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«OBJECT DATABASES AND THE SEMANTIC WEB A THESIS SUBMITTED IN FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY. ING. JAKUB ...»

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Another way to understand a complex system is through categorization, or typing. An object can be better understood by users and used by the system when it's known that its structure corresponds to a certain pattern or prototype. The question "what is it?" is answered in terms of object category. Computers exploit typing for efficient data storage, integrity checking, but perhaps the most importantly, binding algorithms to objects. A given algorithm works for many different inputs, but the inputs are required to conform to a certain pattern. In traditional object-oriented data models without reflection, every object has exactly one type and exactly the structure prescribed by the type.

But rigid typing can also become a limitation. Types need to evolve when our understanding of objects changes, they need to be flexible when objects start playing new roles in the system [HM00]. It is sometimes desirable to add extra properties, construct or transform types dynamically or work with an object that does not provide all the information required by its type. All these properties are rare in strictly typed object-oriented systems but inherent in RDF.

RDF COUNTERPARTS

RDF allows objects to have additional properties and does not place any restrictions on properties of typed nodes. However, it makes sense to define the expected structure using a subproperty of rdf:type that would indicate full structural conformance of an object with its type. It is also important to distinguish between classes with objects that can enter into arbitrary relationships and types that are parts of these objects without separate identification whose extensions are collections, tuples and atomic types.

5.3.5 SUBTYPING AND INHERITANCE The fourth of the [Sutherland93] principles says: "An instance of a subtype is always an instance of its supertype." Cognitive psychology calls this principle in human thinking hierarchization [BvSvS87].

There are several views of what inheritance actually is. The one used here is based on two principles:

extension of a subclass is a subset of the superclass extension, and therefore all individuals of the subtype can be used in place of the supertype. This helps organize the system hierarchically, work with multiple inheritance, and handle large numbers of object in a unified way while preserving their differences (polymorphism).

–  –  –

6.1 FEATURES OF THE MODEL The vocabulary given in this section contains foundational concepts from the area of OODB as specified by the ODMG [CB00] or JDO [Craig03] standards. Moreover, the semantics of this model is practically identical with the CDL (Concept Definition Language) of the G2 database [HM00]. Some

important features of the model1 are:

Contents of the database are separate from its schema. This is not required in RDFS interpretations, but required by most databases for efficient schema management. Formally, ICEXT(IS( soda:Thing)) ∩ ICEX`T(IS(soda:Concept)) = ∅.2 Instances are strongly typed using the soda:type property. Apart from classes and literals, other fundamental types include collections (strongly typed ordered multisets) and tuples. All property values of an instance are mandatory, except where an empty collection is allowed, with the option to use an undefined type value.

Some instances defined by the model have their own unique OID, while others are represented by literal values or blank nodes. Collections, tuples, and literals are embedded in an enclosing object, while classes have unique identifiers.

The model supports multiple inheritance.

LIMITATIONS OF THE MODEL

The model is limited to a static structural description, and does not formalize the dynamic aspects of a database, including updates, methods and side effects, or transactions.

Some structural features that are commonly used for reasons of user comfort or performance but are marginal from the theoretical point of view were omitted — the model does not contain collection indices, named objects, matchcodes, or labels.

a formal description of the model can be found in the following section. The model was published in [Güttner03c].

–  –  –

6.2 OBTAINING THE OODB GRAPH

In RDF, not all information about a certain vocabulary term is known to us since anyone can publish assertions about anything.

If the Semantic Web keeps growing, different companies will publish urirefs, for example ones that denote cars — http://www.ford.com/rdf/2006/mustang/2.6TDI. When someone works with such widely known URI, there is a host of triples on many different servers around the whole planet that mention this subject — stores, repair services, car magazines, newspaper ads or customer reviews. Many of these are not relevant for a given goal, cannot be easily found or trusted.

