EDOAL: Expressive and Declarative Ontology Alignment Language

The Expressive and Declarative Ontology Alignment Language (EDOAL) allows for representing correspondences between the entities of different ontologies. Unlike other formats, the alignment vocabulary allows to represent complex correspondences allowing to precisely describe the relation between the entities. The alignment vocabulary extends the alignment format.

Purpose

Representing ontology alignments is the general purpose of this vocabulary. Particularly, it extends the ontology alignment format in order to enable the representation of complex correspondences.

This format can be used for cases where expressing equivalence or subsumption between terms is not sufficient, when more precise relations need to be expressed. While term equivalence or subsumption might be enough for exchanging documents, more precise relations are needed to exchange and integrate data.

This vocabulary was originally designed with the goal of representing patterns of correspondence between ontologies. It was since then both simplified and extended to obtain a minimal vocabulary on top of the alignment format, able to express all possible kinds of ontology alignments.

Features

• Construction of entities from other entities can be expressed through algebraic operators. Constructed entities allows to overcome the shallowness of some ontologies.
• Restrictions can be expressed on entities in order to narrow their scope. Narrowing the scope of an entity makes possible to better align this entity with the one corresponding in the other ontology.
• Transformations of property values can be specified. Property values using different encoding or units can be aligned using transformations. The current version of Edoal only supports a limited kind of transformations. This will be improved soon.
• Linkkeys can be defined for expressing conditions under which, instances of the aligned entities should be considered equivalent.

Alignment and cells

In the alignment format, an alignment is a set of cells, each cell being a correspondence between two entities. The alignment vocabulary extend this scheme by allowing cells to contain compound entity descriptions. Each entity can be typed according to one of the following category: Class, Instance, Relation, Property. A relation corresponds to an object property in OWL, a property to a datatype property. Each entity can then be restricted, and transformation can be specified on propery values.

While Alignment and Cell are described by the alignment format, we will focus here on the remaining classes.

Namespaces

The namespace for the Alignment format is still http://knowledgeweb.semanticweb.org/heterogeneity/alignment# (usual prefix: align).

EDOAL's own namespace is http://ns.inria.org/edoal/1.0/ (usual prefix: edoal). EDOAL vocabulary is dereferenceable (see below).

Alignment format

An EDOAL alignment is an alignment as specified by the alignment format. It is identified by its level which must be "2EDOAL". This tells tools that the alignment is on level 2, i.e., correspondences are across constructed entities, and that the corresponding entities are specified according to the expressive language. This ensures the compatibility with other extensions of the format. The alignment moreover specifies the two aligned ontologies, and as exemplified in the code below.

Details on each property are available on the alignment format page.

An alignment contains a set of correspondences (Cells). Each cell can be linked to an alignment using the map property.

As the example shows, the EDOAL vocabulary only appears within the "entity" properties and very specificaly in the edoal:transformation and edoal:linkkey properties.

The correspondence between the two entities could have been expressed in the simple Alignment format because these have named entities identified by a URI. However, the correspondence provides more information because it tells that these entities are Classes.

The strength of EDOAL is to express more complex entities which are described below.

Entities

A quick overview of the implemented EDOAL API is provided here (abstract classes are in bold and interfaces in italics):

EDOALAlignment extends BasicAlignment
EDOALCell extends BasicCell
Expression
|- ClassExpression
|  |- ClassId implements Id
|  |- ClassConstruction
|  |- ClassRestriction
|     |- ClassDomainRestriction
|     |- ClassOccurenceRestriction
|     |- ClassTypeRestriction
|     |- ClassValueRestriction
|- PathExpression implements ValueExpression
|  |- PropertyExpression
|  |  |- PropertyId implements Id
|  |  |- PropertyConstruction
|  |  |- PropertyRestriction
|  |     |- PropertyDomainRestriction
|  |     |- PropertyTypeRestriction
|  |     |- PropertyValueRestriction
|  |- RelationExpression
|     |- RelationId implements Id
|     |- RelationConstruction
|     |- RelationRestriction
|        |- RelationCoDomainRestriction
|        |- RelationDomainRestriction
|- InstanceExpression
   |- InstanceId implements Id
Value implements ValueExpression
Apply implements ValueExpression
Transformation
Linkkey
Equals
Includes
TransfService implements Clonable
Variable
Comparator
Datatype

