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 propose 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.
2.1
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 Concept 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 Carriage
Movement Space
Natural Area Natural Area
Vehicle
Movement
Space Airplane
Movement Space
Ground
Air Ground
Air Slot Hierarchy
Reference Referred Concept Hierarchy
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
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 similar.) 2.4
In our refinement method, refinement proposals are 3 types as follows. A correspondence between refinement candidates and proposals are shown at Table.1. (a). (b). (c).
add new Slot add new concept to Basic Concept Hierarchy and new Slot add new concept to Referred Concept Hierarchy and new Slot
At this comparison with brother concept hierarchies, a number of refinement proposal 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 candidates. 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.
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: (
(
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.
No limitation Limitation 1
Limitation 2 4
(
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”.
Previous method
In this paper, we focus on similarity among brother concepts’ hierarchies. However a number of refinement proposals are drastically increased by the explosion of combination. 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.
This work was supported by JSPS KAKENHI Grant Numbers JP25280081, 26240033, JP24120002.
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