i) X > 0 and Y > 0, (ii) X = 0 and Y > 0, (iii) X > 0 and Y = 0, (iv) X = 0 and Y = 0. (X is a number of bother concepts in “Basic Concept Hierarchy, Y is a number of bother concepts in “Referred Concept Hierarchy”. We do not make any proposals for (iv) because it is already simi- lar.) 2.4 Limitations on Refinement Proposals In our refinement method, refinement proposals are 3 types as follows. A corre- spondence between refinement candidates and proposals are shown at Table.1. (a). add new Slot (b). add new concept to Basic Concept Hierarchy and new Slot (c). add new concept to Referred Concept Hierarchy and new Slot Table.1. correspondence between refinement candidates and proposals Concept Where to Acceptable A number of chosen as add new slot Candidate Type proposals class constraint a 1 R_BRy (i) X*Y B_BRx 2 R_Lm (i), (iii) X*M b 1 New concept R_BRy (i), (ii) X(not leaf)*Y 2 in BCH Rn_Lm (i), (ii), (iii) X(not leaf)*M New concept (i), (iii) Y(not leaf)*X c 1 B_BRx in RCH BCH : basic concept hierarchy, RCH : referred concept hierarchy B_BRx: brother concepts that donʼt have slot (x︓1..X) R_BRy: brother concepts that are not referred (y︓1..Y) M︓a number of referred concepts At this comparison with brother concept hierarchies, a number of refinement pro- posal become enormous. Because there are much more comparison concepts in brother concepts hierarchies than comparison among upper and lower concepts. For example, I assume that some numbers M = 2 (lower slot of “S”), X = 40 (brother concept in basic concept hierarchy “B_BRx”) and number of leaf concepts is 18, Y = 3 (brother concept in referred concept hierarchy R_BRy) and number of leaf concepts is 2. This example is X > 0 and Y > 0, then candidate type is (i). From table.1, all proposals, a1 ~ c1, are suggested. Therefore total number of proposals for this example is 328. This number is quite large to consider as refinement proposal, even this example has a few brother concept in referred concept hierarchy. If there are same number of brother concepts in referred concept hierarchy, a number of proposals can be over a thousand per a candi- dates. For the above reasons, we consider 2 limitations on refinement proposals. limitation1: Compare brother concepts that have same parents limitation2: Compare brother concepts that are specialized same level. 3 Evaluation 3.1 Evaluation Methods We conducted a pre-experience to evaluate this refinement proposal method. We use a race ontology that is made by author and this ontology contains 213 concepts. This experience was designed to asses 2 points: (1) how many appropriate candidates are detected and (2) how the 2 limitations work. 3.2 Results and Discussions (1) How many appropriate candidates are detected. Table.2 shows the result. By previous method, 149 candidates are detected and 18% are proposed correctly. While by new method, 11 candidates are detected and 63% are proposed appropriately. Both new and previous method’s candidates are not repeated. However average number of proposals are 1154, which is too much to consider. (2) How the 2 limitations work Table.3 shows the result. By “limitation1”, average number of proposals decreased to 13, it is 100 times fewer than no limitation. In this case, 4 candidates still have correct proposal under “limitation 1”, but 3 candidates cannot be proposed any suggestions.. While by “limitation 2”, average proposals also decreased to 377 but it is still enormous to see. But it has 5 correct candidates, it is better than “limitation1”. Table.2. Comparison between previous and new refinement method All A number of Candidates A percentage of Candidates Average number of candidates that have correct proposals that have correct proposals proposals Previous method 149 27 18% 7 New method 11 7 63％ 1154 Table.3. Result of the 2 limitations All Candidates Candidates Average number of Candidates that have correct proposals that donʼt have any proposals proposals No limitation 7 7 0 1154 Limitation 1 7 4 3 13 Limitation 2 7 5 2 377 4 Conclusion In this paper, we focus on similarity among brother concepts’ hierarchies. However a number of refinement proposals are drastically increased by the explosion of combi- nation. Then we provide 2 types of limitations to prevent this explosion. As a result, we could improve an accuracy of proposals and suppress the number of proposals. In future work, we consider some refinement candidates that we cannot make any proposal and integrate the previous refinement method and the new refinement method. Acknowledgements This work was supported by JSPS KAKENHI Grant Numbers JP25280081, JP 26240033, JP24120002. References 1. [Sirin 07] Sirin, E., Parsia, B., Grau, B. C., Kalyanpur, A., and Katz, Y.: Pellet: A practical owl-dl reasoner, Web Semantics: science, services and agents on the World Wide Web, Vol. 5, No. 2, pp.51–53 (2007) 2. [Horridge 11] Horridge, M.: Justification based explanation in ontologies, PhD thesis, Uni- versity of Manchester (2011) 3. [Noy 01] Noy, N. F., Sintek, M., Decker, S., Crub´ezy, M., Fergerson, R. W., and Musen, M. A.: Creating Semantic Web Contents with Prot´eG´e-2000, IEEE Intelligent Systems, Vol. 16, No. 2, pp. 60–71 (2001) 4. [Mizoguchi 06] Tutorial on ontological engineering - Part 2: Ontology development, tools and languages New Generation Computing, OhmSha & Springer, 22(1), pp.61-96 (2004) 5. [Masuda 15] Masuda, T., Kozaki, K., Komatani, K. : Evaluation of Method to Improve On- tology Consistency based on Similarities among is-a Hierarchies in Referring Relation, JSAI2015, 2M1-3,2015.