Re: status of xsd:duration in OWL (and RIF and SPARQL) - ACTION-164: RDF WG

Hi Jean-Pierre!

Am 08.05.2012 09:25, schrieb Evain, Jean-Pierre:

> I understand the point which is being made being what is useful for reasoning or not.

Replace "useful for reasoning" by "required for the well-definedness of 
the semantics" of OWL 2 or RIF!

It is a basic technical requirement for the specifications of these 
languages that for every syntactically well-formed expression (aka an 
OWL 2 ontology or a RIF rule set), the semantic meaning can be 
determined by mathematical means. At a minimum, for OWL 2 and RIF, this 
means that it can always be determined whether an input ontology is 
satisfiable or not, or whether one given ontology entails another given 
one or not. Only in the cases of OWL 2 DL and its profiles, it is an 
additional requirement (by design) that there are reasoning procedures 
that are able to do these determinations in an automated way for all 
input, because these languages are required to be computationally 
decidable. But having a well-defined semantics is always needed. 
Clearly, if there are ontologies for which it cannot uniquely be deduced 
(mathematically) whether they are satisfiable or not, a reasoner cannot 
give the "right" reasoning result for them, because it cannot then be 
determined whether it's answer is right or not, or just one correct 
answer out of many.

To illustrate this problem, take the case of xsd:duration in its 
definition as of the time of finalizing OWL 2, where each literal of 
xsd:duration would essentially denote a pair (m, s) consisting of a 
certain number m of month plus a certain number s of seconds. Let there 
be two such durations:

     d1 := (2, 0)
     d2 := (1, 30*24*60*60)

Now, depending on what is meant by "a month", these two durations can 
represent either (i) the same value (if a month has 30 days), or (2) d1 
can be greater than d2 (if a month has 31 days), or (3) d1 is smaller 
than d2 (if a month has, say, 28 days = 4 weeks). I may well have missed 
a precise definition of "a month" in the (newest version of the) XSD 
spec, in which case the above example may be void. But if not, then it 
is clear that any OWL 2 (+xsd:duration) ontology for which the question 
of satisfiability depends on whether the above two durations are the 
same or not, or which of them is greater, does not have a uniquely 
defined semantic meaning.

An example for the need of being able to determine whether equality 
between two duration values holds or not would be an ontology with data 
enumerations consisting of duration values (denoted by "d1" and "d2", as 
defined above, but in a real ontology one would use their correct 
literal form, of course):

     :D a rdfs:Datatype ;
        owl:oneOf ( d1 ) .
     :dp a owl:DatatypeProperty ;
         rdfs:range :D .
     :s :dp d2 .

This set of axioms should be satisfiable if and only if d2 = d1, because 
only in this case, the object d2 of the property assertion (last 
statement) would denote an instance of the singleton datatype :D = {d1}. 
But if it cannot be determined whether d2 equals d1 or not, then it 
cannot be determined whether the axiom set is satisfiable or not.

An example for the need of comparison of two durations (greater or 
lesser than) could be constructed from the use of OWL 2 datatype 
restrictions.

> But does that mean that all other information is garbage?

Everyone can say everything about everything. But an OWL 2 or RIF or 
whatever language specification with a formal semantics at its core 
would, if not well-defined, IMO count as just that: garbage. :-)

Best,
Michael

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Dipl.-Inform. Michael Schneider
Research Scientist, IPE / WIM

FZI Forschungszentrum Informatik
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Fax: +49 721 9654-727

michael.schneider@fzi.de
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Received on Tuesday, 8 May 2012 08:39:45 UTC