On the other hand, in the database world it is desirable to have a single RDF graph that is coherent and represents one logical set of data that conforms to a certain schema. Without this, some important questions could not be answered in the database — for example, whether an object’s structure corresponds to its type.

An RDF graph specifies a type called my:CarType and requires that all cars have certain maximum speed and average fuel consumption. One cannot be sure if only this is required or whether some other RDF source adds more required attributes like mileage or price. In such case, the complete definition of a type could not be obtained, which would prevent the database system from enforcing strong typing constraints.





For some applications, limiting the extent of an RDF graph to the triples that are immediately accessible is necessary. In the case of a single organization that publishes its data (ranging in size from a small e-shop to a whole government) it is only natural to seek consistency and stronger typing in its own limited RDF graph or the graphs of its trusted business partners.

The complete database graph for a given task can be obtained by connecting several RDF sources (graphs) using properties similar to rdfs:seeAlso or owl:imports. In RDFS, the semantics of rdfs:seeAlso is only informal, while in OWL, the owl:imports uriref has stricter semantics that requires an OWL ontology to be present at a specific URL address [PHH04].

6.3 A FORMAL DESCRIPTION This section presents model-theoretic semantics of a RDF vocabulary that supports the elementary notions of an object-oriented database (see chapter 3). The semantics is specified for a vocabulary comprised of urirefs that use the soda prefix (Semantic Object–oriented DAtabase) defined as xmlns:soda=http://www.fit.vutbr.cz/~guttner/soda. These semantics do not influence the semantics of core RDF or RDFS vocabularies, which allows the OODB parts of RDF graphs to have special semantics without influencing the rest of an RDF graph1.

Every formal statement in this section is given using two types of notation with an empty line in between. One is a specification using the N-Triples syntax [MM04] where the triples must be true in an RDFS interpretation. Sometimes this is not expressive enough so quantifiers, grouping or logical This feature is especially useful for mining object data from raw RDF/S graphs, see section 7.1 Semantic Web as an Object-oriented Database 50 conjunctions are used although they are not part of N-Triples — in these cases, the corresponding part of the description is only informative.

The second type of notation, however, is strictly formal and exact even in places where the first one goes beyond N-Triples semantics. It uses the RDF model theory explained in section 4.2.

6.3.1 DIVISION OF THE DOMAIN OF DISCOURSE

The SODA vocabulary is:

{ soda:Concept, soda:Class, soda:Tuple, soda:Collection, soda:Thing, soda:Attribute, soda:MemberAttribute, soda:Meta } ∈ IC { soda:type, soda:collectionOf, soda:subTypeOf, soda:member, soda:_1, soda:_2,... } ∈ IP The soda:Meta uriref denotes a class that contains all SODA vocabulary metaexpressions.

{ soda:Meta, soda:Concept, soda:Class, soda:Tuple, soda:Collection, soda:Thing, soda:Attribute, soda:MemberAttribute, soda:Meta, soda:type, soda:collectionOf, soda:subTypeOf } rdf:type soda:Meta.

{soda:Meta, soda:Concept, soda:Class, soda:Tuple, soda:Collection, soda:Thing, soda:Attribute, soda:MemberAttribute, soda:Meta, soda:type, soda:collectionOf, soda:subTypeOf} ∈ ICEXT(IS(soda:Meta)) This interpretation is very strict as far as typing goes, which is similar to strongly typed programming languages. Different levels of abstraction in the domain of discourse are strictly separate. The areas of instances (Thing), model (Concept), metamodel (Meta), tuple attributes and collection membership attributes are divided into pairwise disjoint sets (Figure 6.1).

ICEXT(IS(soda:Meta)), ICEXT(IS(soda:Thing)), ICEXT(IS(soda:Concept)), ICEXT(IS(soda:Attribute), ICEXT(IS(soda:MemberAttribute) are pairwise disjoint.

