Extending DL Reasoning Support for the OWL Datatyping (or "Why Datatype Groups?")

The OWL [2] datatype formalism (or simply OWL datatyping) presents some new requirements for DL reasoning services, in terms of semantics (to allow the use of so-called 'un-supported' datatypes), expressive power (to support enumerated datatypes) and datatype construction mechanism (both datatypes and datatype expressions). On the other hand, OWL datatyping is expected to be extended to include more expressive power. E.g., OWL datatyping does not provide a general framework for user-defined datatypes, such as XML Schema derived datatypes, nor does it support n-ary datatype predicates (such as the binary predicate > for integers), not to mention user-defined datatype predicates (such as the binary predicate > for non-negative integers). In this poster, we explain why it is necessary to extend the existing datatype approaches to the datatype group approach, in order to meet the above new requirements. It was Baader and Hanschke [1] who first presented a rigorous treatment of datatype predicates (or simply predicates). In their approach, a concrete domain [1, 4] is composed of a set of datatype values (such as integers) and a set of n-ary predicates (such as '<') defined over these values with obvious (fixed) extensions. Horrocks and Sattler [3] proposed the so called 'type system approach', which can be seen as a simplified version of the concrete domain approach, where the datatype domain (of a datatype interpretation) is regarded as a universal concrete domain and datatypes are treated as unary predicates in the universal concrete domain. In short, in the above two approaches, datatypes are nothing but unary predicates. In OWL datatyping, however, people take another view. A Datatype d distinguishes from a predicate in that it is characterised not only by the value spaces V (d), but also a lexical space, L(d), which is a set of Unicode strings, and a total mapping L2V (d) from the lexical space to the value space. E.g., boolean is a datatype with value space {true, f alse}, lexical space {T,F,1,0} and lexical-to-value mapping {T → true, F → f alse, 1 → true, 0 → f alse}. Data values can be represented by typed literals or plain literals, where typed literals are combinations of string and datatype URIs, while plain literals are simply strings, with optional language tag. E.g., " 1 " ˆˆxsd:boolean is a typed literal, while " 1 " is a plain literal. Therefore, when we extend OWL datatyp-ing to support predicates, we should not …