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E-Connections

What are E-Connections in a Semantic Web Context?


An E-Connection is a knowledge representation language defined as a combination of other logical formalisms. Each of the component logics has to be expressible in the Abstract Description System (ADS) framework, which includes Description Logics (and hence OWL-DL), Modal and Epistemic logics, as well as many logics of time and space. Obviously, different component logics will give rise to different combined languages, with different expressivity and computational properties.

E-Connections were originally introduced in [1] as a way to go beyond the expressivity of each of the component logics, while preserving the decidability of the reasoning services. An E-Connection language is a formalism, strictly more expressive than any of its component logics, and which is decidable, provided that each of its components is decidable. Hence, E-Connections provide a trade-off between the expressivity gained and the computational robustness of the combination.

Here, we will use E-Connections as a language for defining and instantiating combinations of OWL-DL ontologies, i.e. as a way of combining KBs, rather than logics. We will restrict ourselves to OWL-DL, since OWL-Full is beyond the Abstract Description System framework. Whenever we mention OWL , we will implicitly refer to OWL-DL.

An E-Connection is a set of ``connected'' ontologies. An E-Connected ontology typically contains information about classes, properties and their instances, as in OWL, but also about a new kind of properties, called links, which are somewhat similar in spirit to datatype properties. In OWL, the classes defined in terms of datatype properties ``combine'' information from different domains: the actual application domain of the ontology and the domain of datatypes. The coupling between datatypes and the ontology is always achieved through restrictions on datatype properties. For example, a ``retired person'' can be defined in OWL as a person whose age is greater than 65, by using a class (``Person'') in the ontology and a restriction on a datatype property ``age'' with value ``greater than 65''. Both from a logical and from a modeling perspective, the domain of the ontology and the domain of datatypes are disjoint: from a modeling perspective the (application) domain of ``persons'' is disjoint from the (application) domain of ``numbers''; from a logical perspective, in OWL the domain where classes, properties and individuals in the ontology are interpreted is disjoint from the domain of datatypes, and datatype properties are interpreted as binary relations with the first element belonging to the domain of the ontology and the second on the domain of the datatypes.

In the same vein, Link Properties allow to create classes in a certain ontology based on information from a different ontology, provided that the domains of the ontologies are disjoint, both from a logical and a modeling perspective. For example, a ``Graduate Student'' in an ontology about ``people'' could be defined as a student who is enrolled in at least one graduate course, by using the class ``Student'' in the people ontology and a someValuesFrom restriction on the link property ``enrolledIn'' with value ``GraduateCourse'', which would be a class in a different ontology dealing with the domain of ``academic courses''. Link properties are logically interpreted as binary relations, where the first element belongs to the ``source'' ontology and the second to the ``target ontology'' of the link property. Conceptually, a link property will be defined and used in its ``source'' ontology. For example, the link property ``enrolledIn'' would be defined as a link property in the ``people'' ontology with target ontology ``academic courses''. An E-Connected ontology, in the Semantic Web context, can be roughly described as an OWL-DL ontology, extended with the ability to define link properties and construct new classes in terms of restrictions on them.

From a modeling perspective, each of the component ontologies in an E-Connection is modeling a different application domain, while the E-Connection itself is modelling the union of all these domains. For example, an E-Connection could be used to model all the relevant information referred to a certain university, and each of its component ontologies could model, respectively, the domain of people involved in the university, the domain of schools and departments, the domain of courses, etc.

Why E-Connections for the Semantic Web

Our main motivations for using E-Connections in a Semantic Web context are the following
  1. Alternative to owl:imports : In order to provide support for integrating Web ontologies, OWL defines the \textit{owl:imports} construct, which allows to include by reference in a knowledge base the axioms contained in another ontology, published somewhere on the Web and  identified by a global name (a URI). However, the functionality provided by this construct is unsatisfactory for a number of reasons
    • The only way that owl:imports provides for using concepts from a different ontology is to bring into the original ontology all the axioms of the imported one. Therefore, the only difference between \textit{copying and pasting} the imported ontology into the importing one and using an owl:imports statement is the fact that with imports both ontologies stay in different files. This certainly provides some syntactic modularity, but not a logical modularity, which would be indeed more desirable.
    • The components of an ontology, such as classes and properties, are, as the ontologies themselves, identified by unique names (URIs) on the Semantic Web.  For example, suppose that we are developing an ontology about ``People" and we want to define the concept of a ``Dog Owner". It may seem natural for such a purpose to use the URI of a certain class ``Dog", that appears in an ontology about ``Pets" that we have found on the Web. We may think then that we are committing to the meaning of ``Dog" in that ontology, i.e., that a dog is an animal, for example. However, if we use the URI for ``Dog" without importing the corresponding ontology, we are bringing \emph{nothing} from the meaning of the term in the the foreign ontology, while if we import it, we are bringing all the axioms of the ``Pet" ontology to our logical space, even if we are only interested on dogs, and not on cats or hamsters.
    • The use of owl:imports results in a completely flat ontology, i.e., none of the imported axioms or facts retain their context. While it is possible to track down the originator(s) of some assertions by inspection of the imported ontology, OWL reasoning does not take such context into account.
  2. Identification of sub-parts of Ontologies: Finding coherent, tightly coupled sub-parts of and discovering the logical dependencies (if any) between these sub-parts is indeed an important and hard task. First, defining what makes a set of axioms a relevant sub-part of an ontology is a controversial issue. The E-Connections formalism provides a sensible, strongly-motivated way for grouping relevant sets of axioms into distinguished, yet connected, knowledge bases.
  3. Well-founded Logical Framework:  Any method for combining ontologies should be based on a solid formal background, in order to be properly understood and applied. A solid theory justifies algorithmic design decisions and motivates heuristics. E-Connections constitute a well-motivated, powerful framework for representing  combinations of logics and knowledge bases, which offers computational guarantees and modeling guidelines.
  4.  Reasoning: One of the main motivations of OWL is the ability to reason with the language. Therefore, any formalism or methodology for coupling OWL ontologies should provide a suitable infrastructure for logical reasoning on the resulting combinations. We have proved that practical (i.e, optimized and efficient) reasoning can be achieved and implemented on E-Connections by extending existing Description Logics reasoners and that the computational cost of reasoning on E-Connected ontologies not higher than the cost of reasoning with OWL itself.
  5. Integrability into OWL: Any formalism for connecting ontologies on the Semantic Web must fit into the Semantic Web architecture, and particularly it must be compatible with OWL. We have shown that the E-Connections formalism can be smoothly integrated on the Semantic Web as a simple and natural extension of the Web Ontology Language.
  • [1] O.Kutz, C.Lutz, F.Wolter and M. Zakharyaschev E-Connections of Abstract Description Systems. Artificial Intelligence 156(1):1-73, 2004.

    • Publications


    Tutorials

    This tutorial is a gentle introduction to E-Connections using the ontology editor  SWOOP , which currently provides browsing and editing support for E-Connections

    Presentations

    The slides of a  presentation on E-Connections made at ISWC-2004 are available  here.
    The slides on a presentation at NIST in April 2005 are available here.
    The slides on a presentation for SWIG in February 2005 are available here.
    The slides on a presentation on Partitioning are available here.
    The slides on a presentation at IBM Watson in June 2005 are available here.


    Example E-Connected Ontologies

    A library of E-Connected ontologies written in an extension of OWL is available here. These ontologies can be loaded, browsed and edited in SWOOP.

    Online Pellet Demo

    Pellet is an open-source OWL-DL reasoner. Pellet currently provides support for E-Connections An online Pellet demo is available here.

      

     

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