OWL-Full Metamodeling with SWCLOS
Seiji Koide1 and Hideaki Takeda2
1The Graduate University for Advanced Studies (SOKENDAI), 2-1-2, Hitotsubashi,Chiyoda-ku, Tokyo 101-8430 Japankoide@nii.ac.jp,
WWW home page: http://www-kasm.nii.ac.jp/~koide/2
National Institute of Informatics and SOKENDAI
takeda@nii.ac.jp

Abstract. There are some logic-based approaches to metamodeling inOWL. We enabled OWL metamodeling with an object-based approach.
In this paper, we introduce criteria for metamodeling, that are derived
from the principles of object-oriented metamodeling, and demonstrateexamples of metamodeling with SWCLOS.

1Introduction

Metamodeling in OWL has been discussed in the OWL 1.1 activity and othereﬀorts [1, 2]. All of them are logic-based, and they discuss how to extend DLbased OWL to OWL-Full, not how to accomplish RDF(S) semantics in OWL. Incontrast, RDF(S) per se has potential for metamodeling. We developed SWCLOS [3], an OWL-Full modeling language based on the Common Lisp Object
System, by leveraging RDF(S) semantics. As in RDF(S), SWCLOS provides thecapability to capture a class as an individual in OWL. One still must abide byRDF(S) semantics to deal with classes as individuals.

2Metamodeling Criteria from an OO Perspective

To capture an object as an instance, a class of an object must be establishedfrom an object-oriented (OO) perspective. This principle is extended to theclass-metaclass relationship for metamodeling. Namely, in order to capture aclass as an individual, we establish a class of classes (metaclass). In the objectoriented embodiment, an entity inherits the attributes and virtues of metaclasses(metaclass-hood) from a superclass as a metaclass. The source of the metaclasshood is rdfs:Class in the RDF universe. Therefore, every metaclass must be asubclass of rdfs:Class.
Some ontologies, e.g. SUMO and Cyc, embrace embarrassing class-instance
relationships, e.g. cyclic membership and disorder between classes and metaclasses. We introduce metamodeling criteria to increase reasoning decidability
while paying attention to membership classiﬁcation and extension inclusiveness.
If a class C is an instance of another class whose extension includes the extensionof class C, we distinguish such classiﬁcation from normal ones and denote therelation by ∈⊆ . The metamodeling criteria we set up are as follows.

2– If a class C is an instance of but not a subclass of D (normal), then D canbe a metaclass. CEXT I (DI ) denotes the extension of the denotation of D.
{C I ∈ CEXT I (DI ) | CEXT I (C I ) ⊆ CEXT I (rdfs : Resource I )}|= CEXT I (DI ) ⊆ CEXT I (rdfs : Class I )(1)– If a class C is an instance of and a subclass of D (abnormal), then D cannot
be a metaclass.
{C I ∈⊆ CEXT I (DI ) | CEXT I (C I ) ⊆ CEXT I (rdfs : Resource I )}
̸|= CEXT I (DI ) ⊆ CEXT I (rdfs : Class I )(2)

These criteria yield a guideline for metamodeling on how to resolve classinstance disorder; if a class C is a subclass of and an instance of class D (abnormal) through B that is a subclass of D, and if C is an instance of but not a
subclass of class B (normal), then we can accept such an abnormal C by making
B a subclass of rdfs:Class (metaclass).

rdfs:Classrdfs:subClassOfrdf:typerdfs:ResourceB
rdfs:subClassOfD

rdf:type

CFig. 1. Example of Meta-Modeling Criteria

3Concluding Remarks and Demonstration

rdfs:Class plays multiple roles, as a metaclass, meta-metaclass, meta-meta-metaclass,and so forth because of its membership loop. Therefore, the above criteria create
an inﬁnite number of clearly separated layers of metamodeling, i.e. class layer,metaclass layer, meta-metaclass layer, and so forth. We demonstrate several examples of metamodeling with SWCLOS at the poster and demos.

References
1. Motik B.: On the Properties of Metamodeling in OWL. Int. Semantic Web Conf.,
ISWC2005 (2005) 548–562
2. Pan, J. Z., Horrocks, I.: OWL FA: a metamodeling extension of OWL DL. Proc.
15th Int. Cof. WWW, WWW ’06 (2006) 1065–1066
3. Koide, S. Takeda, H.: OWL-Full Reasoning from an Object Oriented Perspective.
Asian Semantic Web Conf., ASWC2006 (2006) 263–277

OWL-Full Metamodeling with SWCLOS:
Demonstration
Seiji Koide1 and Hideaki Takeda211

The Graduate University for Advanced Studies (SOKENDAI), 2-1-2, Hitotsubashi,
Chiyoda-ku, Tokyo 101-8430 Japankoide@nii.ac.jp,
WWW home page: http://www-kasm.nii.ac.jp/~koide/2
National Institute of Informatics and SOKENDAI
takeda@nii.ac.jp

Introduction of SWCLOS

In the demonstration, we show the performance of SWCLOS3 as an OWL reasoner at ﬁrst. For example, we demonstrate loading Wine and Food Ontology,
it takes about 4 seconds from two RDF/XML ﬁles, and then show several OWL
entailments and satisﬁability checking by SWCLOS.

2About SUMO Ontology

In SUMO ontology,4 sumo:Meter, which is an instance of sumo:SystemeInternationalUnit,
is a subclass of sumo:PhysicalQuantity. However, sumo:SystemeInternationalUnit
is a subclass of sumo:UnitOfMeasure, which is also a subclass of sumo:PhysicalQuantity.
Therefore, these assertions hold following abnormal conditions.
sumo : Meter I ∈⊆ CEXT I (sumo : PhysicalQuantity I )
I

I

I

(1)
I

CEXT (sumo : Meter ) ⊆∈ CEXT (sumo : PhysicalQuantity )(2)

We demonstrate SWCLOS signals an alarm against this abnormal classinstance relationship on one hand, and on the other hand, show SWCLOS canaccept this abnormality with making sumo:SystemeInternationalUnit a metaclass through adding the following assertion.
<rdfs:Class rdf:ID= "UnitOfMeasure"><rdfs:subClassOf rdf:resource ="&rdfs;Class"/></rdfs:Class>3

Metamodeling Programming using SWCLOS

We also demonstrate how to program ontology with metamodeling using SWCLOS and discuss the details with audience.
3
4

It is available from http://www-kasm.nii.ac.jp/~koide/.
http://www.ontologyportal.org/