Mapping OWL-DL into ORM/RIDL

Mapping OWL-DL into ORM/RIDL Dang Bui Bach, Robert Meersman, Peter Spyns, and Damien Trog Vrije Universiteit Brussel - STAR Lab, Pleinlaan 2 Gebouw G-10, B-1050 Brussel - Belgium Tel.: +32-2-629.1237; Fax: +32-2-629.3819 {dbuibach,meersman,pspyns,dtrog}@vub.ac.be

Abstract. In this paper, we analyze the semantics of OWL-DL and ORM, and explain how to represent OWL-DL constructs in ORM without losing semantics. We demonstrate this in a formal manner as much as possible. We show it is possible to convert most constructs, except for what are called property restrictions, and discuss the implications.

1

Introduction

Ontology acquisition is an important part of any ontology engineering methodology. DOGMA (Developing Ontology-Grounded Methodologies and Applications) as an ontology engineering framework has its roots in database semantics and model theory. OWL on the other hand is a logic-based language that is used to formalize a domain of knowledge. In recent years, OWL has emerged as a standard Web ontology language. The number of ontology-based applications that make use of the OWL language is rapidly increasing. Automatically acquiring ontologies from existing sources is a research topic that has not yet been tackled within the DOGMA framework (except for textual sources). By converting from OWL-DL to ORM, we can acquire a large pool of publicly-available existing domain knowledge and represent it in the DOGMA notation. In addition, we can take advantage of a number of available tools. The remainder of this paper is organized as follows. In the subsequent section (2), the main characteristics of DOGMA are explained with its commitment language Ω-RIDL (Sect. 2.2). Before detailing in Sect. 4 how to convert from OWL-DL to ORM, we a give a short introduction to OWL in Sect. 3. Some comments and plans for future work are presented in Sect. 5. We end this paper with concluding statements in Sect. 6.

2

DOGMA

In this section we briefly explain the principles behind DOGMA and Ω-RIDL and the background of the conversion exercise. 

The authors are listed in alphabetical order as their contributions are of equal importance.

R. Meersman, Z. Tari, P. Herrero et al. (Eds.): OTM 2007 Ws, Part I, LNCS 4805, pp. 742–751, 2007. c Springer-Verlag Berlin Heidelberg 2007 

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General Principles

DOGMA (Developing Ontology-Grounded Methods and Applications) is an ontology approach and framework [19]. One of its most characteristic features is that the “meaning space” can be subdivided in different ways according to the needs of a specific application that will add its particular semantic restrictions according to its intended usage [15]. Hence, a DOGMA ontology consists of a lexon base layer and a commitment layer. This layering approach allows for scalability in representing and reasoning about formal semantics [22], as a generative approach can be adopted (with a reduced set of meaning building blocks, a large space of meaning combinations can be generated). In analogy with a principle stemming from the linguistics fields, this has been dubbed the “double articulation principle” [18]. The lexon base is meant to reach a common and agreed understanding about the ontology terminology and hence is aimed at human understanding. Natural language terms are associated, via the language and context combination, to a unique word sense represented by a concept label (e.g. the WordNet [7] identifier person#2). The commitment layer, with its formal constraints [13], is meant for interoperability issues between information systems, software agents and web services. These kinds of constraints are mathematically founded and concern rather typical DB schema constraints. The choice for certain constructs/constraints rather than others has been mainly inspired by the tradition of ORM DB modeling, its application inside the DOGMA theoretical framework, and some practical experiences. A formalization of DOGMA can be found in [4]. 2.2

Ω-RIDL Commitments

DOGMA ontologies are stored in the DOGMA ontology server and manipulated by the Ω-RIDL commitment language. The ontology engineer, using the DOGMA Studio Workbench with T-Lex [20], can define commitment rules in the commitment layer using the Ω-RIDL language. This language was initially developed by Verheyden et al. [21] and is inspired by the RIDL language developed by Meersman [14]. It can commit application symbols of relational databases, providing a groundwork for semantic interoperability of heterogeneous databases. Although RIDL was intended for database modeling, most of the language is reused for specifying ontological commitments. There are many parallels between ontology engineering and data modeling as both consist of conceptual relations and rules [16]. Just as ORM needs some adaptations when using it to model ontologies [17], also the RIDL language has to be tuned to its use as an ontological commitment language (hence Ω-RIDL). The main advantage of RIDL (and thus Ω-RIDL) is that it has a strong methodological grounding (in NIAM), and it is very close to natural language. This allows for easier communication with domain experts to create and verify conceptualizations and domain rules. Besides this, the NIAM methodology supports the generation of relational databases by a methodological and automated

