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Modularization Approaches


Introduction to Part I

This part is meant to convey a general introduction to the domain of knowledge modularization. Chapter 1 overviews the issues and the proposed solutions that are relevant to ontology modularization. This chapter is deliberately informal to be accessible to the largest audience, so that readers can quickly get familiar with what will make up the rest of the book. Questions addressed in this initial chapter range from what is a module and how it can be characterized and assessed, to an overview of strategies to build modules and link them whenever needed. Chapters 2 to 4 explore in deeper detail and more formally specific issues that are nevertheless generic in the sense that they can be discussed independently from a specific approach to modularization. Chapter 2 establishes a formal characterization of the concept of module, introducing formal concepts that allow making a clear distinction among different types of modules and different relationships between the modules and the ontologies they come from. Each type of module exhibits different properties in terms of its potential functionalities, so it is important for a module designer to understand exactly how to proceed to get the desired modularity framework. Chapter 3 reports on an experimentation with various modularity techniques in various use case scenarios. Results show significant differences, namely in the size of the modules produced by the modularization techniques. They also provide a feedback on the qualities of the techniques. Next, Chapter 4 investigates how knowledge can be imported into a module from an external source. The aim of the chapter is to establish a clear and sound classification of various import techniques, which again should support designers with ways to choose the most appropriate technique given the goals to be achieved. Finally, Chapter 5 contains the detailed description of the Mads database modularization approach that currently best represents the efforts from the database community in terms of modularization techniques. It also includes, for comparison purposes, a short overview of one of the oldest approaches to modular ontologies, namely the Cyc project. This project represents the main achievement in terms of approaches where the definition and building of the modules and of the ontology they belong to are done in parallel at the same time. A short comparison between Cyc and Mads is also provided.
Heiner Stuckenschmidt, Christine Parent, Stefano Spaccapietra

An Overview of Modularity

Modularization is a familiar concept in IT, widely used in e.g. software development. It has been somehow neglected in knowledge management. Database research has only marginally addressed the topic, mainly for the development of cooperative database systems. Instead, research on ontologies, seen as the knowledge provider for the semantic web, has significantly invested on modularization techniques, seen as a key capability in the current efforts towards scalable solutions that will enable ontologies to grow to the huge size that we can foresee in real world future applications. Many different approaches exist to tackle ontology modularization, corresponding to different goals or building on different initial hypotheses. This chapter aims at clarifying the vision of the domain by providing a detailed yet generic characterization of the issues and solutions related to the various facets of modularization.
Christine Parent, Stefano Spaccapietra

Formal Properties of Modularisation

Modularity of ontologies is currently an active research field, and many different notions of a module have been proposed. In this paper, we review the fundamental principles of modularity and identify formal properties that a robust notion of modularity should satisfy. We explore these properties in detail in the contexts of description logic and classical predicate logic and put them into the perspective of well-known concepts from logic and modular software specification such as interpolation, forgetting and uniform interpolation. We also discuss reasoning problems related to modularity.
Boris Konev, Carsten Lutz, Dirk Walther, Frank Wolter

Criteria and Evaluation for Ontology Modularization Techniques

While many authors have argued for the benefits of applying principles of modularization to ontologies, there is not yet a common understanding of how modules are defined and what properties they should have. In the previous section, this question was addressed from a purely logical point of view. In this chapter, we take a broader view on possible criteria that can be used to determine the quality of a modules. Such criteria include logic-based, but also structural and application-dependent criteria, sometimes borrowing from related fields such as software engineering. We give an overview of possible criteria and identify a lack of application-dependent quality measures. We further report some modularization experiments and discuss the role of quality criteria and evaluation in the context of these experiments.
Mathieu d’Aquin, Anne Schlicht, Heiner Stuckenschmidt, Marta Sabou

On Importing Knowledge from Ontologies.