–  –  –

It will be convenient to define a mapping, I2EXT, from metaclass types to extensions of classes. For example, for soda:Collection, this mapping returns all collection objects.

I2EXT(z) = { x | ∃ y: x,y ∈ IEXT(IS(soda:type)) ∧ y,z ∈ ICEXT(z) }

–  –  –

can be the target of relationships based on its uriref (OID), as opposed to collections, tuples, and literals. Semantics is defined only for part of the RDF world so the meaning of vocabulary outside of SODA remains unchanged.

soda:Concept rdfs:subClassOf rdfs:Class.

soda:Class rdfs:subClassOf soda:Concept.

soda:Tuple rdfs:subClassOf soda:Concept.

soda:Collection rdfs:subClassOf soda:Concept.

ICEXT(IS(soda:Concept)) ⊂ ICEXT(IS(rdfs:Class)) ICEXT(IS(soda:Class)) ⊂ ICEXT(IS(soda:Concept)) ICEXT(IS(soda:Tuple)) ⊂ ICEXT(IS(soda:Concept)) ICEXT(IS(soda:Collection)) ⊂ ICEXT(IS(soda:Concept)) The following subclassing statement has no semantic meaning since RDF does not impose any conditions on rdf:Bag. The statement is supposed to indicate that the informal understanding of a bag is preserved (and actually, as show later, formally imposed) in SODA. It also helps to infer object data from RDF structures.

soda:Collection rdfs:subClassOf rdf:Bag.

soda:Datatype rdfs:subClassOf soda:Concept.

soda:Datatype rdfs:subClassOf rdfs:Data type.

ICEXT(IS(soda:Collection)) ⊂ ICEXT(IS(rdf:Bag)) ICEXT(IS(soda:Datatype)) ⊂ ICEXT(IS(soda:Concept)) ICEXT(IS(soda:Datatype)) ⊂ ICEXT(IS(rdfs:Datatype)) This division of the following class extents is depicted in Figure 6.1.

ICEXT(IS(soda:Class)), ICEXT(IS(soda:Tuple)), ICEXT(IS(soda:Collection)), ICEXT(IS(soda:Datatype)) are pairwise disjoint and their union is ICEXT(IS(soda:Concept))

6.3.3 TYPING AS A MANDATORY INDIVIDUAL–TYPE RELATIONSHIP

The notions of typing and subtyping are introduced here. They connect individuals to their types and types among each other, imposing structure on the individuals that corresponds to the attributes and other properties of their types and supertypes. Structural restrictions on instances of different kinds of concepts are described in the following sections.

SODA typing is a special case of RDF typing that has additional semantics but does not alter the original rdf:type semantics.

soda:type rdfs:subPropertyOf rdf:type.

soda:type rdfs:domain soda:Thing.

soda:type rdfs:range soda:Concept.

IEXT(IS(soda:type)) ⊂ IEXT(IS(rdf:type)) x,y ∈ IEXT(IS(soda:type)) ⇒ x ∈ ICEXT(IS(soda:Thing)) x,y ∈ IEXT(IS(soda:type)) ⇒ y ∈ ICEXT(IS(soda:Concept)) Every instance in the SODA world must have at least one type, and everything that is SODA typed is a SODA instance.

–  –  –

x ∈ ICEXT(IS(soda:Thing)) ⇔ ∃ y: x,y ∈ IEXT(IS(soda:type)) Blank nodes cannot represent class instances since they do not have a universal OID — uriref.

_xxx soda:type yyy. ⇒ yyy rdf:type (soda:Tuple ∪ soda:Collection).

_xxx is a blank node ∧ IS+A(_xxx),y ∈ IEXT(IS(soda:type)) ⇒ y ∈ ICEXT(IS(soda:Tuple)) ∪ ICEXT(IS(soda:Collection)) SODA subtyping is a special case of RDFS subtyping.

soda:subTypeOf rdfs:subPropertyOf rdfs:subClassOf.



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