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process [5] that provides many insights on how to commit relational database schemas to conceptual models (and thus ontologies). Because the version of Ω-RIDL as it was published only supports a subset of ORM constraints, we illustrate with RIDL examples. Currently there is a new version of Ω-RIDL under development that will support the RIDL constraints shown in this paper.

3

OWL

The OWL language is to a large extent considered as a (scientific) standard of the Semantic Web. We refer to the W3C web site1 and [1] for more detailed information on OWL. We limit ourselves to mention that OWL-DL has been designed to offer sufficient expressiveness and strong reasoning support. Therefore, in this paper we choose the OWL-DL species for our conversion. OWL-DL restricts pairwise combination between classes, properties, individuals and data values. Unlike OWL-Full, object properties and datatype properties are disjoint in OWL-DL. This implies that we cannot apply property characteristics on datatype properties, such as: inverse of, inverse functional, symmetric and transitive. Another restriction is that no cardinality constraint (local nor global) can be placed on transitive properties or their inverses, or any of their superproperties.

4

Mapping Methods

In this section we explain how to convert OWL-DL constructs into ORM and RIDL. 4.1

The Primitives

OWL and DOGMA use two different paradigms, the latter is fact-oriented while the former is logic-oriented. Nevertheless, we need to make some assumptions on a close-relatedness of elements of their meta-models. The overview in Table 1 shows where fundamental concepts of the two formalisms are related. Table 1. Overview of metamodel elements Meta-model element Type: has Instances as its members Instance: primitive elements Relation: the relationship between two Types 1

http://www.w3.org/

OWL class, datatype

ORM entity type, value type

instance, literal

referenced literal, literal

object property, datatype idea relation, bridge relation property

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An OWL class containing instances corresponds to an ORM entity type containing referenced literals. A datatype corresponds to a value type as both contain literals. An OWL instance is identified by a URI (not by its literal representation). As a result it is uniquely identified on the Internet. An ORM literal is only uniquely identified in a value type. The property extension of an object property in OWL corresponds to the population of a binary fact type in ORM. Therefore the object property and its inverse correspond to the role/co-role. This pair is considered as a relation. Unlike ORM, the property sufficiently identifies a relation while the inverse is provided as an aid for reading in both directions [9, p.4-3]. This explains the lack of co-role labels in the ORM diagrams below. An object property has a domain and a range, which define the allowable population of the participating classes that play the relation. Therefore the domain and range correspond to the two object types that play the roles. 4.2

Conversion Principles and Methods

Our conversion principle is that if M is a model of an OWL schema then M must also be a model for the converted ORM schema. The procedure for our mapping is to first formalize the OWL construct in first-order-logic [3,9,6]. Next, we propose the ORM construct that is semantically the closest to the OWL construct, together with its formalization. If both formalizations are the same, we have achieved a bi-directional mapping. If every model of an OWL construct is a model of the suggested ORM construct, the mapping is valid. Otherwise, we prove that the mapping is not possible. Finally, for each OWL construct we provide the corresponding RIDL textual constraint. Since we formalize both constructs in first-order logic, we can prove their equivalence [10], either manually or automatically [2]. 4.3