This chapter focuses on the notion of importing terms from an ontology. Rather than proposing a specific formalism for this task and proving theorems about its properties, it starts by surveying a sample of lesser known papers on this topic in both the AI and Database literature. Based on this, it then derives a list of desirable properties for the notion of “importing a set of identifiers from an exporting to an importing knowledge base”, and provides a framework for alternate formal definitions of this notion. Some of the more novel aspects are the idea of modifying the exporting ontology before the subset of axioms to be imported is determined, and limiting the use of imported terms. The chapter concludes with a review of the concept of “expressive power”, and how it might apply to importing mechanisms.
Alexander Borgida

Modularity in Databases

Modularization can be sought for as a technique to provide context-dependent perspectives over a given shared information repository. This chapter presents an approach to database modularization where the modules represent application-specific perspectives over the shared database. The approach is meant to support the creation/definition of the modules as part of the conceptual schema definition process, that is to say the modules and the database they are a subset of are simultaneously defined. This is similar to Cyc’s approach to ontological microtheories definition. The chapter develops both intuitive and formal definition of the proposed approach. It also shows the basics of how the modules are used by user transactions and of how the overall multiperception database can be implemented on a commercial database management system.
Christine Parent, Stefano Spaccapietra, Esteban Zimányi

Partitioning and Extraction of Modules


Introduction to Part II

In an ideal world, ontologies would be build in a modular way from the start thus showing the benefits well known from modularization in software engineering. The first part of this book contained an example of how this can be done for databases. Unfortunately, the field of ontology engineering has not yet developed comprehensive models and methods to fully support the development of modular ontologies. There are some approaches aiming at developing principles and formalisms in this direction, but they have not yet found their way into mainstream ontology engineering. As a result, existing ontologies are monolithic models without a clear internal structuring. As the size and complexity of these models can be quite significant (the NCI cancer ontology contains about 27.500 the Gene ontology about 22.000 concepts and the Formal Model of Anatomy (FMA) even 75.000 concepts). A viable way of handling such large models is to chop them up into manageable parts. This part of the book deals with approaches for this task of partitioning large ontologies into smaller parts.
Heiner Stuckenschmidt, Christine Parent, Stefano Spaccapietra

Extracting Modules from Ontologies: A Logic-Based Approach

The ability to extract meaningful fragments from an ontology is essential for ontology reuse. We propose a definition of a module that guarantees to completely capture the meaning of a given set of terms, i.e., to include all axioms relevant to the meaning of these terms. We show that the problem of determining whether a subset of an ontology is a module for a given vocabulary is undecidable even for OWL DL. Given these negative results, we propose sufficient conditions for a for a fragment of an ontology to be a module. We propose an algorithm for computing modules based on those conditions and present our experimental results on a set of real-world ontologies of varying size and complexity.
Bernardo Cuenca Grau, Ian Horrocks, Yevgeny Kazakov, Ulrike Sattler

Structure-Based Partitioning of Large Ontologies

In this chapter we describe a method for structure-based ontology partitioning and its implementation that is practically applicable to very large ontologies. We show that a modularization based on structural properties of the ontology only already results in modules that intuitively make sense. The method was used for creating an overview graph for ontologies and for extracting key topics from an ontology that correspond to topics selected by human experts. Because the optimal modularization of an ontology greatly depends on the application it is used for, we implemented the partitioning algorithm in a way that allows for adaption to different requirements. Furthermore this adaption can be performed automatically by specifying requirements of the application.
Heiner Stuckenschmidt, Anne Schlicht

Web Ontology Segmentation: Extraction, Transformation, Evaluation

In this chapter we present an algorithm for extracting relevant segments out of large description logic ontologies for the purposes of increasing tractability for both humans and computers. We offer several variations on this algorithm for different purposes. The segments are not mere fragments, but stand alone as ontologies in their own right. This technique takes advantage of the detailed semantics captured within an OWL ontology to produce highly relevant segments. However, extracted segments make no guarantee for preserving the semantics of the complete ontology.
Julian Seidenberg

Traversing Ontologies to Extract Views

One of the original motivations for ontology research was the belief that ontologies can help with reuse in knowledge representation. However, many of the ontologies that are developed with reuse in mind, such as standard reference ontologies and controlled terminologies, are extremely large, while the users often need to reuse only a small part of these resources in their work. Specifying various views of an ontology enables users to limit the set of concepts that they see. In this chapter, we develop the concept of a Traversal View, a view where a user specifies the central concept or concepts of interest, the relationships to traverse to find other concepts to include in the view, and the depth of the traversal. For example, given a large ontology of anatomy, a user may use a Traversal View to extract a concept of Lung and organs and organ parts that surround the lung or are contained in the lung. We define the notion of Traversal Views formally, discuss their properties, present a strategy for maintaining the view through ontology evolution and describe our tool for defining and extracting Traversal Views.
Natalya F. Noy, Mark A. Musen

