Multiagent and Grid Systems An International Journal 2 (2006) 455 471 455
IOS Press
Reasoning support for Semantic Web
ontology family languages using Alloy
Hai H. Wang
a,∗
, Jin Song Dong
b
, Jing Sun
c
and Jun Sun
b
a
Department of Computer Science, The University of Manchester, UK
E-mail: hai.wang@cs.manchester.ac.uk
b
School of Computing, National University of Singapore, Singapore
E-mail: {sunj, dongjs}@comp.nus.edu.sg
c
Department of Computer Science, The University of Auckland, New Zealand
E-mail: j.sun@cs.auckland.ac.nz
Received 28 November 2005
Revised 8 May 2006
Accepted 5 July 2006
Abstract. Semantic Web (SW), commonly regarded as the next generation of the Web, is an emerging vision of the new
Web from the Knowledge Representation and the Web communities. To realize this vision, a series of techniques has been
proposed. Semantic Web Ontology Langauge (OWL) and its extension Semantic Web rule Language (SWRL) and Semantic
Web Logic Language (SWRL-FOL) are some of the most important outputs from the SW activities. However the existing
reasoning and consistency checking tools for those languages are primitive. This paper proposes using the existing formal
modelling tool, in particular Alloy, to provide an automatic reasoning service for the Semantic Web ontology family languages
(OWL/SWRL/SWRL-FOL).
Keywords: Semantic Web, Alloy, OWL, SWRL, FOL
1. Introduction
The power of the Semantic Web [1], as the next generation of the Web, will be realized when software agents are
able to understand the Web content, process the information and exchange the results with other software agents.
Adding logic to the Web is one of the key requirements. This logic must be powerful enough to describe complex
properties of web resources but not so complicated that agents could be tricked by being asked to consider a paradox.
To achieve these two contradictory requirements, researchers attempt to adopt the layered approach, where the upper
layer is extended from the lower layer with enhanced expressive power. This allows that different applications can
choose the logic language suiting their needs most.
The bottom layer is Web Ontology Language (OWL) [14]. OWL, a recommendation by the World Wide Web
Consortium (W3C), is the latest standard to de ne the ontology. It is based on Description Logic (DL). Although
OWL adds considerable expressive power to the Semantic Web, to retain the decidability of key inference problems
in OWL DL and OWL Lite, OWL has its expressive limitations. Certain desired properties can not be expressed for
some applications. Semantic Web Rule Language (SWRL) [9] extends OWL by combining the OWL DL and OWL
Lite with the Unary/Binary Catalog sub-languages of the Rule Markup Language. It introduces a new kind of axiom,
∗
Corresponding author: Hai H. Wang, School of Computer Science, The University of Manchester, M13 9JPL, UK. Tel.: +44 161 275 0686;
Fax: +44 161 275 6204; E-mail: hai.wang@cs.manchester.ac.uk.
ISSN 1574-1702/06/$17.00  2006 IOS Press and the authors. All rights reserved

456 H.H. Wang et al. / Reasoning support for Semantic Web ontology family languages using Alloy
named Horn clause rules, to OWL DL. Recently, Semantic Web Rule Language First Order Logic (SWRL-FOL) [15]
has been proposed to further extend the SWRL to handle unary/binary rst-oder logic.
Reasoning can be useful at many stages during the design, maintenance and deployment of ontology. Using the
reasoning service provided by Semantic Web reasoners, software agents can autonomously infer new knowledges
from the given knowledges and perform different tasks. For example, Pizza nder,
1
as a small application developed
by our research group, demonstrates how the reasoner could be used by a web software agent for their application.
Pizza nder uses the Pizza Ontology, and a reasoner to dynamically generate pizza toppings and pizza topping
categories. The user can include toppings that they would like on their pizza and exclude any toppings that they
do not want on their pizza. The description logic reasoner is used to determine if the choices that have been made
contradict each other for example, choosing to include Jalapeno Pepper topping, but choosing to exclude all hot
toppings the choices are automatically adjusted to modify any decisions that could potentially lead to contradictions
and inconsistent results.
Because autonomous software agents may perform their reasoning and come to conclusions without human
supervision, it is essential that the shared ontology is consistent. However, since the Semantic Web technology is
still in the early stage, the reasoning and consistency checking tools are primitive. The existing OWL reasoning
tools such as FaCT [8] and RACER [6] have been developed speci cally for the decidable description logic, which
are based on tableaux algorithm. They are far from perfect. Furthermore, currently there does not exist a tableaux
algorithm that can support the reasoning of SWRL-FOL, or even SWRL. Hence, it would take some effort and
time for people to research into new algorithms and build new tools to support SWRL and SWRL-FOL reasoning.
However, as it can been foreseen that it is critical and urgent to provide some reasoning service to SWRL and
SWRL-FOL in order to make them to be integrated into ontology languages hierarchy and to have their impacts on
the practical web applications.
Alternatively, rather than developing new algorithms and tools, a light-weight approach to provide reasoning
service which can complement existing OWL reasoners and support SWRL and SWRL-FOL is to customize and
reuse some existing tools. After decades of research and development, some mature formal modelling/reasoning
tools have been established successfully. These tools could well be adopted to reasoning about OWL, SWRL and
SWRL-FOL.
This paper proposes to develop a reasoning environment using the software modelling language Alloy and its
Analyzer [11] for web ontology families language. It complements the existing OWL reasoning tools like RACER,
and also supports the newly extended SWRL and SWRL-FOL.
The rest of the paper is organized as follows. Section 2 brie y introduces the OWL, SWRL, SWRL-FOL and Alloy.
In section 3, we present the Alloy semantics for the OWL/SWRL/SWRL-FOL language and the transformation from
the ontologies into their corresponding Alloy models. Section 4 presents a case study to demonstrate the reasoning
processes of SWRL-FOL ontology models in the Alloy Analyzer. Section 5 concludes the paper and discusses the
future work.
This paper is substantially extended and revised from the early conference paper Reasoning Support for SWRL-
FOL Using Alloy [19].
2. Backgrounds
2.1. Semantic Web overview
2.1.1. Semantic Web and OWL
The Semantic Web is a vision for a new kind of Web with enhanced functionality which will require semantic-
based representation and processing of Web information. W3C has proposed a series of technologies that can be
applied to achieve this vision. The Semantic Web extends the current Web by giving the web content a well-de ned
meaning, better enabling computers and people to work in cooperation. XML is aimed at delivering data to systems
1
http://www.co-ode.org/downloads/pizza nder/.