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Why do datatypes defined by datatype definition axioms have empty lexical spaces?

From: Shaw, Ryan <ryanshaw@unc.edu>
Date: Mon, 29 Mar 2021 21:26:33 +0000
To: "semantic-web@w3.org" <semantic-web@w3.org>
Message-ID: <36FDFB49-58BB-4637-9079-BAF74A7E4332@unc.edu>
Section 9.4 Datatype Definitions<https://www.w3.org/TR/owl2-syntax/#Datatype_Definitions> of the OWL 2 Web Ontology Language Structural Specification shows how custom datatypes can be defined, giving the following example:

a:SSN rdf:type rdfs:Datatype .

a:SSN owl:equivalentClass [
  rdf:type rdfs:Datatype ;
  owl:onDatatype xsd:string ;
  owl:withRestrictions (
    [ xsd:pattern "[0-9]{3}-[0-9]{2}-[0-9]{4}" ]
] .

a:hasSSN rdfs:range a:SSN .

So here we’re defining a new datatype a:SSN by restricting the xsd:string datatype via the xsd:pattern facet. So far so good.

But then the specification says something I don’t understand:

The datatypes defined by datatype definition axioms … have empty lexical spaces and therefore they must not occur in literals.

Why would a:SSN have an empty lexical space here? It was defined by constraining the value space of xsd:string via xsd:pattern facet. Section 4.3.4 pattern<https://www.w3.org/TR/2012/REC-xmlschema11-2-20120405/datatypes.html#rf-pattern> of XSD 1.1 Part 2: Datatypes says that

… pattern is a constraint on the ·value space· of a datatype which is achieved by constraining the ·lexical space· to ·literals· which match each member of a set of ·regular expressions·.

So we’re constraining the value space of xsd:string, but we’re doing that by constraining the lexical space of xsd:string (the set of finite-length sequences of zero or more characters … that ·match· the Char production from XML<https://www.w3.org/TR/2012/REC-xmlschema11-2-20120405/datatypes.html#string>) to literals that match the regular expression. So why does the OWL spec say that the lexical space of a:SSN is empty, rather than the the set of finite-length sequences of zero or more characters (as defined in XML) that match the regular expression [0-9]{3}-[0-9]{2}-[0-9]{4}?

More pragmatically, the OWL spec says

… there can be no literals of datatype a:SSN.

So does that mean that a:SSN cannot be used as follows?

a:Jane a:hasSSN "123-45-6789"^^a:SSN .

If so, how is one supposed to use the a:SSN datatype? Is the idea that one should write

a:Jane a:hasSSN "123-45-6789"^^xsd:string .

and infer from the declared range of a:hasSSN what the actual datatype is and thus whether value is valid?

Received on Monday, 29 March 2021 21:26:48 UTC

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