Connecting Existing Ontologies


Introduction to Part III

Another valid view on modularity is ontologies that differs from the one taken in part II of the book is the idea that modules are not created by splitting up a large ontology into smaller parts but by composing a number of small ontologies that have been created independently of each other into a larger model. In this scenario that was investigated in more detail in chapter 4 the original ontologies become modules in a large modular ontology. The advantage of this scenario is not easier maintenance and analysis of the overall system - in fact integrating different ontologies normally makes both more complicated compared to the individual models. The rationale for this approach is the benefit of being able to reuse knowledge that has been created by other people as well as the Data that might be associated with the ontologies to be integrated. This scenario is much closer to the original vision of the semantic web, where information sources describe their information using ontologies and information is found and reused by linking it on the level of ontologies thus creating a system of interlinked ontologies in which information can be interpreted in a uniform way.
Heiner Stuckenschmidt, Christine Parent, Stefano Spaccapietra

Formal and Conceptual Comparison of Ontology Mapping Languages

The compositional approach where several existing ontologies are connected to form a large modular ontology relies on the representation of mappings between elements in the different participating ontologies. A number of languages have been proposed for this purpose that extend existing logical languages for ontologies in a non-standard way. In this chapter, we compare different proposals for such extensions on a formal level and show that these approaches exhibit fundamental differences with respect to the assumptions underlying their semantics. In order to support application developers to select the right mapping language for a given situation, we propose a mapping metamodel that allows us to encode the formal differences on the conceptual level and facilitates the selection of an appropriate formalism on the basis of a formalism-independent specification of semantic relations between different ontologies by means of a graphical modelling language.
Saartje Brockmans, Peter Haase, Luciano Serafini, Heiner Stuckenschmidt

Ontology Integration Using ε-Connections

The standardization of the Web Ontology Language, OWL, leaves (at least) two important issues for Web-based ontologies unsatisfactorily resolved, namely how to represent and reason with multiple distinct, but linked ontologies, and how to enable effective knowledge reuse and sharing on the Semantic Web. In this paper, we present a solution for these problems based on ε-Connections. We aim to use ε-Connections to provide modelers with suitable means for developing Web ontologies in a modular way and to provide an alternative to the owl:imports construct.
Bernardo Cuenca Grau, Bijan Parsia, Evren Sirin

Composing Modular Ontologies with Distributed Description Logics

This chapter demonstrates the use of the Distributed Description Logics framework (DDL) and the distributed reasoner DRAGO as formal and practical tools for composing modular ontologies from purely terminological \({\mathcal SHIQ}\) ontology modules. According to DDL vision, a modular ontology can be formally represented by a distributed T-box, comprising a set of separate T-boxes (one for each ontological module), which are pairwise interrelated by “bridge rules” (inter-module connectives allowing to access and import knowledge contained in modules). The chapter gives the semantic explanations of knowledge import via bridge rules as well as presents the distributed tableaux reasoning technique for its computation. Practically, the implementation of the distributed tableaux in DRAGO reasoner and its use for modular ontology composition is described and experimentally evaluated.
Luciano Serafini, Andrei Tamilin

Package-Based Description Logics

We present the syntax and semantics of a family of modular ontology languages, Package-based Description Logics (P-DL), to support context- specific reuse of knowledge from multiple ontology modules. In particular, we describe a P-DL \({\mathcal SHOIQP}\) that allows the importing of concept, role and nominal names between multiple ontology modules (each of which can be viewed as a \({\mathcal SHOIQ}\) ontology). \({\mathcal SHOIQP}\) supports contextualized interpretation, i.e., interpretation from the point of view of a specific package. We establish the necessary and sufficient conditions on domain relations (i.e., the relations between individuals in different local domains) that need to hold in order to preserve the unsatisfiability of concept formulae, monotonicity of inference, transitive reuse of knowledge across modules.
Jie Bao, George Voutsadakis, Giora Slutzki, Vasant Honavar


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