rigoris Antoniou and Frank van Harmelen we need an ontology language that is richer than RDF Schema, a language that offers these features and more. In designing such a language one should be aware of the tradeoff between expressive power and efficient reasoning sup port. Generally speaking, the richer the language is, the more inefficient the reasoning support becomes, often crossing the border of non-computability Thus we need a compromise, a language that can be supported by reasonably efficient reasoners, while being sufficiently expressive to express large classes of ontologies and know ledge Compatibility of OWL with RDF/RDFS Ideally, OWL would be an extension of RDF Schema, in the sense that OWL would use the RDF meaning of classes and properties( rdfs: Class rdfs: subClassOf, etc), and would add language primitives to support the richer expressiveness identified above Unfortunately, the desire to simply extend RDF Schema clashes with the trade-off between expressive power and efficient reasoning mentioned be- fore. RDF Schema has some very powerful modelling primitives, such as the rdfs: Class(the class of all classes) and rdf: Property(the class of all prop erties). These primitives are very expressive, and will lead to uncontrollable computational properties if the logic is extended with the expressive primitives dentified above Three species of OWL All this as lead to a set of requirements that may seem incompatible: efficient reasoning support and convenience of expression for a language as powerful as a combination of RDF Schema with a full logic. Indeed, these requirements have prompted w3C's Web Ontology Working Group to define Owl as three different sublanguages, each of which is geared towards fulfilling different aspects of these incompatible full set of require- OWL Full: The entire language is called OWL Full and uses all the OWL languages primitives(which we will discuss later in this chapter). It also allows to combine these primitives in arbitrary ways with RDF and RDF Schema. This includes the possibility(also present in RDF)to change the meaning of the pre-defined(RDF or OWL) primitives, by applying the language primitives to each other. For example, in OwL Full we could im- pose a cardinality constraint on the class of all classes, essentially limiting the number of classes that can be described in any ontology. The advantage of OWL Full is that it is fully upward compatible with RDF, both syntactically and semantically: any legal rdF document is also a legal OWL Full document, and any valid RDF/RDF Schema conclusion is also a valid OWL Full conclusion4 Grigoris Antoniou and Frank van Harmelen So we need an ontology language that is richer than RDF Schema, a language that offers these features and more. In designing such a language one should be aware of the tradeoff between expressive power and efficient reasoning sup￾port. Generally speaking, the richer the language is, the more inefficient the reasoning support becomes, often crossing the border of non-computability. Thus we need a compromise, a language that can be supported by reasonably efficient reasoners, while being sufficiently expressive to express large classes of ontologies and knowledge. Compatibility of OWL with RDF/RDFS Ideally, OWL would be an extension of RDF Schema, in the sense that OWL would use the RDF meaning of classes and properties ( rdfs:Class, rdfs:subClassOf, etc), and would add language primitives to support the richer expressiveness identified above. Unfortunately, the desire to simply extend RDF Schema clashes with the trade-off between expressive power and efficient reasoning mentioned be￾fore. RDF Schema has some very powerful modelling primitives, such as the rdfs:Class (the class of all classes) and rdf:Property (the class of all prop￾erties). These primitives are very expressive, and will lead to uncontrollable computational properties if the logic is extended with the expressive primitives identified above. Three species of OWL All this as lead to a set of requirements that may seem incompatible: efficient reasoning support and convenience of expression for a language as powerful as a combination of RDF Schema with a full logic. Indeed, these requirements have prompted W3C’s Web Ontology Working Group to define OWL as three different sublanguages, each of which is geared towards fulfilling different aspects of these incompatible full set of require￾ments: • OWL Full: The entire language is called OWL Full, and uses all the OWL languages primitives (which we will discuss later in this chapter). It also allows to combine these primitives in arbitrary ways with RDF and RDF Schema. This includes the possibility (also present in RDF) to change the meaning of the pre-defined (RDF or OWL) primitives, by applying the language primitives to each other. For example, in OWL Full we could im￾pose a cardinality constraint on the class of all classes, essentially limiting the number of classes that can be described in any ontology. The advantage of OWL Full is that it is fully upward compatible with RDF, both syntactically and semantically: any legal RDF document is also a legal OWL Full document, and any valid RDF/RDF Schema conclusion is also a valid OWL Full conclusion