Scope of Conversion

The following OWL language constructs are not considered in our paper: instance-related constructs, owl:Nothing, versioning-related constructs, import constructs, annotation-related constructs, RDF(S) container and collectionrelated constructs, RDF(S) reification, OWL-Full constructs and Datatype constructs. We assume that the input OWL documents for our conversion methods are consistent. One example of inconsistency is when A and B are defined as disjoint classes and at the same A and B are defined as equivalent classes. To detect inconsistencies in OWL documents, we can use the many OWL validators available on the Web (such as Racer2 ). Because of space limitations, not all conversion methods are given in the following sections. 2

http://www.racer-systems.com/

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Property Restriction

A property restriction is a special kind of class description. It describes an anonymous class, namely a class of all individuals that satisfy the restriction. There are four specific restrictions in OWL, namely Universal, Existential, hasValue and Cardinality. We present here the Universal restriction mapping as an example. Universal Restriction. The Universal restriction is specified in OWL by the following statement: restriction(p allValuesFrom B). This is formalized in first order-logic as3 : ∀x[N (x) ⇔ ∀y [p(x, y) → B(y)]].

(1)

The semantically closest ORM construct is shown in Fig. 1 and is formalized as [9]: ∀x∀y [p(x, y) → N (x) ∧ B(y)]. (2) The meaning of the OWL statement in (1) is that for every instance of class N, if it has a property p then the value of this property must be of class B, and for every instance that have property value (p) of class B must be of class A.

Fig. 1. A failed attempt to represent Universal Restriction in ORM

Supposedly, we have a universe of discourse including a, b, a state-of-affairs ¬N (a) ∧ p(a, b) ∧ ¬B(b), is a model of (1), but not of (2). Therefore, the solution above violates our principle of conversion. Any constraint applied on the binary fact type will further restrict the valid models of the ORM schema. Our solution in RIDL is: N is equal to (Dp not p (Rp minus B))4 . 4.5

Boolean Class Description

There are three types of boolean class descriptions: Union, Intersection and Complement. The Union and Intersection class mappings are given below. Union Class description. The Union class description is specified in OWL by the following statement: unionOf (A B). This is formalized in first order-logic as: ∀x[N (x) ⇔ A(x) ∨ B(x)]. (3) The ORM diagram shown in Fig. 2 is equivalent to the Union class in OWL as they share the same formalization. An alternative solution is written in RIDL as: N is equal to A union B. 3 4

As a convention we name the class description N . Dp and Rp are the domain and range of p respectively and B is a subytpe of Rp .

Mapping OWL-DL into ORM/RIDL

Fig. 2. Union class in ORM

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Fig. 3. Intersection class in ORM

Intersection Class description. The Intersection class description is specified in OWL by the following statement: intersectionOf (A B). This is formalized in first order-logic as: ∀x[N (x) ⇔ A(x) ∧ B(x)]. (4) The semantically closest ORM representation is shown in Fig. 3, which is formalized as: ∀x[N (x) → A(x) ∧ B(x)]. (5) We conclude that |= (4) → (5). An alternative solution in RIDL is: N is equal to A intersection B. 4.6

Class Axioms

There are three types of class axioms: Subclass, Equivalence and Disjointness. The mappings of Subclass and Disjointness axioms are discussed below. Subclass Axiom. In ORM, a subtype is not necessarily a proper subtype contrary to NIAM [9, p.4-15], so it fits with the semantics of a subclass in OWL. A being a subclass of B in OWL is equivalent with A being a subtype of B in ORM, as they have the same formalization: ∀x[A(x) → B(x)].

(6)

In RIDL we define this as: add nolot A subtype of B Class Disjointness. The Class Disjointness is specified in OWL by the following statement: DisjointClasses (A,B). This is formalized in first order-logic as: ∀x[A(x) → ¬B(x)]. (7) Although ORM supports disjointness constraints between object types, only subtypes are allowed (the primitive entities are disjoint by default). In contrary to the strong-typing system of ORM [6], OWL classes can be arbitrarily overlapped. Because of this, we cannot infer which classes need to be primitive entity types and which have to be subtypes. Our solution is to make all converted OWL classes subtypes of the converted class Thing (from owl:Thing). Therefore, Thing becomes the only primitive type in the ORM diagram. With this solution, we can easily represent the OWL disjointness in ORM, which is shown in Fig. 4. An alternative solution is written in RIDL as: A is disjoint from B.