The Id interface is implemented by expressions identified by an URI: these are the named entities of ontologies that may be used in basic URIAlignments. The ValueExpression is implemented by expressions that identify in context a particular value or instance. This can be an instance or a literal as well as a path expression that leads to that value in the context of an instance.

Hence, the entities that can be found in cells are:

Class expressions

Class entities can be constructed using one of the three operators and, or, not.

• and represents the interesection of the classes in the expression
• or represents the union of the classes in the expression
• not represents the negation of a given class.

• AttributeDomainRestriction which restricts the values of relations to be in a particular class;
• AttributeTypeRestriction which restricts the values of properties to be in a particular type;
• AttributeValueRestriction which restricts the value of properties or relations to a particular value;
• AttributeOccurenceRestriction which constrains the cardinality of a property or relation;

This grammar relies on base values described in the following table:

Comparators have to be defined as specific URI, usually in the edoal namespace. They are currently described by: edoal:equals, edoal:lower-than, edoal:greater-than, the latter morally corresponding to the op:numeric-less-than and op:numeric-greater-than from the XQuery 1.0 and XPath 2.0 Functions and Operators recommendation.

Note that and and or can take no argument. This may be useful in some circumstances. They are interpreted as follows:

• <and rdf:parseType="Collection"/> is equivalent to owl:Thing;
• <or rdf:parseType="Collection"/> is equivalent to owl:Nothing.

Property expressions

Properties correspond to data properties in OWL. Properties entities can be constructed using one of the operators and, or, not and compose:

• and
• or
• not
• compose

• PropertyDomainRestriction
• PropertyTypeRestriction
• PropertyValueRestriction

Relation expressions

Relations correspond to object properties in OWL. Relation expressions can be constructed using one of the operators and, or, not and compose as well as "closure" operator inverse, symmetric, transitive and reflexive:

• and denotes the conjunction of several relations, i.e., the set of pairs of individuals which are in all the relations,
• or denotes the disjunction of several relations, i.e., the set of pairs of individuals which are in one of the relations,
• not denotes the complement of a relation, i.e., the set of pairs of individuals which are not in the relation,
• compose denotes the
• inverse denotes the converse of a relation,
• symmetric denotes the symmetric closure of a relation (this is equivalent to or( p inverse( p ) ),
• transitive denotes the transitive closure of a relation,
• reflexive denotes the reflexive closure of a relation.

• RelationDomainRestriction
• RelationCoDomainRestriction

Their syntax is the following:

Note that compose may take no argument in case of relations. This may be useful in some circumstances. <compose rdf:parseType="Collection"/> is equivalent to the identity relation, hence when applied to an object has for unique value the object itself (it is the equivalent self or this in some languages).

Values

A value expression may be used in alignments for denoting an individual things (not a class, a property or a relations). These values may be:

• a litteral value;
• an individual instance;
• a value reachable to a property or relation;
• a value computable by a function from arguments which are values.

They obey the following grammar:

Instances are always single entities refering to an individual through its URI:

URIs to use as the operator attribute of Apply are not specified. It is however advised, when possible, to use operators from the XQuery 1.0 and XPath 2.0 Functions and Operators recommendation. (fn: prefix used for http://www.w3.org/2005/xpath-functions).

Transformations

The development of transformations is still work in progress and you can contribute by providing your requirements. Transformations are expressed in the cell itself. Transformations do not express constraints on the classes or properties, but constraints on instances that should match.

Transformations can be invoked, for example for dynamic transformations like currency conversions (see examples).

