NOMSA: Automated modularisation for abstraction modules

Abstract

Large and complex ontologies lead to di culty in usage by humans and causes processing problems with software agents. Modularity has been proposed to address this problem. Current methods and tools can be used to create only some of the existing types of required modules. To augment options for modularisation, we present novel methods to create ve types of abstraction modules: axiom abstraction, vocabulary abstraction, high-level abstraction, weighted abstraction, and feature expressiveness. They have been implemented in the novel tool NOMSA for automated modularisation, which also o ers a GUI.

Introduction

Modularisation methods

We focus on designing algorithms to match those modularisation options that do not have any means of realising them, as was observed in an existing evidencebased ontology modularisation framework [ 4 ]. In particular, there are ve types of abstraction modules that are fall short with respect to algorithms and implementations, which we summarise here and are illustrated afterward. { Axiom abstraction Axiom abstraction generates a module without complex relations between classes; therefore, the technique decreases the mesh structure of the ontology (if present) and makes it a `bare' taxonomy of classes and unused object properties. { Vocabulary abstraction Applying this abstraction to an ontology generates a module where a certain vocabulary element is removed from the ontology, or a whole group of elements is removed (e.g., all data types, if present). { High-level abstraction generates a module where entities at a higher level in the hierarchy are regarded more important than others. This introduces the notion of desired depth to specify in the abstraction process. { Weighted abstraction deals with removing entities from an ontology that are deemed less important than others by assigning weight to the classes, properties, and individuals in an ontology. We determine importance by assessing entities that other entities are highly dependent on. For instance, in the pizza ontology, the class TomatoTopping is the most widely used, being referenced 61 times by other entities. Of course, what is used `often' and what is `less important' may be relative and thus depend on the ontology. Therefore, the weighted abstraction includes a user-de nable threshold, which may be absolute or relative. { Feature expressiveness modules deal with removing some axioms of the ontology based on the language features, e.g., cardinality constraints, disjointness, object property features etc. By manipulating complex constructs of the ontology language features, the feature expressiveness algorithm results in a simpli ed model of the ontology. We have designed 7 rules for this. The algorithm takes these 7 rules, and removes them, from the least important to the most important. At each rule removal, a `layer' of the ontology is produced where that ontology is represented in a language of lower expressivity than the previous layer. Once the algorithm is complete, seven modules (layers) are produced, each having a lower level of expressivity than the previous. We summarise the seven rules here, with the type of axioms that are to be removed. R1: Quali ed cardinality deals with cardinality constraints between classes and properties. R2: Domain and range pertains to axioms that have been speci ed using domain and range for object properties. R3: Object property characteristics are those axioms pertaining to logical characteristics of object properties such as symmetry and transitivity. R4: Disjointness are those axioms pertaining to the disjointness of classes. R5: Assertions are those axioms that are assertions between individuals and classes, or properties. R6: Atomic equivalence and equality are those axioms that state equivalence between entities. R7: Complex classes are those axioms that contain intersection and union logical operators.

Consider the axioms in a toy Burger ontology in Fig. 1 (entity declaration axioms omitted). Running axiom abstraction on this ontology would remove the axioms numbered 4, 10, and 24-28, for they involve object properties of classes. For vocabulary abstraction there are several options. Let us remove all the instances, as most ontologies focus on the TBox anyway. This would remove the axioms numbered 30-33 and as knock-on e ect, also axiom numbers 29 and 36. The high level abstraction is, perhaps, not of much interest in this sample ontology, for there are few hierarchies. Setting the depth at level 1 is the only way to actually have something removed, as there are only two levels. This would remove all the types of burgers, of buns, and of llings, i.e., the axioms numbered 2, 3, 5-13, and 15-21.

To generate a weighted abstraction module, let us assume we wish to create a module whereby we remove 25% of the entities. To achieve this, we set the threshold value to 25%. The threshold value represents an amount of the ontology that is to be removed. First we weigh each class in the ontology with its number of referencing axiom. Thereafter, 25% of the classes with the lowest values are removed (amounting to 5), as displayed in Table 1. That is, the classes that are deemed least important are those with the lowest number of referencing axioms; e.g., WhiteBun is only referred to in axioms 19 and 21, whereas Filling is referred to in axioms 4, 6, 12, 16, 17, hence, WhiteBun is removed. We omit the feature abstraction illustration due to space limitations. 3

Implementation of NOMSA

To solve the problem of manual modularisation, we have created the tool NOMSA to modularise ontologies, which incorporates the ve abstraction algorithms. NOMSA allows the user to upload an ontology (including any imports), and select an approach to modularise it. Each approach is satis ed by a novel algorithm which correspond to the abstractions described in Sect. 2. The algorithms are available as online supplementary material (http://www.thezfiles.co.za/ modularisation). NOMSA is a stand-alone application that can be downloaded from the aforementioned URL as well as a screencast.

We have evaluated the algorithms on 128 ontologies. All the generated modules are notably di erent from the source ontologies, as is the case also for the Burger example (see Table 2) whose metrics were generated with TOMM [ 3 ]. We are looking into re ning and module quality metrics to compare modules.

Size No. of axioms Correctness Completeness Burger (Original) 29 58 - Burger (WeiAbs) 15 26 True False Burger (AxAbs) 29 44 True False Burger (HLAbs level 3) 26 52 True True

References

1. Amato , F. , Santo , A.D. , Moscato , V. , Persia , F. , Picariello , A. , Poccia , S.R. : Partitioning of ontologies driven by a structure-based approach . In: IEEE ICSC'15 . pp. 320 { 323 . IEEE ( 2015 ), anaheim, CA, USA, Feb 7- 9 , 2015

2. Kalyanpur , A. , Parsia , B. , Sirin , E. , Cuenca Grau , B. , Hendler , J.A. : Swoop: A Web Ontology Editing Browser . J. of Web Semantics 4 ( 2 ), 144 { 153 ( 2006 )

3. Khan , Z.C. , Keet , C.M. : Dependencies between modularity metrics towards improved modules . In: Proc. of EKAW'16. LNAI , vol. 10024 , pp. 400 { 415 . Springer ( 2016 )

4. Khan , Z.C. , Keet , C.M.: An empirically-based framework for ontology modularisation . Applied Ontology 10 ( 3-4 ), 171 { 195 ( 2015 )

5. Lee , D. , Cornet , R. , Lau , F., de Keizer , N.: A survey of SNOMED CT implementations . J. of Biomedical Informatics 46 ( 1 ), 87 { 96 ( 2013 )

6. Romero , A.A. , Kaminski , M. , Grau , B.C. , Horrocks , I. : Module extraction in expressive ontology languages via datalog reasoning . J. of Arti cial Intelligence Research 55 , 499 { 564 ( 2016 )

7. Rosse , C. , Mejino Jr , J.L.V. : A reference ontology for biomedical informatics: the foundational model of anatomy . J. of Biomedical Informatics 36 ( 6 ), 478 { 500 ( 2003 )