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Fig. 4. Disjoint class in ORM

4.7

Property Axioms

There are four types of property axioms: Subproperty, Equivalence, Transitiveness, Symmetry. We show the mapping of the Subproperty axiom as an example. Subproperty. The Subproperty axiom is specified in OWL by the following statement: SubPropertyOf (p,q). This is formalized in first order-logic as: ∀x∀y[(p(x, y) → (q(x, y) ∧ Dp (x) ∧ Rp (y))) ∧ (q(x, y) → Dq (x) ∧ Rq (y))]5 . (8) The corresponding conversion in ORM is shown in Fig. 5.

Fig. 5. Subproperty Axiom in ORM. Note that all OTs are subtypes of the primitive entity Thing (not shown on diagram).

An alternative solution is written in RIDL as: for each Dp dp , Rp rp holds dp p rp implies dp q rp end holds. ∀x∀y[(p(x, y) → (q(x, y) ∧ Dp (x) ∧ Rp (y))) ∧ (q(x, y) → Dq (x) ∧ Rq (y))]

5

(9)

Discussion and Future Work

We have shown that most OWL constructs can be translated into ORM constructs. However, some of them are only mappable in one direction, e.g. owl:intersectionOf. Among those that could not be converted are property restrictions. As we already argued in Sect. 4.4, the closest approach to represent a property restriction is to use a binary fact type. As seen in Fig. 6, the property restriction on p between two classes A and B is represented by a binary fact type A, p, , B. However, adding another property restriction is forbidden because ORM only allows a maximum of one binary fact type between subtypes (formalization (2) explains this). 5

Dq and Rq are the domain and range of q respectively.

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Fig. 6. Illustrating that two Property Restrictions could not represented in ORM

RIDL, being a language based on NIAM, is able to represent the OWL-DL constructs which we have shown to be unconvertible into ORM, e.g. the property restrictions. This is due to the fact that it is a language that places constraints on paths. RIDL also allows set operations (union, intersection, minus) to be used to construct these paths, allowing a lot of flexibility in representing constraints. One upcoming task is to finalize the formalization of Ω-RIDL as the DOGMA ontology commitment language on the one hand, and to build a tool that implements the mappings we described. Another (pressing) task relates to defining a correct mapping from the OWL name space (basically a short hand notation for a pointer) and a DOGMA context identifier. A DOGMA context is an organizing and disambiguating mechanism that links the conceptual level to the linguistic level. Future work also includes an aspect that is of particular importance for ontology engineering. It concerns the way a logical term or concept is defined. Next to the constraints – independently whether these have been expressed by ORM, Ω-RIDL or OWL-DL – that formally restrict the intended meaning of the logical vocabulary (see also [8]), there is the informal, “natural” commonly used meaning. Good OWL ontology engineers add an explanation, definition or gloss (using the < rdf s : comment > tag) to the concepts they define. Following the URI (or a chain of URIs), eventually one should be able to discover the “informal” meaning of a concept. DOGMA uses a different mechanism to store this informal meaning. More sophisticated mechanisms must be deployed to cater for a better conversion of these glosses (in both directions). Another element of future work we will investigate is the conversion from ORM/RIDL into OWL-DL. Insights can be gained from existing work that describes mapping ORM into DLR [12,11].

6

Conclusions

By designing a conversion routine between OWL-DL and ORM/RIDL, we not only try to enhance the potential to re-use ontologies implemented in one or the other language and profit from various existing tools. Obviously, OWL-DL reasoning engines can be applied on ORM schemes, e.g. for consistency checking purposes. Perhaps more important is that the graphical language and verbalization aspects of ORM can turn the creation of OWL-DL constructs into a more human-understandable task.

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The larger picture is that we are trying to reconcile in practice model-theoretic and proof-theoretic approaches to the semantic web. Proof-theory has found its way, through description logics, in an ontology implementation language as OWL, while model-theory, through a fact oriented modeling methodology as ORM, offers a clean way to separate conceptual models from its actual implementation. Or stated otherwise, it is our conviction that the OWL community is still in need of well developed general modeling methodologies, while most of the traditional database modeling and software engineering methods do not take into account the particularities of ontologies. We believe that this paper has prepared the ground works for this ambitious endeavor that combines these two facets of the same coin.

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