Linkkeys

Linkkeys which are a generalisation to several data sets of keys in relational databases. A linkkey is a statement such as:

Such keys are slightly more complex than in databases because in RDF properties are not necessarily functional (they may have several values) and their values may be other objects. For this reason, it is necessary to indicate if it is required that all values must be the same (Equals) or if some of them must instersect (Intersects).

Linkkeys are primarily used for identifying identical objects. For instance, it may be that a instance of the Livre class is equivalent to an instance of the Novel class as soon as their properties auteur and titre on the one side and creator and title on the other side have the same values. This is expressed in the following example:

It is then possible to identify duplicates or to generate owl:sameAs links.

Longer examples

The best examples are the alignment files found in the "examples/omwg" directory of the Alignment API release zip.

The following examples illustrate various kids of usage of the vocabulary.

Class partition

This example shows how to express a correspondence between a class in one ontology corresponding to a set of classes in the other ontology. In order to graps the precise correspondence, the one class is partitioned according to the value of one of its attributes. In this example one ontology has a class LED which has a property color, while the other ontology has three classes RedLED, BlueLED, and GreenLED. The LED class is aligned with the three corresponding classes by specifying a restriction of its scope to the corresponding value of the color attribute.

Property value transformation (XPath function)

This exemple shows how to use a transformation between property values. Two cases can be considered: static transformations such as unit conversion, and transformations which vary over time such as currency conversions. This example illustrates a static conversion from pounds to kilograms using a XPath function.

Property value transformation (other service)

This example illustrates the conversion between two currencies. A transformation service is specified.

Class with attribute value restriction

This alignment pattern makes use of three variables. Var3 is a property variable representing a property having in its domain the class identified by the variable Var1. Moreover, the property Var3 has an integer value. This pattern thus captures all correspondences between two classes, the scope of one class being restricted to only those instances having a specific value (not specified by the pattern) for one of its property whith datatype "integer".

EDOAL Pattern

EDOAL also contains a pattern language with allows for expressing generalised correspondences in which entities can be abstract. This language is not very different from EDOAL (beside its introduction of variables which are already present in the previous example).

It will be released at a later stage. Ask François Scharffe for a more complete description of the EDOAL Pattern language.

Dereferenceable vocabulary (Please: XHTML+RDFa)

Due to popular demand, here is the derefenceable version of the RDF vocabulary used in the format. Official URI is http://ns.inria.org/edoal/1.0/.

Beware, that EDOAL has been designed as a format and an API rather than a generic RDF vocabulary. A natural ontology would be closer to the API but would give a more verbose EDOAL format. The EDOAL format is in RDF and compact. In consequence, not any RDF graph using the EDOAL vocabulary is a well-defined EDOAL alignment. In particular, RDF can express incomplete knowledge while the EDOAL API requires complete knowledge of the alignment.

Not yet declared:

History

This language has been first designed by François Scharffe as the SEKT Mapping language. It then became the OMWG Ontology Mapping language developed under the Sourceforge mappingapi project (http://sourceforge.net/projects/mediation/). This language was further described by François Scharffe, Jérôme Euzenat and Antoine Zimmermann in Knowledge web deliverable 2.2.10, in particular through the semantics of the language. Its implementation was also reengineered as an extension of the alignment format so that it could be manipulated through the Alignment API tools (starting version 3.1).

It has now been redesigned and reimplemented under the name of EDOAL. It is a plain component of the Alignment API and is maintained together with it.

The linkkey idea has been promoted by Jérôme Euzenat, further refined with Jérôme David and Manuel Atencia and finally implemented in the Alignment API (version 4.7) by Nicolas Guillouet.

Thanks

Thanks to Jonathan Snook and Robert Nyman for the syntax toggling scripts borrowed from the OWL Recommendation web page. http://www.robertnyman.com/2005/11/07/the-ultimate-getelementsbyclassname/.